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Hydrodynamics of Tidal Inlets on Tidal and Subtidal Timescales

Permanent Link: http://ufdc.ufl.edu/UFE0042315/00001

Material Information

Title: Hydrodynamics of Tidal Inlets on Tidal and Subtidal Timescales
Physical Description: 1 online resource (187 p.)
Language: english
Creator: Waterhouse, Amy
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: bathymetry, hydrodynamics, stratification, subtidal, tidal
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Coastal and Oceanographic Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: HYDRODYNAMICS OF TIDAL INLETS ON TIDAL AND SUBTIDAL TIMESCALES The hydrodynamics of inlets are studied using observational data as well as a simple analytical model on tidal and subtidal temporal scales. These inlets, where the momentum balance is typically between pressure gradient, friction and advection, are subject to variability due to bathymetry, winds and stratification. Three main research topics are studied in this work. The first research topic investigates a basin of connected inlets. In this basin with two inlets, frictional influences decrease tidal velocity and sea surface elevation away from the inlets to a minimum in the middle of the waterway. Secondly, tidal flow over a hollow is studied and along-channel velocities are found to be asymmetric between ebb and flood tides. Along-channel depth-averaged velocities follow Bernoulli dynamics with decreased velocity over the hollow. Enhanced mixing occurs along the seaward slope of the hollow which decreases stratification at the end of ebb and increases stratification during flood. Lastly, the variability in the subtidal flow in three inlets is studied. This investigation provides observational evidence for theoretical results on tidal, wind-driven and density-driven flows in semienclosed bodies of water with lateral variations in bathymetry.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Amy Waterhouse.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Valle-Levinson, Arnoldo.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042315:00001

Permanent Link: http://ufdc.ufl.edu/UFE0042315/00001

Material Information

Title: Hydrodynamics of Tidal Inlets on Tidal and Subtidal Timescales
Physical Description: 1 online resource (187 p.)
Language: english
Creator: Waterhouse, Amy
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: bathymetry, hydrodynamics, stratification, subtidal, tidal
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Coastal and Oceanographic Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: HYDRODYNAMICS OF TIDAL INLETS ON TIDAL AND SUBTIDAL TIMESCALES The hydrodynamics of inlets are studied using observational data as well as a simple analytical model on tidal and subtidal temporal scales. These inlets, where the momentum balance is typically between pressure gradient, friction and advection, are subject to variability due to bathymetry, winds and stratification. Three main research topics are studied in this work. The first research topic investigates a basin of connected inlets. In this basin with two inlets, frictional influences decrease tidal velocity and sea surface elevation away from the inlets to a minimum in the middle of the waterway. Secondly, tidal flow over a hollow is studied and along-channel velocities are found to be asymmetric between ebb and flood tides. Along-channel depth-averaged velocities follow Bernoulli dynamics with decreased velocity over the hollow. Enhanced mixing occurs along the seaward slope of the hollow which decreases stratification at the end of ebb and increases stratification during flood. Lastly, the variability in the subtidal flow in three inlets is studied. This investigation provides observational evidence for theoretical results on tidal, wind-driven and density-driven flows in semienclosed bodies of water with lateral variations in bathymetry.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Amy Waterhouse.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Valle-Levinson, Arnoldo.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042315:00001


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HYDRODYNAMICSOFTIDALINLETSONTIDALANDSUBTIDALTIMESCALESByAMYFRANCESWATERHOUSEADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2010

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c2010AmyFrancesWaterhouse 2

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TomyMumandDad,JennandChrisandHarry 3

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ACKNOWLEDGMENTS ThankstoArnoldoValle-Levinsonforbeingaverysupportiveandpatientadviser.IamgratefulforthefreedomthathegavemetodothethingsthatImostenjoyandforthetremendousopportunitiesofconductingeldworkininterestingplaces.Iwouldalsoliketothankmycommitteemembers.ToDr.BobDeanforhishelpfulcommentsregardingthecomplexnatureoftidalinletsandconnectedwaterways,toDr.PeterShengforhisinsightfulcommentsandinterestindoingeldworkinSt.AugustineInletandtoDr.JohnJaegerwhoencouragedmetothinkabouttheimportantbroaderimplicationsofthiswork.IamverygratefultoDr.ClintonWinantwhoseinsistencethatIdeploysensorsintheIntracoastalWaterwayresultedinaveryinterestingprojectandforhisverypatientexplanationofthetidalmodel.TheeldworkthatIdidwhileinFloridawouldnothavebeenpossiblewithouthelpfromtwopeopleandtothemIamverygrateful:VikAdamsandUriahGravois.I'dliketothankDrs.JaramilloandArboleda-RiosforconvincingmetoleaveVancouverandmovetoGainesville.Itwasagreatidea.IwouldalsoliketothankmyfellowstudentsandfriendswhohavenotonlyhelpedmewitheldworkbutalsomademytimeinGainesvilleamazing,particularlyChloeandLuciano.Mostly,I'dliketothankmyfamilywhoareabsolutelywonderful. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 8 LISTOFFIGURES ..................................... 9 ABSTRACT ......................................... 14 CHAPTER 1INTRODUCTION ................................... 15 2TIDESINASYSTEMOFCONNECTEDESTUARIES .............. 18 2.1Introduction ................................... 18 2.2Model ...................................... 20 2.2.1SeaLevelFluctuations,N0 ....................... 22 2.2.2TransportVelocities ........................... 23 2.2.3N(0)and[U]:Phases .......................... 24 2.3Observations .................................. 26 2.3.1SeaLevelFluctuations,N(0) ..................... 28 2.3.2TransportVelocity,[U] ......................... 28 2.3.3N(0)and[U]:Amplitudes ....................... 29 2.3.4N(0)and[U]:Phases .......................... 30 2.4Discussion ................................... 31 2.5Conclusions ................................... 33 3TIDALASYMMETRIESINSTRATIFICATIONOVERABATHYMETRICDEPRESSION .................................... 45 3.1Introduction ................................... 45 3.2ChacahuaInlet ................................. 46 3.3FieldMeasurements .............................. 47 3.3.1MeteorologicalData .......................... 49 3.3.2WaterLevelData ............................ 49 3.4EbbandFloodAsymmetry .......................... 49 3.4.1Along-channelStructure ........................ 49 3.4.2Cross-channelStructure ........................ 50 3.5Along-channelMomentum ........................... 52 3.5.1Along-channelAdvection ........................ 53 3.5.2BottomFriction ............................. 53 3.5.3PressureGradients ........................... 54 3.5.3.1Barotropicpressuregradient ................ 54 3.5.3.2Baroclinicpressuregradient ................ 55 3.5.4BernoulliEquation ........................... 55 5

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3.6MechanismsCausingDensityVariabilityandStratication ......... 57 3.6.1PotentialEnergyAnomaly ....................... 57 3.6.2DensityAlongtheChannel ....................... 58 3.6.2.1Largeebbandmixing .................... 58 3.6.2.2Smalloodandlaterallyshearedalong-channelvelocity 59 3.6.3TidalVelocityandWaterColumnStability .............. 60 3.6.3.1Prolesandstability:dryseason(July,2009) ....... 61 3.6.3.2Prolesandstability:wetseason(November,2009) ... 62 3.6.3.3Transitionfromweakebbtolargeood .......... 63 3.7Conclusions ................................... 64 4TRANSVERSESTRUCTUREOFSUBTIDALFLOWINAWEAKLYSTRATIFIEDSUBTROPICALTIDALINLET .................... 83 4.1Introduction ................................... 83 4.2StudyArea ................................... 86 4.3DataCollection ................................. 87 4.3.1UnderwaySurveys ........................... 87 4.3.2MooredSurvey ............................. 88 4.3.3AtmosphericData ........................... 89 4.4TidalandSubtidalFlow ............................ 89 4.4.1TidalInformation ............................ 89 4.4.2LongTermMeanFlows ........................ 91 4.4.3TidalandResidualows ........................ 91 4.4.3.1Tidalows .......................... 92 4.4.3.2Streamwiseresidualows ................. 94 4.4.3.3Lateralresidualows .................... 95 4.5SubtidalModulation .............................. 96 4.6Conclusions ................................... 99 5RESPONSEOFRESIDUALFLOWSTOTWOTROPICALSTORMSINASUBTROPICALTIDALINLET ............................ 112 5.1Introduction ................................... 112 5.2StudyArea ................................... 114 5.3FieldObservations ............................... 115 5.4ResidualFlows ................................. 117 5.4.1LateralStructureofResidualExchange ............... 117 5.4.2Baroclinicity ............................... 119 5.4.3RemoteandLocalWindEvents .................... 120 5.4.4WindsandAlong-basinVelocityAnomaly .............. 122 5.4.4.1Pre-stormvelocities ..................... 122 5.4.4.2Stormvelocities ....................... 123 5.4.5Along-basinMomentumBalance ................... 125 5.5Conclusions ................................... 128 6

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6SUBTIDALFLOWANDITSVARIABILITYATTHEENTRANCETOASUBTROPICALLAGOON .............................. 143 6.1Introduction ................................... 143 6.2StudyArea ................................... 144 6.2.1St.AndrewBaySystem ........................ 144 6.2.2WestPassandEastPass ....................... 144 6.3DataCollectionandMethods ......................... 145 6.3.1MeteorologicalForcingandWaterLevels ............... 145 6.3.2ProlesofPhysicalParameters .................... 145 6.3.3TowedADCPData ........................... 146 6.3.4GriddedRawMeasurements ..................... 147 6.3.5ResidualFlowandAnalyticalModel ................. 148 6.3.6MooredADCPData .......................... 148 6.4ResultsandDiscussion ............................ 149 6.4.1ExternalForcing ............................ 149 6.4.2TidalWaveandEllipses ........................ 149 6.4.3DensityField .............................. 150 6.4.4ResidualFlow .............................. 151 6.4.5FrictionandCoriolisImportanceattheInlet ............. 152 6.4.6TemporalVariationsinExchangeFlow ................ 153 6.5Conclusion ................................... 156 7CONCLUSION .................................... 173 7.1Summary .................................... 173 7.1.1TidesinanInter-connectedEstuary ................. 174 7.1.2ObservationsofTidalandResidualFlows .............. 174 7.1.3StratiedFlowOverHollows ...................... 175 7.2FutureResearch ................................ 176 REFERENCES ....................................... 177 BIOGRAPHICALSKETCH ................................ 187 7

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LISTOFTABLES Table page 2-1RatiooftransportvelocityoverseasurfaceelevationfromADCPsmooredatthreelocationsinFlorida'sIntracoastalWaterwaycomparedwithdimensionalizedratiosfromthemodel. ...................... 30 3-1SummaryofmeasurementsconductedinChacahuaInletin2009includingbothmooredandsurveyobservations. ...................... 48 4-1Tidalamplitude(A)andphase()andphasedifference()ofthelargestofthediurnal(K1),semi-diurnal(M2)andquarter-diurnal(M4)frequenciesacrossPoncedeLeonInlet ............................. 90 8

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LISTOFFIGURES Figure page 2-1Analyticalmodelsetupwithtwoentrances(inlets)toaninlandwaterway. ... 34 2-2Seasurfaceelevation(N(0))amplitudeandphaseascalculatedfromthemodelforhighvaluesoffriction,rangingfrom=1to5forthesemi-diurnal(M2)anddiurnal(K1)tides. ................................ 35 2-3Amplitudeandphaseofthealongchanneltransport([U])fromtheanalyticalmodelwith=1.5,=1.0andf=0forthesemi-diurnaltide. ......... 36 2-4Amplitudeandphaseofthecrosschanneltransport([V])fromtheanalyticalmodelwith=1.5,=1.0andf=0forthesemi-diurnaltide. ......... 37 2-5Phasesofseasurfaceelevation(N(0))andalongchanneltransport([U];AandB)andthephasedifferencebetweenN(0)and[U]forvariousvaluesofrangingfrom1to5(CandD)forthesemi-diurnal(M2)tidewith=1.0andf=0. ......................................... 38 2-6Phasesofseasurfaceelevation(N(0))andalongchanneltransport([U];AandB)andthephasedifferencebetweenN(0)and[U]forvariousvaluesofrangingfrom1to5(CandD)forthediurnal(K1)tidewith=0.5andf=0. 39 2-7Mapshowinglocationsofsixpressuresensors(x)mooredintheIntracoastalwaterwayfromDecember3untilDecember17,2009. .............. 40 2-8Observationsofseasurfaceelevation(N(0))amplitudeandphase(solidcircles/dottedline)betweenPoncedeLeonInlet(x=0)andSt.AugustineInlet(x=2). ..................................... 41 2-9Amplitudeandphaseoftheobserved(*)andmodelled(solidline)alongchanneltransport([U])forA)semi-diurnal(=1.5,=1.0)andB)diurnal(=2,=0.5)tideswithf=0. .............................. 42 2-10AmplitudesofmodeledN(0),[U]andratioofN(0)=[U].Theamplitudeoftheobservedratiocompareswellwiththemodelratio,indimensionalunits(seeTable 2-1 ).Toconverttodimensionalunits(soastocomparewithresultsinTable 2-1 ),non-dimensionalratiosheremustbemultipliedby!0L0foreachsemi-diurnalanddiurnalfrequency.x=0.3representslocationofADCPmooringatPortOrange. ............................... 43 2-11ModelledandobservedlocalphasedifferencebetweenvelocityandseasurfaceelevationatthethreeADCPlocationsalongtheinlandwaterway. ........ 44 3-1ChacahuaInlet,Mexico.Bathymetryofthehollowwithintheinletisshownwithgreycontours. ................................. 66 3-2PredictedtidalsignalduringsurveysamplinginJulyandNovember,2009. .. 67 9

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3-3MeteorologicaldatafromChacahuaInlet,2009 .................. 68 3-4Observationsatthehollowofsurfaceelevation,depth-averagedvelocity,verticalprolesofalong-channelvelocityanddensity. ................... 69 3-5July2009:A,D)depthaveraged(solid)andsurface(dashed)along-channelvelocities(m/s);B,E)along-channelvelocity(vectorsandcontours;m/s);C,F)surfacevelocity(m/s) ............................... 70 3-6November2009:A,D)depthaveraged(solid)andsurface(dashed)along-channelvelocities(m/s);B,E)along-channelvelocity(vectorsandcontours;m/s);C,F)surfacevelocity(m/s) .......................... 71 3-7Transectacrossthehollow(Transect3)withalong-channelvelocitycontoursduringmaximumoodandebbtides(m/s)withlateralvelocities(vectors)forA)JulyandB)November2009surveys. ...................... 72 3-8Depth-averagedadvectiveterm(u@u=@x;ms)]TJ /F4 7.97 Tf 6.58 0 Td[(2)alongtheaxisofthechannel 73 3-9Contoursofbottomstress(b=H;ms)]TJ /F4 7.97 Tf 6.58 0 Td[(2)fromthealong-channeltransectovertimeduringA)JulyandB)November2009surveys. ............ 74 3-10Barotropicpressuregradient(ms)]TJ /F4 7.97 Tf 6.58 0 Td[(2)andthesmoothedsurfacevelocity(ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)fromthemooredcurrentmeterinthehollow(dashedgreyline). ......... 75 3-11Depthaveragedvelocity(ms)]TJ /F4 7.97 Tf 6.58 0 Td[(1)andalong-channelbaroclinicpressuregradient(ms)]TJ /F4 7.97 Tf 6.58 0 Td[(2)betweenCTDstations2-3,3-4and4-5forA-B)JulyandC-D)November2009surveys. ..................................... 76 3-12Potentialenergyanomaly()ascalculatedfromStation2to4fromNovember2009.Station3aretheprolesfromthehollowandebbtidesaredenotedbythegreyshadedregions. .............................. 77 3-13Densityvariability(tinkgm)]TJ /F4 7.97 Tf 6.59 0 Td[(3)alongtheinletfromtheNovembersurveys. 78 3-14Surfacevelocity(1to3m)acrosstransect2to4duringA-C)JulyandD-F)November2009surveysoverthediurnaltidalcycle.Dashedlinesrepresentthetimesatwhichthetransectrepetitionoccurred. ................ 79 3-15Prolesofdensity(kgm)]TJ /F4 7.97 Tf 6.58 0 Td[(3;thicklines)andvelocity(cms)]TJ /F4 7.97 Tf 6.58 0 Td[(1;thinlines)fromCTDStations4,3and2duringebbandoodtidesinJuly2009. ........ 80 3-16Prolesofdensity(kgm)]TJ /F4 7.97 Tf 6.58 0 Td[(3;thicklines)andvelocity(cms)]TJ /F4 7.97 Tf 6.58 0 Td[(1;thinlines)fromCTDStations4,3and2duringebbandoodtidesinNovember2009. .... 81 3-17(A-C)Prolesofdensity(kgm)]TJ /F4 7.97 Tf 6.59 0 Td[(3;thicklines)andvelocity(cms)]TJ /F4 7.97 Tf 6.58 0 Td[(1;thinlines)fromCTDStations4,3and2atthetransitiontooodtide. ........... 82 4-1StudyareaofPoncedeLeonInlet,FloridawhichconnectstheIntracoastalWaterway(IWW)totheAtlanticOcean. ...................... 101 10

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4-2TidalamplitudeandsubtidalwaterlevelasmeasuredbytheADCPinmetersatStation2. ..................................... 102 4-3CoherencesquaredandphaseofthestreamwisevelocityandwatersurfaceelevationfromStation1(thickline,o's)andfromStation2(thinline,x's)fromthebottombinsofeachADCP. ........................... 103 4-4DeploymentlongmeanowvectorsatthethreeADCPmooringsitesinPoncedeLeonInlet,Florida.Meanowsduringmaximumoodandebbmeansshowthedifferenceinlateralvelocitiesbetweenthetwophasesofthetide. ..... 104 4-5StreamwiseandlateralcurrentsduringA)maximumoodandB)maximumebbacrossTransectAfromPoncedeLeonInletonSeptember5,2007. .... 105 4-6StreamwiseandlateralcurrentsduringA)maximumoodandB)maximumebbacrosstransectAfromPoncedeLeonInletonFebruary21,2008. .... 106 4-7Centrifugalacceleration,surfacet,prolesofdensityattheendofebbandood,lateralbaroclinicpressuregradient,bottomfrictionparameterizationsandstreamwisetidalvelocityfromPoncedeLeonInletonSeptember5,2007. 107 4-8Centrifugalacceleration,surfacet,prolesofdensityattheendofebbandood,lateralbaroclinicpressuregradient,bottomfrictionparameterizationsandstreamwisetidalvelocityfromPoncedeLeonInletonFebruary21,2008. 108 4-9Lateralvelocities,un(m/s),fromthesurface(solid)andbottom(dotted;positivenorthward)fromStation2andverticalshearinthelateralvelocities(vnsurface)]TJ /F3 11.955 Tf -400.03 -14.45 Td[(unbottom)fromStation2(m/s). ............................ 109 4-10Contoursofresidualstreamwiseow(cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)ascalculatedfromtheleastsquaresttothesemi-diurnaltidalconstituentacrossTransectAfromPoncedeLeonInletonSeptember5,2007. ....................... 110 4-11Contoursofresidualstreamwiseow(cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)ascalculatedfromtheleastsquaresttothesemi-diurnaltidalconstituentacrosstransectAfromPoncedeLeonInletonFebruary21,2008. ........................ 110 4-12Tidalamplitude,low-passedwaterlevel,lowpassedalongandcross-shelfwindstress,subtidalstreamwisecurrents,lateralshearbetweenthestreamwisesubtidalcurrents,streamwiselateraladvectivetermandbottomfriction. .... 111 5-1Studyarea,St.AugustineInlet,ontheEastcoastofFlorida. .......... 130 5-2MeteorologicalconditionsforSt.AugustineInletfrom2008 ........... 131 5-3TracksoftropicalStormsFayandHannafromAugustandSeptember,2008.Dotsonthestormtracksrepresentthelocationofthecentreofthetropicalstormat6hourintervalsasthestormspropagatefromSouthtoNorth. .... 132 11

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5-4ResidualvelocitiesacrossthemouthofSt.Augustineinletfrom2006to2008(cm/s). ......................................... 133 5-5Lowfrequencywaterlevelandsealevelpressure,tidalamplitudeanddepthaveragedvelocities,residualalong-andcross-channelvelocitiesfromthemooredADCPinthechannelofSt.AugustineinletfromJulytoSeptember2008. ......................................... 134 5-6Meanprolesofdensityaveragedoverthesemi-diurnaltidalcycleofeachsurveyasmeasuredfromtheCTDstationatthemouthoftheinlet,inthechannel. ....................................... 135 5-7Precipitation,densityandhorizontalbaroclinicpressuregradientfromSt.AugustineInletfrom2008. .............................. 136 5-8Variationsindepthaveragedvelocity,waterlevelatthemouthoftheinlet,thechangeinwaterlevelwithtime,thealong-channelchangeinwaterlevelandwindstresses. .................................... 137 5-9Velocityproleandresultingvelocityanomalies. ................. 138 5-10Observationsofthevelocityanomalybeforethetropicalstorms. ........ 139 5-11Observationsofthevelocityanomalyduringthetropicalstorms. ........ 140 5-12Accelerationsfromthealong-basindepth-averagedmomentumequationfromJuly21toSeptember19,2008. ........................... 141 5-13Comparisonofthebarotropicpressuregradienttotheothertermsinthealong-basinmomentumequation. ......................... 142 6-1StudyareaofSt.Andrew'sBayInlet ........................ 158 6-2GridsuperimposedonFebruary14-15,2008surveyroute. ........... 159 6-3A)Tidalheight(m),B)windspeed(ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1),C)sealevelpressure(mbar),andrainfall(cm)duringthestudyperiod. ........................ 159 6-4Coherencesquaredandphasebetweenalong-channelvelocityandseasurfaceelevationfromFebruary14-15,2008atSt.AndrewsBayInlet. ......... 160 6-5Surface(1.86m)K1tidalellipsesoverlaidoncontoursofK1tidalphaseforFebruary14-15,2008 ................................ 161 6-6ObservedtvaluesandtidallyaveragedtateachtransectthroughthetowedADCPsamplingperiodatA)StationB0andC)StationD0. ............ 162 6-7A)ThepotentialenergyanomalycalculatedfromtheobserveddensityprolesatstationsB0andD0.ComparisonsbetweenpotentialenergyanomalychangesandtheforcingfromtidalstrainingatB)Transect1andC)Transect2. ..... 163 12

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6-8A)Contoursrepresenttheobservedresidualmeanow(cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)inTransect1rotatedtotheangleofmaximumvariance.B)Contoursrepresenttheanalyticalsolutionofthemeanow(cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)withthebathymetryofTransect1(Ke=0.8andEk=0.01). .................................... 164 6-9SameasFigure 6-8 butforTransect2(Ke=1.82andEk=0.03). ....... 165 6-10Bi-harmonicsplineinterpolationofsurface(1.36m)subtidalcirculationresultingfromremovalofdiurnalandsemidiurnaltidalsignalsduringFebruary14-15,2008survey. ..................................... 166 6-11A)Wind(ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)andtidalamplitude(m),B)depthaveragedsubtidalalongchannelcurrents,subtidalC)alongandD)cross-channelcurrentsofthemooredADCPlocatedattheentranceofWestPass(cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1). .............. 167 6-12Variationinsubtidalalongchannelvelocities(cms)]TJ /F4 7.97 Tf 6.58 0 Td[(1)withA)tidalamplitudeandB)winddirection.C)Thevariationinthesubtidalmeansealevelheightwithwinddirection. ................................. 168 6-13Variationinsubtidalcross-channelvelocities(cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)withA)tidalamplitudeandB)winddirection.Winddirectionisinoceanographicconvention. ..... 169 6-14EOFofthealongchannelsubtidalvelocity. .................... 170 6-15EOFofthecrosschannelsubtidalvelocity. .................... 171 6-16TemporalevolutionofthealongchannelsubtidalverticalshearcalculatedbetweensurfaceandbottombinsofthemooredADCPlocatedattheentranceofWestPass. ..................................... 172 13

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyHYDRODYNAMICSOFTIDALINLETSONTIDALANDSUBTIDALTIMESCALESByAmyFrancesWaterhouseDecember2010Chair:ArnoldoValleLevinsonMajor:CoastalandOceanographicEngineering Thehydrodynamicsofinletsarestudiedusingobservationaldataaswellasasimpleanalyticalmodelontidalandsubtidaltemporalscales.Theseinlets,wherethemomentumbalanceistypicallybetweenpressuregradient,frictionandadvection,aresubjecttovariabilityduetobathymetry,windsandstratication.Threemainresearchtopicsarestudiedinthiswork.Therstresearchtopicinvestigatesabasinofconnectedinlets.Inthisbasinwithtwoinlets,frictionalinuencesdecreasetidalvelocityandseasurfaceelevationawayfromtheinletstoaminimuminthemiddleofthewaterway.Secondly,tidalowoverahollowisstudiedandalong-channelvelocitiesarefoundtobeasymmetricbetweenebbandoodtides.Along-channeldepth-averagedvelocitiesfollowBernoullidynamicswithdecreasedvelocityoverthehollow.Enhancedmixingoccursalongtheseawardslopeofthehollowwhichdecreasesstraticationattheendofebbandincreasesstraticationduringood.Lastly,thevariabilityinthesubtidalowinthreeinletsisstudied.Thisinvestigationprovidesobservationalevidencefortheoreticalresultsontidal,wind-drivenanddensity-drivenowsinsemienclosedbodiesofwaterwithlateralvariationsinbathymetry. 14

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CHAPTER1INTRODUCTION Incoastalareas,estuariesandinletsareregionswherefreshriverinewaterconuencewithdenseroceanicwater.Theseregionsareoftenhighlyproductiveasaresultofenhancedmixingandrichnutrientsupplyfromcoastalupwellingandriverineinput.Duetothehighproductivityandnearbyoceanaccess,theyarevaluableregionsforcommercialandnavigationalpurposes.Circulationwithinestuaries,bothontidalandsubtidaltimescales,isdeterminedbythedifferenttermsinthemomentumequations.Variationsinthemomentumbalancewithinestuariesoccurasaresultofinuencesofwinds,variationsinbathymetryandstratication. Themajorityofresearchinestuarinedynamicshasconcentratedintemperateregions.Subtropicalcoastalsystemsarefoundinregionswhereprecipitationisgenerallyweakandepisodicwhereastropicalsystemsaretypicallyfoundinregionswhereprecipitationisstrongestduringoneseason.Thesecoastalsystemsdifferfromtemperateestuariesinthestrongseasonalityinprecipitationandstratication.Therefore,studyingthehydrodynamicsofthesesystemsisimportanttodeterminehowprocesseschangeinsubtropicalinletscomparedwiththeirtemperatecounter-parts.Dependingontheshapeandphysicalparametersaffectinganinlet,differentforcingmechanismswilldominatethetidalandsubtidalvelocitiesinthealong-channelandlateraldirections.Ascoastalinletsareoftensituatedinhighlypopulatedareaswhereanthropogenicactivityishigh,thedeterminationofushingtimes,sedimenttransportratesandmechanismsaffectingtheseprocessesareessentialforthehealthandsustainabilityofinlets.Theseprocessesoccurovertidaltoseasonaltimescalesandthisstudyseekstodeterminerelevantparametersinvolvedinthedynamicsoftidalinletsovertidaltosubtidaltimescales.Specicphenomenahighlightedinthisstudyareattenuationoftides,straticationinducedbyabathymetricvariationandbathymetriceffectsontidalandsubtidalexchange. 15

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Theattenuationoftidesinshallowsystemshavebestudiedtopredicttheevolutionoftidalamplitudesandphasesofseasurfaceelevationofvelocityalongenclosedbasins.Intheseshallowbasins,theforcebalancegoverningthedynamicsistypicallydominatedbyfrictionandthebarotropicpressuregradient.Tidesinshallowinterconnectedbasinshavenotbeenmodeledandthus,therstcomponentofthisstudyistouseananalyticalmodel,inconjunctionwithobservations,todeterminethetidalattenuationinalong(100km)interconnectedbasin.Thephaserelationshipbetweenseasurfaceelevationandvelocityisdeterminedalongthebasin,aswellashowthisphaserelationshipchangeswithvariationsinfriction.ThebackgroundforthisworkandresultsaredescribedinChapter 2 Straticationactstosuppressturbulentprocesses.However,whentidalvelocitiesaremodiedasaresultofbathymetricvariability,verticalgradientsinvelocitymayoverwhelmstratication,initiatingturbulentmixing.Inthiswork,observationsofthephysicalpropertiesalonganinletwithabathymetricdepressionarestudiedtodeterminehowstraticationevolvesoveratidalcycle.Asthebathymetrywithintheinletisatypical,currentsgeneratedasaresultofthedepressionmodifystraticationandenhancemixing.ResultsfromtheanalysisofcurrentvelocitiesandhydrographicprolesinatropicalinletduringthewetanddryseasonsaredescribedinChapter 3 Tidallydominatedinlets,acommonfeaturealongthecoastofFlorida,exhibitparticulartidalandresidualows.Residualowsinshallowbasinsareoftendominatedbypressuregradients,frictionandadvection.ThreedifferenttidalinletsarestudiedinChapters 4 5 and 6 ,usingobservations,todeterminethemajorforcingmechanismsaffectingtheseowsovertidaltoseasonaltimescales.Processesaffectingtidalowsareoftenassociatedwithvariabilityinthesubtidalows,andhowtheseinteractarediscussedineachcase.Thebackgroundandresultsforeachinlet,aswellasestimatesoftherstorderforcingtermsfromthemomentumequationsarediscussed. 16

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Aseachchapterdiscussesaseparatestudyforthisdissertation,backgroundinformationforeachtopicwillbedescribedindetailatthebeginningofeachchapter.Conclusions,inChapter 7 ,willunifytheworkspresentedherebasedonthehydrodynamicsstudied. 17

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CHAPTER2TIDESINASYSTEMOFCONNECTEDESTUARIES 2.1Introduction Astidesenterbasins,avarietyofinteractionsmodifythetidalsignalincludingfriction,Earth'srotationandbathymetry1.Earlyworksonco-oscillatingtidesfoundthatobservedtidalsignalsweresuperpositionsofoppositelytravelingKelvinwaves[ Taylor 1921 ]andthatenergywasabsorbedattheheadofbasinswhichaccountedfortheobserveddissipationoftidalenergy[ HendershottandSperanza 1971 ].Asfrictionbecomesimportant,thephasedifferencebetweenvelocityandelevationdepartsfromtheclassicalfrictionlessco-oscillatingsolution[ Friedrichs 2010 ; FriedrichsandAubrey 1994 ; Prandle 2003 ].Tidalpropagationinshallowriverswasfoundtobemoreproperlydescribedasadiffusiveprocessratherthanawavepropagationphenomenon[ FriedrichsandMadsen 1992 ; LeBlond 1978 ].Furtherstudiesonamplitudeandphasechangesintidalchannelswitharbitrarylateraldepthvariationsfoundthatseasurfaceelevationwasone-dimensionalalongtheestuary[ LiandValle-Levinson 1999 ].Velocitieshadstronglateralshearandwerethree-dimensional,dependentonthelateraldepthvariations[ LiandValle-Levinson 1999 ]. Whiletheidealizationofasemi-enclosedbasintsmanyrealisticestuaries,therearealsomanysystemsofinterconnectedestuariesalongcoastlines.Thesesystemscanresultfromnaturalprocessesortheycanbeman-made,tofacilitatenavigation,asinthecaseoftheIntracoastalWaterwayontheEastandGulfcoastsoftheUnitedStatesortheDutch-WaddenSeaintheNetherlands.Theseregionsareofteninhabitedonboththemainlandandbarriersidesandaretypicallyecologicallysensitive,verysusceptibletoanthropogenicactivities.Flushingmechanismsandthesubsequent 1SubmittedforpublicationasWaterhouse,A.F.,A.Valle-Levinson,andC.D.Winant,Tidesinasys-temofconnectedestuaries,J.Phys.Oceanogr.,submittedMay2010. 18

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healthofthesesystemsdependmostlyontidalandwinddrivencirculation.Therefore,developmentandplanningintheseregionsneedrigorousevaluationofwhatphysicalmechanismsforcetheow,includingappropriatemodels. Ananalyticalmodeloftidalcirculationinasemi-enclosedestuary[ Winant 2007 ]ismodiedhereintorepresentthecirculationinasystemoftwoconnectedestuaries,asabuildingblockformorecomplicatedsystems.Thelinearmodelassumesconstantdensity,ano-slipbottomboundaryconditionandmayincludetheeffectsoftheearth'srotation.Thismodelhasbeenusedtodescribetidalowinlowtomoderatelyfrictionalbasinswithoneopening[ Winant 2007 ],residualowsinbothtidallydominated[ Winant 2008 ]andestuarieswithgravitationalcirculation[ Winant 2010 ].Dynamicallyimportantnon-dimensionalparametersrequiredforthemodelare,thehorizontalaspectratioofthebasin(widthtolength),,thelengthofthebasintothewavelengthofthetidalwaveratioand,therelativeimportanceoffrictiontolocalaccelerations.Theparametersdescribingfrictionandrelativelengthinthismodelaredenedas =p 2K0=!0H02,=!0L0=p gH0(2) whereK0isaconstantverticaleddyviscosity,!0isthefrequencyofthetide,H0isthemaximumbasindepth,L0isthelengthofthebasin,gisthegravitationalaccelerationand0representsadimensionalparameter.Forourpurposes,parametersandareimportantwhilerotationcanlargelybeignored.Previousstudieshaveexplainedtidalowwithlowfrictionconditions(1; Winant 2007 ),whilethisworkconcentratesonastronglyfrictionalsystem(1).Inlowfrictionalsystems,therelationshipbetweenvelocityandseasurfaceelevationisdescribedbythewaveequation,whileinfrictionallydominatedsystem,therelationshipisdenedbythediffusionequation. Thecentralresultofthisworkisthattidalvelocityandseasurfaceelevationarestronglydampeduponenteringintoashallowinterconnectedwaterway.Tidalamplitudedecreasesrapidlywithentranceintotheinlets,withtidalphaseincreasing 19

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withincreasingfriction.Alongandcrosschanneltidalvelocitiesvaryclosetotheentrancestothewaterway.Alongbasinowisdominantwithinthechannelwhilecrossbasinowsaremoredominantovertheshoals.FrictionaleffectsdominatethedynamicswithinthisinterconnectedsystemandCoriolisandlocalaccelerationsaresmall. 2.2Model Thelinearanalyticalmodelisbasedonatidalmodelforasemi-enclosedbasindescribedin Winant [ 2007 ].Themodelisdenedashavinganinnitelylongcoastlinealongthexaxiswithabarrierseparatedfromthecoastlinebyaconstantdistance,B0,thewidthofthebasin.Thebarriermayhaveirregularlyspacedinlets,althoughforthisstudyonlytwoinletsareconsidered,separatedfromeachotherbyalength2L0.Thedepthacrosstheinlandwaterway,betweenthecoastandthebarrier,isconstantinthexdirection,buthasanarrow,deepchannelinthecross-waterwaydirectionofdepthh(Figure 2-1 ).Thecrosswaterwaydepthisdenedbyanexponentialfunction h=0.25+0.75exp)]TJ /F4 7.97 Tf 6.58 0 Td[(20y2.(2) ThisnormalizeddepthissimilartothecrosswaterwaybathymetryinFlorida'sIntracoastalWaterwaywherethemaximumdepth(H0)is5minanarrowchannelwithwideshoalsof1mdepth.Positivex-directionrunsalongthechannelwithx=0attheSouthendofthechannel,andx=2attheNorthendofthechannel.Theyaxisextendsacrossthechannelwithy=0alongthecenteraxisofthewaterway.Thesolutionof Winant [ 2007 ]isappliedtoonehalfofthewaterwayassumingsymmetry.Becausetheobservedphaselagbetweenthetideatthetwoinletsisnegligible(10minutes),thesolutionisusedforbothsidesofthewaterway.Thesymmetricnatureofthesolutionisappropriateinthiscasegiventhestronglyfrictionalnatureoftheinlandwaterway,andthesubsequentdampingofthetidalsignal.BetweenSt.AugustineandPoncedeLeonInlet,theIntracoastalWaterwayhasahalf-basinlength(L0)of50kmgivingthenon-dimensionallengthparameter=1.0forthesemi-diurnal(M2)tide.Aninitial 20

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estimateofthefrictionalparameter,,rangesfrom0.8to1.7(usingK0between0.001and0.005m2s)]TJ /F4 7.97 Tf 6.58 0 Td[(1).Inthiswork,willbekeptconstantwhilewillbevaried. In Winant [ 2007 ],complexamplitudeswereusedtoapproximatetheperiodicsolutionsofthetidesuchthat u=Re(U(x,y,z)e)]TJ /F8 7.97 Tf 6.58 0 Td[(it)v=Re(V(x,y,z)e)]TJ /F8 7.97 Tf 6.58 0 Td[(it)(2) w=Re(W(x,y,z)e)]TJ /F8 7.97 Tf 6.59 0 Td[(it)=Re(N(x,y)e)]TJ /F8 7.97 Tf 6.59 0 Td[(it)(2) whereU,VandWarethealong,acrossandverticalvelocitiesinthebasinandNistidalelevation. Winant [ 2007 ]usesthelinearizedmomentumequationsassumingshallow-waterwaveswithahydrostaticapproximationinthevertical.Aconstantverticaleddyviscosityandnegligiblehorizontalviscositiesarealsoused.Boundaryconditionsonthebottomareno-slip,andatthesurfacearethekinematicanddynamicboundaryconditions.Attheopenendsofthewaterway,thetidalamplitudeisassumedtobe N=1atx=0,2(2) whichindicateszerophaselagbetweeninletsforthetidalamplitude,giventhecomplexnatureofN.Inthemiddleofthebasin,atx=1,thevelocitynormaltotheboundaryisassumedtobezero(Nx=0)meaningnotransportoccursbetweenthetwoadjacentbasinsatx=1. Assumingthatdepthorwidthdependonlyony,theclosed-formsolutionfortherstordeructuationinsealevelis N(0)=cos((1)]TJ /F3 11.955 Tf 11.96 0 Td[(x)) cos(2) where = p (2) 21

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wheretheanglebracketsdenotealateralaveragesuchthat =Z10M0dy.(2) ThedenitionofM0=f2Q20 P0)]TJ /F3 11.955 Tf 12.55 0 Td[(P0,whereP0andQ0arecomplexfunctionsoff,andh.Whenfrictionisverylowandgoestozero,bothP0andQ0tendtoh=(f2)]TJ /F5 11.955 Tf 12.94 0 Td[(1).Integratingthelocalvelocitiesindepthgiveshorizontaltransportvelocities,whichinthealongandcrosschanneldirections,are [U]=)]TJ /F3 11.955 Tf 10.5 8.09 Td[(iN(0)xM0 2(2) and [V]=iN(0)xxG 2(2) whereGequalsRy0(M0)]TJ /F6 11.955 Tf 12.67 0 Td[()dy0.ThefullderivationoftheequationsandfullformofP0andQ0canbefoundin Winant [ 2007 ]. 2.2.1SeaLevelFluctuations,N0 Whenthefrictionalparameterequals1,theseasurfaceelevation,N(0),isindependentoffastheparametersinequation 2 approachvaluesthatdonotdependonf,asin Winant [ 2007 ].ThephaseandamplitudeofN(0)areshowninFigure 2-2 forbothsemi-diurnal(M2)anddiurnal(K1)tidalfrequencies.Inthesecases,thelengthofthebasinisapproximatelyequaltoandlessthanonequarterthetidalwavelength(=1.0and0.5)forthesemi-diurnalanddiurnaltides,respectively.Thus,maximumtidalamplitudesareexpectedinthemiddleofthebasinwhen<1[ Winant 2007 ],representativeoftidalamplicationwithlowfriction.However,for=1,theamplitudeoftheseasurfacedecreasestowardthemiddleofthewaterwayandthenincreasesslightly,asobservedin Winant [ 2007 ].Forallcaseswithgreaterfriction(>1),thetidalamplitudedecreasesexponentiallyuponentranceintothebasinanddoesnotchangewhenfisvaried.For=2,N(0)atx=1is0.03oftheamplitudeattheentranceofthebasins.For>4,theamplitudeatx=1approacheszero. 22

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When!0decreasesfromthesemi-diurnaltothediurnalfrequency,increasesbyafactorofp 2,fromequation 2 .Therefore,thechangeinamplitudefromthesemi-diurnaltothediurnalsignalsissimilartochangesbetweenlowertohigherfriction.Theamplitudeofthediurnalsignalfor=1,decreasesfromtheentrancesatx=0and2,thenincreasestowardthemidpointatx=1.Asincreasesabove2,theamplitudeofthetidalsignalattenuatesmorequickly.Thetidalamplitudedecaysmoreslowlythanthesemi-diurnaltide.Forlarge,theequationdeterminingtheowbetweenthetwoinletsisdominatedbypressuregradientandfriction,andneitherCoriolisnorlocalaccelerationsareimportantinthealong-channeldynamics. Phaseincreasesfromzeroatx=0withalongchanneldistancetothemidpointofthebasin,wherethephasesthendecreasebacktotheoriginalinputtidalphase(zeroatx=2).Thisisconsistentwithatidalwavepropagatingalongthebasinfrombothsides(x=0andx=2)towardx=1.Asfrictionincreases(>1),thephasedifferencebetweentheentranceandmidpointofthewaterwayalsoincreases.Thisindicatesthatthetidepropagatesmoreslowlyasfrictionincreasesandthepeakfromtheentrancewillnotbefeltatx=1untilalongertimethanforlowerfrictionalvalues.Withincreasingfriction,thegoverningdifferentialequationchangesfromawaveequationtoadiffusionequation.Thewaveequationindicatesthatthephasespeedwouldbeindependentoffriction,whereasthediffusionequationwouldmakethephasespeeddependentonfriction.For=1,thephasechangebetweentheentranceandthemidpointofthebasinis170.Forthesemi-diurnaltide,thisindicatesalagof5.9hoursbetweenthehightideattheentranceandthatatx=1,whileforthediurnaltide,thelagbetweentheentranceandx=1is82.25(5.5hours). 2.2.2TransportVelocities Transportvelocity,[U],alongthebasin,issymmetricacrossthebasinwithhighestamplitudesinthechannelandlowestovertheshoals(Figure 2-3 ).Asthetideentersthebasinfrombothinlets,themajorityofthetidalenergyentersthroughthedeepnarrow 23

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channel.Duetohighfriction(=2,inthiscase),thealongchanneltransportdecreasesinthechannelasitapproachesthemid-pointofthewaterway.Thephasechangeinthechannelisverysmallcomparedwiththatontheshoals.However,itdoeschangewithdistancealongthechannelfrompositive(attheentrance)tonegativeinsidethebasin.Thealongchanneltransportvelocityrespondsmorequicklyontheshoalsthaninthechannelasthereislessinertiainshallowerow,andshoaltransportleadstransportvelocityinthechannel(Figure 2-3 ). Themagnitudeofthelateraltransport,[V],isweakerthanthealongchanneltransportwithmaximaoccurringontheshoals,localizedattheentrancetothebasin(Figure 2-4 ).Thephasesoneachsideofthechannelareopposite(constant180difference)indicatingowtowardtheshoalsduringoodandofftheshoals(towardthechannel)duringebb.Theamplitudeandphaseindicatethatthereistransportofwatertotheshoalsasthetideentersthroughthechannel.However,proceedingfurtherintothebasin,theamplitudeof[V]decreases.Combinedwith[U],mixingandtransportofwater(ushing)toandfromtheshoalsmayonlybelocalizedtoanareaneartheentrancetothewaterwayasobservedby Smith [ 1983 ]. 2.2.3N(0)and[U]:Phases Givenadynamicallywide,frictionlessbasin,whenthelengthofthebasinisgreaterthanonequarterofthetidalwavelength(1),anodeexists.Onthebasinsideofthisnode,currentsleadseasurfaceelevationby-90whereasontheothersideofthenode,theleadis90.Whenthelengthofthebasindecreasestolessthanonequarterofthetidalwavelength(<1),thenodedisappearsandcurrentsleadelevationby90.Whenfrictionincreases,however,thephaserelationshipbetweenN(0)and[U]isnolonger90.Thedeviationfrom90isdiscussednextasfrictionincreasesfrom=1to5. ThephaseofN(0)issettobezeroattheentrancestothewaterway(N(0)=1),andthephaseof[U]attheentranceisrelatedtothenon-dimensionallengthofthebasin.Thesephasesareplottedatx=0andx=0.25alongthemiddleofthebasin 24

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(aty=0)forbothsemi-diurnalanddiurnaltidalfrequencies(Figures 2-5 and 2-6 ).Thephaseof[U]atx=0variesasincreaseswhile,giventheboundaryconditionattheentrance,thephaseofNremainszero.When=0forthesemi-diurnaltide,currentsleadseasurfaceelevationby)]TJ /F5 11.955 Tf 9.3 0 Td[(90attheentranceofthebasinsince=1.0andanodewouldbeexpectedgiventhetidalwaveoscillationinafrictionlessbasin(Figure 2-5 ).However,asfrictionincreases,thephasedifferenceapproaches45,butnotlinearly.Smallchangesinfrictionbetween=0and2resultinasignicantlydifferentphaselagbetweenseasurfaceelevationandvelocity.Above=2,thephaselagapproaches45moreasymptoticallythanfor<2.Theimportanceoffrictioninmodifyingthetidalpropagation(andsubsequentnode)ishighlightedasthecurrentschangefromaphaselagof)]TJ /F5 11.955 Tf 9.29 0 Td[(90to45overrelativelysmallchangesinfrictionalparameter(=0to2). Furtheralongthebasinatx=0.25,thephaseofbothseasurfaceelevationandvelocityvarywith(Figure 2-5 ).Thephaselagbetweenelevationandvelocityasymptoticallyapproaches45,for>2withtheminimumphaselagoccurringatx=0.5of)]TJ /F5 11.955 Tf 9.3 0 Td[(12.6.Foraparticularinletwithafrictionalvalueof=1,thephaselagbetweenseasurfaceelevationandvelocitywillvarydependingonthesamplinglocationwithintheinlet.For=1atx=0,thephaselagwillbe19whileatx=0.25,thephaselagwillbe13. Phaselagsforthediurnalsignal(Figure 2-6 )varyfrom90to45differentlythanforthesemi-diurnalsignalsince<1.Atx=0,thephaseofthetransportvelocityincreasesfrom=0to2atwhichpointbecomessteadyat,approximately,45.Theminimuminphaselagbetween[U]andN(0)occursfor=1at24.Furtheralongtheinlandwaterway,atx=0.25,thephaselagdecreasesfrom90to45asymptoticallyapproaching45for>2. Phaselagsbetweentransportvelocityandelevationrangingfrom-90to90,asdescribedin Friedrichs [ 2010 ],arecapturedbythisanalyticalmodel.Inthecasewithahighlyfrictionalbasinwithtwoopenings,thephaselagisfoundtobedependenton 25

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frictionaleffects.Inamoregeneralcase,dependingonthebasinlength,lateraldepthvariationsandtidalfrequency,thephaselagbetweentransportvelocityandseasurfaceelevationwillvarywithdistancealongthebasin. 2.3Observations InsituobservationsareusedtodeterminewhetherthetidalbehaviorfromtheinlandwaterwayofFlorida'sIntracoastalWaterwaymatchesthatpredictedbytheanalyticalmodel.Florida'sIntracoastalWaterwayisadredgedwaterwayextendingalongtheeasterncoastofFlorida.ThemeanwidthoftheIntracoastalWaterwayis55mwithexpansiveshoals(1mdepth)andamaximumdepthof5m[ KenworthyandFonseca 1996 ; Smith 1983 ]inanarrownavigationalchannel.PoncedeLeonInletandSt.AugustineInletaretwoof19coastalinletsconnectingtheIntracoastalWaterwaytotheAtlanticOcean[ DeanandO'Brien 1987 ].Tidalowswithinthesetwoinletsareforcedbythesemi-diurnal(M2)tideandmoreweaklybythediurnal(K1)tide,withtypicaltidalcurrentsexceeding1ms)]TJ /F4 7.97 Tf 6.58 0 Td[(1.Tidalowsenteringthroughtheseinletswillinteractbothwiththevariablebathymetrybutalso,possibly,withthetidalsignalwithinthewaterwayasaresultoftheopencommunicationbetweentheinlets. AtotalofninepressurerecordswereusedtodeterminethetidalamplitudeandphasealongtheIntracoastalWaterway.Sixpressuresensors,developedfor Kennedyetal. [ 2010 ],weredeployedover14daysfromDecember3untilDecember17,2009atvariouslocationsbetweenSt.AugustineInletandPoncedeLeonInlet(Figure 2-7 ).Surfaceelevationwasrecordedatburstsof60seconds,every14minutes,samplingat5Hz.Thedatawereaveragedovereachsamplingperiodleavingoneensembleaverageevery15minutes. Theharmonicconstituentsfromthreeotherpressure(andtwovelocity)records,whichweredeployedpriortoDecember2009,wereobtainedusingT TIDEwithoutinference[ Pawlowiczetal. 2002 ].Pressureandvelocityrecordswerereconstructedusingtheharmonicconstituents,withoutinference,forthesamplingperiodbetween 26

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December3and17,2009.TherstreconstructedserieswaspressurefromSensor8,deployedfromDecember13,2009untilJanuary9,2010atalocationsouthofSt.AugustineInlet(Sensor8;Figure 2-7 ).ThetwoothersensorswerefromtwoAcousticDopplerCurrentProlers(ADCPs)deployedatthemouthsofPoncedeLeonandSt.AugustineInlets.TheseADCPsweredeployedfromJanuarytoMarch2008(PoncedeLeonInlet,depthof8m)andfromJulytoSeptember2008(St.Augustine,depthof15m)inthedeepestpartofeachinlet.EachADCPrecordedpressureandprolesofvelocity.Ensembleaveragesof0.5mbinswererecordedatapingrateof1.5secondswith400pingsperensemble.Currentvelocitieswererotatedtobealignedwiththeprincipalaxisofmaximumvariancesuchthatpositivealongchannelvelocitywasdirectedintotheinletandpositiveacrosschannelvelocitywassouthward. TwomoreADCPsweremooredatPortOrange,FL(betweenpressuresensors2and3;Figure 2-7 )fromDecember3toDecember17,2009.A600kHzADCPwasmooredinthenavigationchannelat5mdepth,whilethesecondADCPwasmooredontheeasternbankinahole(4m).BothADCPsmeasuredensembleaveragesof0.5mbinsatapingrateof1.2secondswith400pingsperensemble.Datafromthechannelwererotatedtotheprincipalaxisofmaximumvariance(by76)suchthatpositivealong-channelvelocitywasnorthwardandpositiveacrosschannelvelocitywaseastward.ThesecondADCPwasnotdeployedexactlyontheshoal,butinaholeintheshoalregion,andthereforethesedataarenotdiscussedinthispaper. Allpressureandvelocityrecordswerebandpassltered,isolatingthesemi-diurnal(1to18hours)anddiurnal(20to36hours)components.TheamplitudeandphasechangeofthepressuresignalsalongtheIntracoastalWaterwaywasthenfoundusingaHilbertorthogonaleigenfunction(HilbertEOF)analysis.TheHilbertEOFanalysiscapturesthechangeinamplitudeandphaseofasignalthathasthesamefrequenciesbutdifferentphasesofthatfrequency[ EmeryandThomson 2004 ; Hannachietal. 2007 ; Horel 1984 ; MerrieldandGuza 1990 ; VonStorchandZwiers 2001 ].Incontrast 27

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tothetraditionalEOFmethod,HilbertEOFsreturnboththeamplitudeandphaseofacomplexieddatasetrelativetotherstinputsignal(seasurfaceelevationorvelocity),whichisassignedzerophase.Forthiswork,allphasesarethusrelativetothesouthernmostinlet,PoncedeLeonInlet.Thesixpressuresensors(Sensors2to7)haddifferenttimestampsassociatedwiththestarttimeofthesensor,andthisdifferencewasaccountedforbysubtractingtheappropriatephaseshift(intime)fromthephaseoutputfromtheHilbertEOFanalysisforeachofthosesensors.ThephaselagbetweentheelevationandalongchannelvelocitywerealsofoundusingaHilbertEOFanalysis. 2.3.1SeaLevelFluctuations,N(0) PressurerecordscollectedalongtheIntracoastalWaterwaywerecomparedwithmodelresults(Figure 2-8 ).Likethemodelresults,thetidalamplitudedecreasesfrombothopeningsofthechanneltowardthecenterpoint(x=1).Thephaseincreaseswithdistancealongthechannelfrombothinlets,consistentwiththemodelresults.Thephaselagfromx=0andx=1is152and89forthesemi-diurnalanddiurnalsignals,respectively.Thiscorrespondstoa5.2and5.9hourphaselagbetweentheinletsandthemidpointoftheinlandwaterway.Usingthefrictionalparameterof=1.5(fromthebesttbetweenobservationsandthemodelresults)andamaximumdepthof5minequation 2 ,theconstanteddyviscosityisK0=0.004m2s)]TJ /F4 7.97 Tf 6.58 0 Td[(1.Usingthiseddyviscositywiththediurnaltidalfrequency,!0,gives=2.1,whichcorrespondstotheobservedtbetweenthemodelresultandobservationsforthediurnaltide. 2.3.2TransportVelocity,[U] Thetransportvelocityisdenedinthiscontextastheverticallyintegratedvelocity.ThetidalamplitudeandphaseofthetransportvelocitywithintheIntracoastalWaterwaywasobtainedfromtheHilbertEOFanalysisofdepthaveragednon-dimensionalizedvelocitiesfromeachofthethreedeployedADCPsandusingthepressurefromPoncedeLeonInletasthereferencepressure.AllrstmodeamplitudesfromtheHilbertEOFwerenormalizedtotherstmodeamplitudeofthepressuresensor. 28

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Theamplitudeof[U]decreasestowardthecenterofthebasin(Figure 2-9 ).Atx=0,thesemi-diurnalamplitudeofthetransportislessthanatx=2indicatinganimbalanceintheinputtidalsignalfromeachofthelocations.Thediurnaltransportvelocityamplitudeisalsoover-predictedbythemodelatbothentrancesbutitsshaperesemblestheobservations,showingadecreaseintransportvelocitywithdistanceintothebasin. Thephaseofthetransportvelocityvariesfromnegativeclosetothemouthsofthewaterway,topositiveatthestationwithintheIntracoastalWaterwayatPortOrangeforboththesemi-diurnalanddiurnaltransportvelocities.Theobservationsareinagreementwiththephasesfromthemodelwhereasmallerphaselaginthediurnalsignalatx=1wasobservedcomparedwiththesemi-diurnalsignal. 2.3.3N(0)and[U]:Amplitudes Tocomparethechangeinamplitudesofbothvelocityandseasurfaceelevation,theratioof[U]andN(0)wascomparedbetweenthemodelandtheobservations.ModelresultsofthealongchannelamplitudesofN(0),[U],andtheratioofthetwoareshowninFigure 2-10 .Theratioofthestandarddeviationbetweenalongchanneltransportvelocityandsurfaceelevationarecalculatedatallcurrentmeterlocations.TheaccuracyofthepressuresensorfromtheADCPislessthanthechangeinwaterlevelandtherefore,thepressurefromsensor3isusedasthepressurefromthePortOrangeADCP.Theratiosoftheobservedstandarddeviationswerecomparedtothedimensionalizedmodelresultsfrom=1.5,=1.0andf=0.Toobtaindimensionalizedvaluesfromthemodel,themodelratiosweremultipliedbythetidalfrequency(!0)andthechannellength(L0)givenby [U]obs obs=[U]model N(0)model!0L0(2) FromthecurrentmetermooredatPortOrange(betweensensors2and3),theratiosfromboththeobservedsemi-diurnalanddiurnaltidesareincloseagreementwiththe 29

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Table2-1. Ratioof[U]=N(0)fromADCPsmooredatthreelocationsinFlorida'sIntracoastalWaterwaycomparedwithdimensionalizedratiosfromthemodelfrom=1.5,=1.0forthesemi-diurnaltideand=2,=0.5forthediurnaltide.Rotationisnotconsidered(f=0). MooringUobs obsUmodel Nmodel Semi-DiurnalPoncedeLeon16.69.4PortOrange14.69.3St.Augustine41.69.4DiurnalPoncedeLeon8.07.5PortOrange8.58.3St.Augustine7.47.5 modelpredictions(Table 2-1 ).Theratioof[U]modeloverN(0)modelincreasestoamaximumatx=0.7and1.3andx=0.5and1.5,decreasingtozeroatx=1forthesemi-diurnalanddiurnalsignals,respectively(Figure 2-10 ).AtSt.Augustine,thesemi-diurnaltideratioismuchlargerthanthemodelpredicts.Thisinconsistencyislikelyrelatedtothesensitivityofvelocitytoaccuratebathymetryinthealongandcrosschanneldirectionswhileseasurfaceelevationisnotasdependentonaccuratebathymetry.Thediurnalobservedratiosfollowthemodeloutput,whichshowslargerpredictedandobservedamplituderatiosatPortOrange(x=0.3). 2.3.4N(0)and[U]:Phases Atallthreemooringlocations,velocityleadstheseasurfaceelevation.Thechangeinthespatial(local)leadofcurrentsoverelevationwascalculatedfromtheHilbertEOFanalysisofthealongchanneltransportwithpressure(normalizedbythestandarddeviationofthecurrentsoverthepressure).Forthesemi-diurnaltide,with=1.5,thephaseleadofcurrentsoverseasurfaceelevationisconsistentwiththemodelresults(Figure 2-11 ).Thesemi-diurnalphasedifferenceislessthan45neartheentrancesoftheinlandwaterwayasobservedinFigure 2-5 .Modelpredictionsindicatethatthephasedifferencewillonlyreach90closetothemiddleofthewaterwayatx=1withthephasedifferencesstayingconstantuntilx=0.45andx=1.6.Themodeloutput 30

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predictsthatthephasedifferencebetweenelevationandvelocityforthediurnalsignalis45atthemouthsoftheinletand90atx=1.TheobserveddiurnalphasedifferencesatPoncedeLeonInlet(x=0)andPortOrange(x=0.3)aresimilartothosepredictedbythemodel.However,atSt.AugustineInlet(x=2),theobservedphasedifferenceismuchlargerthanpredictedbythemodel(90),closertoastandingwaveforthediurnaltide.Withoutadditionalinformation,theobservedphasedifferenceislikelyduetoinuencesofMatanzasinlet,whichwillbediscussedinthenextsection. 2.4Discussion Analyticalmodelresultsandobservationsofseasurfaceelevationandtidalowdemonstratethatthetide,synchronousbetweenPoncedeLeonInletandSt.AugustineInlet,entersatbothinletsandquicklyattenuateswithintheIntracoastalWaterway.Thetidediffusesthroughtheinlandwaterway,ratherthanpropagates,duetofrictionaleffects.Theeddyviscosityisestimatedtobe0.004m2s)]TJ /F4 7.97 Tf 6.59 0 Td[(1,giventhebesttbetweentheobservationsandthemodelforthesemi-diurnalanddiurnaltides.Therefore,theshallowdepthaccountsforthestrongattenuationofthetidewithdistancealongtheinlandwaterway. LeBlond [ 1978 ]cametothesameconclusionindevelopingasimplediffusivemodelfortidalriversofmuchlargerscalesuchastheFraserandSt.LawrenceRivers. ThetideintheIntracoastalWaterwayalongtheEastcoastofFloridaisprescribed,atirregularintervals,bytheopenoceantide.ThedynamicsintheIntracoastalWaterwayaredeterminedbyabalancebetweenfrictionandpressuregradient.Whenacharacteristiclengthinthexdirection,separatingthetwoinlets,islargesuchthattidalamplitudesandvelocitiesattenuatetozero,therewillbenoushingaroundthemiddleregionofthewaterway.Similarobservationsby Smith [ 1983 ]showedthattherewasrelativelyrapidushingneartheinlet,butwithlittletononetmovementofwaterintheinterioroftheIntracoastalwaterway. Smith [ 1983 ]suggestedthatduetothelackoftidalushing,low-frequencyvariationswouldbemoreimportantintheinteriorofthe 31

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waterway,intermsofushingtimes.FromourobservationsbetweenPoncedeLeonandSt.AugustineInlet,thewaterlevelvariationsdonotreachzero(0.2m),however,predictedtransportvelocitygoestozero.Thisindicatesthatminimaltonoushingisoccurringatthemidpointbetweenthetwoinlets. Thetidalvelocitystrengthalongthebasinisdeterminedbythelateraldimensionsofthebasin.Inourcase,thechannelisverynarrowanddeepwithrespecttotheshoals.Asthetideentersthroughtheinlets,thetidaltransportfollowsthechannelandthetidalvelocitydecreasesquicklyovertheshoals.Theamplitudeofthesurfaceelevation,however,isconstantlaterally(iny)varyingonlyalongx.Astheowspreadsoutlaterallyovertheshoalsclosetotheentranceofthechannel(Figure 2-4 ),ushingwillonlyoccurasaresultofthislocalmixing.Studiesoftheinterconnectivityofthesebasinsonthetidalevolutionwithinthewaterwayhaveshowntheexistenceofmeanowsasaresultoftidalandwaterleveldifferencesalongthewaterway[ Huangetal. 2002 ; Liu 1992 ; Smith 1983 ; vandeKreekeandDean 1975 ].Modellingfrom vandeKreekeandDean [ 1975 ]showedthatresidualowsresultedfromdifferencesintidalamplitudesandphasesbetweentwoinlets.Althoughmeanowswouldeffectivelyincreaseushingandhavenotbeenconsideredinthismodel,ushingasaresultoftidalprocessesarestilllikelyimportantatinletmouths.Furthersimplicationsofthebathymetryinthemodelattheinletmouthswillunderestimatethedifferentamountoftidalushingoccurringbetweenthetwoinlets.Asthecrosssectionalarea(andresultingtidalprism)islargerinSt.AugustineInletthaninPoncedeLeonInlet[ WaltonandAdams 1976 ],enhancedtidalushingislikelyoccurringinSt.AugustineInletrelativetoPoncedeLeonInlet[ O'Brien 1931 1969 ]. Inconsistencyinthecomparisonsbetweenthemodelandobservationsintheregionbetweenx=1andx=2,closetoSt.AugustineInlet,hasbeenattributedtotwolikelysources.TherstistheinteractionoftidalsignalsfromMatanzasInlet,whichisanarrowshallow,undredgedchannel24kmSouthofSt.AugustineInlet.Although 32

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thetidalsignalislikelydampedthroughitslong,sinuousentranceintotheIntracoastalWaterway,giventheresultsshownfromtheobservations,theincreaseintidalamplitudeobservedinpressuresensorsbetweenx=1andx=2islikelyaresultofthetidefromMatanzasInlet.AlthoughthetidalsignalisdampedoncereachingtheentrancetotheIntracoastalWaterway(atx=1.5),theinuenceofthistidalsignalcanbeseeninFigures 2-8 fromx=1tox=2asthetidalamplitudeislargerthanfromthemodel.Thephaseofthesemi-diurnalsignal,beyondx=1indicatesadecreaseinpropagationspeedasaresultofthehigherthanexpectedphase,perhapsfromtheinuenceofMatanzasInlet.ThesecondexplanationfortheincreasedamplitudeatSt.Augustineislikelyassociatedwiththedifferenceinmooringdepthbetweenbothinlets.St.AugustineisamuchwideranddeeperinletthanPoncedeLeonInletandtheADCPwasmooredat15m(comparedwith8minPoncedeLeonInlet).ThetidalwavewasunderdifferentfrictionalconditionsduetodifferentdepthsandwaslikelymoredampedwhenmeasuredinsidePoncedeLeonInletthaninSt.AugustineInlet. 2.5Conclusions Inashallowinlandwaterwaywithopeningstotheadjacentocean,themaintidaldynamicsaredrivenbythebalancebetweenpressuregradientandfriction.Observationsofvelocityandseasurfaceelevationarewelldescribedwithananalyticalmodelthatusesthelinearizedequationsofmomentum.Inhighlyfrictionalenvironments,suchasFlorida'sIntracoastalwaterway,thetidalamplitudedecaysrapidlyawayfrombothopenings.Asfrictionincreases,decayofthetidalamplitudeoccursclosertotheentrancesandthepropagationofthetidalsignalisslower. Transportvelocityfollowsthebasinbathymetry,withstrongestalongchanneltransportvelocitiesinthechannel.Theshallowdepthoftheshoalsallowsfortheshoalstoreactmorequicklytotidalsignals,andalongchanneltransportinthechannellagsthoseontheshoals.Lateraltransportattheentrancestotheinlandwaterwayisontothe 33

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shoalsduringoodtideandofftheshoalsduringebbs.Thisindicateslocalizedmixingatthemouthsoftheinlets,decreasingtowardthecenteroftheinlandwaterway. Inafrictionlessbasin,thephaselagbetweenseasurfaceandelevationis90,asexpectedinaco-oscillatingtidalsolution.However,thephaseapproaches45athighfrictionbuttendstodecreasebelow45formoderatelyhighfriction.Thephaselagbetweenseasurfaceelevationandcurrentvarieswithlocationwithintheinlandwaterway,andmayincreaseto90atthecenterofthewaterway.Overall,themodeldescribeswellthepropagationandattenuationofthetidewithinaninlandwaterway. Figure2-1. Analyticalmodelsetupwithtwoentrances(inlets)toaninlandwaterway.Dimensionsofthemodeldomainare2L0,B0andh0.Thedashedlineatx=1denotesthelocationofthesealevelminimumandzerotransport.Thetideentersthetwoinletssynchronouslyatx=0andx=2.Thesolutionofseasurfaceelevationandtransportvelocityofthetidalsignaliscalculatedbetweenthetwoinlets. 34

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ASemi-Diurnal,=1.0,f=0 BDiurnal,=0.5,f=0 Figure2-2. Seasurfaceelevation(N(0))amplitudeandphaseascalculatedfromthemodelforhighvaluesoffriction,rangingfrom=1to5forthesemi-diurnal(M2)anddiurnal(K1)tides. 35

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Figure2-3. Amplitudeandphaseofthealongchanneltransport([U])fromtheanalyticalmodelwith=1.5,=1.0andf=0forthesemi-diurnaltide. 36

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Figure2-4. Amplitudeandphaseofthecrosschanneltransport([V])fromtheanalyticalmodelwith=1.5,=1.0andf=0forthesemi-diurnaltide. 37

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Figure2-5. Phasesofseasurfaceelevation(N(0))andalongchanneltransport([U];AandB)andthephasedifferencebetweenN(0)and[U]forvariousvaluesofrangingfrom1to5(CandD)forthesemi-diurnal(M2)tidewith=1.0andf=0. 38

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Figure2-6. Phasesofseasurfaceelevation(N(0))andalongchanneltransport([U];AandB)andthephasedifferencebetweenN(0)and[U]forvariousvaluesofrangingfrom1to5(CandD)forthediurnal(K1)tidewith=0.5andf=0. 39

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Figure2-7. Mapshowinglocationsofsixpressuresensors(x)mooredintheIntracoastalwaterwayfromDecember3untilDecember17,2009.SensorswhoseharmonicconstituentswereusedtoreconstructpressureandvelocitysignalsarethetwoADCPsatthemouthsofSt.AugustineandPoncedeLeon(circles)aswellaspressuresensor8,SouthofSt.AugustineInlet(diamond).Allnumberedstationsareusedintheseasurfaceelevationamplitudeandphasecalculations.TransportvelocitiesandpressurewereusedfromtheADCPsmooredforatleastonefortnightlytidalcycle(circles). 40

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ASemi-Diurnal,=1.0,f=0 BDiurnal,=0.5,f=0 Figure2-8. Observationsofseasurfaceelevation(N(0))amplitudeandphase(solidcircles/dottedline)betweenPoncedeLeonInlet(x=0)andSt.AugustineInlet(x=2).Modeldataareshownbelowforthosewhichmatchwiththeobservedresults. 41

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ASemi-Diurnal BDiurnal Figure2-9. Amplitudeandphaseoftheobserved(*)andmodelled(solidline)alongchanneltransport([U])forA)semi-diurnal(=1.5,=1.0)andB)diurnal(=2,=0.5)tideswithf=0. 42

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ASemi-Diurnal,=1.5,=1.0,f=0 BDiurnal,=3,=0.5,f=0 Figure2-10. AmplitudesofmodeledN(0),[U]andratioofN(0)=[U].Theamplitudeoftheobservedratiocompareswellwiththemodelratio,indimensionalunits(seeTable 2-1 ).Toconverttodimensionalunits(soastocomparewithresultsinTable 2-1 ),non-dimensionalratiosheremustbemultipliedby!0L0foreachsemi-diurnalanddiurnalfrequency.x=0.3representslocationofADCPmooringatPortOrange. 43

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ASemi-Diurnal BDiurnal Figure2-11. Modelled(solidline)andobserved(*)localphasedifferencebetweenvelocityandseasurfaceelevationatthethreeADCPlocationsalongtheinlandwaterway. 44

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CHAPTER3TIDALASYMMETRIESINSTRATIFICATIONOVERABATHYMETRICDEPRESSION 3.1Introduction Bathymetricvariationsinuencetidalandresidualowswithininletsandestuaries.Flowoversillsinstratiedenvironmentsisawell-studiedphenomenonwhereenergyistransferredfromthebarotropictidetotheinternaltide[e.g. FarmerandArmi 2006 ].Inahollow,owdynamicsaremodiedastheowmovesfromshallowtodeepareasandbacktoshallows. Hollowshavebeenfoundtomodifytidalowsduringebbandoodtides[ ParkandWang 1991 ]withvariabilityintheseowsoccurringasaresultofdensitygradients[ ChengandValle-Levinson 2009 ; Salas-MonrealandValle-Levinson 2009 ].IntheDyestuary,tidalowoverahollowdeceleratedduringbothphasesofthetidalcycle,inagreementwithBernoulli-typedynamicswhichwouldpredictaslowingoftheowoverthehollow[ DaviesandBrown 2007 ].However,inestuarieswithmoredevelopeddensitygradients,tidalowswerefoundtobecontrarytobasicBernoullidynamicsduringoodphases.IntheChesapeakeBay,owoverahollowwasfoundtoaccelerateduringoodtides[ Salas-MonrealandValle-Levinson 2009 ]duetoaddedeffectsfromhorizontaldensitygradients[ ChengandValle-Levinson 2009 ].IntheSetoInlandSea,owoverahollowwasconsistentwithresultsfromtheChesapeakeBaywithaccelerationsoverthehollowduringood(anddecelerationsduringebb)asaresultofalong-channelbaroclinicpressuregradients. Valle-LevinsonandGuo [ 2009 ]foundatransitionfromfrictionallydominatedtoadvectiondominatedregimesastheowmovedfromshallowertodeeperregionstothehollow. Previousobservationshaveconcentratedinregionswherethebathymetricdepressionsarerelativelywide(>1km)anddeep(>15m),withlargeexpansesthatvarybathymetricallylittleawayfromthehollows.Thisworkfocusesonanarrowinlet,ChacahuaInlet,onthePaciccoastofMexicothatcontainsanearlysymmetric 45

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hollowacrosstheentirewidthoftheinlet.Thevariationofstraticationandtheobservedtidalowalongandacrosstheinletwillbediscussedtodeterminehowthedynamicsvarywithperiodicinuencesofstratication. 3.2ChacahuaInlet ChacahuaLagoonNationalPark,locatedonthePacicCoastofMexico,iscomprisedoftwolagoons(ChacahuaandPastoria)connectedbyanarrowshallowchannel.Chacahualagoonhasasurfaceareaof6km2andameandepthof1.8m[ Mendozaetal. 2009 ]borderedbymangroves.ChacahuaInletisanarrow,dredgedinletwithawidthof120mandatotallengthof1300m(Figure 3-1 ),theonlypresentconnectiontotheoceanforthelagoons.Pastorialagoonhadaninletbutithasbeennaturallyclosed.Thebathymetryintheinletisveryshallowatthemouth(<2m),changingto15minabathymetricdepressionmid-waythroughtheinletandreturningto3mdepthinthelagoon.Thisinlethasbeensubjecttoclosureasaresultoflittoraldriftandinstability,andiscurrentlymaintainedbydredging(lastdredgingwasin2003).TheclosureoftheeasterninletofPastorialagoonandunstablenatureofChacahuaInletareacauseforecologicalconcerntothehealthofthelagoon[ Sanay 1997 ]. Thelagoonisfedwithfreshwater,primarilyfromtheVerdeRivertotheWest.Overrecentyears,inputoffreshwaterfromtheVerdeRiverhasdecreasedasaresultofdivertingwaterforlocalirrigation[ Contreras 1993 ; Rosetal. 2005 ].AlsoaffectingthefreshwaterinputarethetwodominantmeteorologicalseasonsinthesouthwestcoastofMexico:therainy(MaytoOctober)anddryseasons(JanuarytoApril; Mendozaetal. 2009 ). Watertemperatureinsidethelagoonvariesannuallybetween28and34.5C[ Pantaleon-Lopezetal. 2005 ],andsalinityvariesbetween31andaslowas1.3inOctober[ Contreras 1993 ; Rosetal. 2005 ].Duringamooringdeploymentin2009,temperaturevariedbetween21.3and32.8C.Hypersalineconditionswereobservedinsidethelagoon(salinityof43)whenChacahuainletwaspronetoseasonalclosures 46

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duringthedryseasons[ Mendozaetal. 2009 ].Howeversince2003,theinlethasremainedopen. Microtides[ Sanay 1997 ]withintheinletaremixedwithK1andM2inuencesof0.4mand0.1m,respectivelydrivingcurrentsupto0.6ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1intheshallowestregionsoftheinlet.Tidalinuencesareobservedinpressurerecordsthroughoutthelagoon,bothinPastoriaandChacahualagoons.Tidalsignalattenuateswithinthelagoons,indicativeofachokedlagoon[ KjerfveandKnoppers 1991 ]. 3.3FieldMeasurements SurveydatawerecollectedinChacahuaInletoverthetwometeorologicalseasonsinJulyandNovember,2009alongvecross-channeltransects(Transects1to5)andonealong-channeltransect(Transect6;Figure 3-1 ).Bothsurveysobtainedverticalprolesofvelocity,collectedusinga1200kHzRDIacousticDopplercurrentproler(ADCP)measuring0.25mbinsat1Hz(Mode1)duringtheJulysurveyandat1.25Hzwith4subpingsperensemble(Mode12)duringtheNovembersurvey.Datafromtherstsurveywerecollectedovertwoperiods,foratotalof29transectrepetitionsasdetailedinTable 3-1 andFigure 3-2 .ThesecondsurveyoccurredbetweenNovember18andNovember20,2009foratotalof34transectrepetitions.Bothsurveyscontainedgaps,andgiventheconsistencyofthemooredcurrentvelocitiesbetweendiurnalcycles(discussedinthenextsection),datacollectedovertheseconddiurnalcycleinJulyandoverthersteighthoursinNovemberweretransformedtotheappropriatepositioninthetidalcyclebysubtracting(July)andadding(November)atidalday(24hrs,48mins). Velocitydatawereseparatedintotransectrepetitionsandinterpolatedontosectionsofequallength,centeredaboutthedeepestpointofeachtransect,with5mand10mgridcellsforcrossandalong-channeltransects,respectively.Velocitiesalongeachtransectwererotatedtotheprincipalaxisofmaximumvariance[ EmeryandThomson 2004 ]givingalongandcross-channelvelocities.Positivealong-channelvelocities,u, 47

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Table3-1. SummaryofmeasurementsconductedinChacahuaInletin2009includingbothmooredandsurveyobservations.TimesareinGMTandT/Pindicatesubsurfacemeasurementsoftemperatureandpressure. StartEnd MooringsADP17:302009/11/1814:302009/11/21ChacahuaLagoon(T/P)2008/12/62009/11/21PastoriaLagoon(T/P)2008/12/62009/11/21Connection(T/P)2009/10/272009/11/21Survey1ADCP12:502009/7/307:332009/7/412:452009/7/414:212009/7/408:052009/7/515:152009/7/5CTD13:522009/7/306:192009/7/412:462009/7/413:062009/7/408:052009/7/514:222009/7/5Survey2ADCP21:092009/11/1810:032009/11/1914:162009/11/1915:192009/11/20CTD08:412009/11/1913:382009/11/20 weredirectedoutoftheinletalongitsaxisandpositivecross-channelvelocities,v,were90counter-clockwisefromu. Duringthesecondsurvey,a500kHzSonTek/YSIacousticDopplerproler(ADP)wasmooredinthehollow(14mdepth)overthreediurnaltidalcycles.Verticalprolesofvelocityweremeasuredat1mbinswithanaveragingintervalof1800s.Velocitieswererotatedtotheprincipalaxisofmaximumvariance(5.6counter-clockwise)suchthatpositivealong-channelvelocitiesweredirectedoutoftheinlet(similartothetowedvelocitydata). Verticalhydrographicprolesofpressure,conductivityandtemperaturewereobtainedusingaconductivity-temperature-depth(CTD)proler,SeabirdSBE19Plus,atasamplingrateof4Hz.Prolesweretakenalongthecentreaxisoftheinletatsixstationspriortothecross-channeltransectrepetitions(Figure 3-1 ).Densitywascalculatedusingtemperature,salinityandpressureandbothrawandbinned(0.5m)CTDdatawereused. 48

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3.3.1MeteorologicalData Longtermmeteorologicaldata(windspeed,precipitation,airtemperatureandpressure)aswellaswaterlevelvariationswerecollectedatvariouslocationswithinthelagoons(Figure 3-3 ).MeteorologicaldatafromChacahuaInletwereobtainedfromSeptember20,2008toJuly5,2009.Datafortheremainingmonthsof2009wereobtainedfromAcapulcoAirport,locatedat1646N,9945W,230kmtothenorthofChachuaInlettodetermineregionalatmosphericconditions. 3.3.2WaterLevelData Pressuresensors(HOBOs)weremooredintheinletaswellasinChachualagoon.TheHOBOsdeployedinChacahualagoonandinletweredeployedover11months(December62008untilNovember21,2009)samplingonceevery5minutes.Waterleveldatawerecorrectedbysubtractingtherecordedatmosphericpressure.Anannualcyclewasobservedinboththewaterlevelandwatertemperaturedataandwasremovedusingapolynomialtofthethirdorder.Oncetheannualcyclewasremoved,thetidalconstituentswerecalculatedusingt tideandthepredictedtidewascalculated[ Pawlowiczetal. 2002 ].LowfrequencyvariationsofmeteorologicalandwaterleveldatawasobtainedusingaLanczoslterwithahalf-powerpointof34hours.Thesedatawereusedtodeterminethetidalvariabilityintheinletdependingonvaryingseasonalparameters. 3.4EbbandFloodAsymmetry 3.4.1Along-channelStructure Inthehollow,theverticaldistributionofalong-channelvelocitiesfromthemooringwasasymmetricbetweenebbandoodtides(Figure 3-4 ).Largeoodtideswerecharacterizedbynegativevelocitiesthroughoutthewatercolumnwithasub-surfacemaximum.Smalloodtidesweresimilartolargeoods,withlesswelldenedowbelow6mandasub-surfacemaximumat5to6m.Ebbtideswherecharacterizedbypositivesurfacevelocitiesdownto6mwithaweakreturnowatdepth(below6m). 49

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Asaresultoftheasymmetryintheverticaldistributionofowsbetweenebbandood,depthaveragedvelocities(Figure 3-4 A)werelargerinmagnitude(0.2ms)]TJ /F4 7.97 Tf 6.58 0 Td[(1)duringoodtidethanduringebbtide(maximumof0.1ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1).SincethecurrentsmeasuredwiththeADPwereaveragedoverrelativelylongperiods(every1800s),thevelocitystructureoverthehollowduringdifferentperiodsofthetidalcyclewasbetterresolvedwithinthesurveydata. Thesurveyswerecharacterizedbymixedsemidiurnaltideswithbothalargeandsmallebbandood.Duringmaximumood,asthealong-channelowtravelledfromtheentranceoftheinletoverthehollow,depth-averagedvelocitiesdecreasedinmagnitude(Figures 3-5 Aand 3-6 A).Velocitiesthenincreasedasthedepthdecreasednearthelagoonentrance.ThiswasconsistentwithBernoullidynamicswhereowspeeddecreasesthroughanexpansion.Maximumvelocitieswereobservedattheseawardentrancetotheinletasowwasconstrictedthroughtheshallowentrance(2m;Figures 3-5 A,Band 3-6 A,B).Along-channelcurrentswereunidirectionalwithdepth,exceptoverthehollowandalongtheseawardentrancetotheinlet,intheNovembersurvey. Ebbcurrentswereweakerthanoodcurrentsandwerenotuniformwithdepth(Figures 3-5 Eand 3-6 E).Ebbowsexitedtheinletfromthelagoonwithasurfacemaximum.Overthehollow,aweakreturnowatdepthwasobservedbelow5to6m,consistentwiththemooredcurrentproles.Inbothsurveys,thedepthaveragedvelocitydecreasedoverthehollow(consistentwithBernoullidynamics)whilesurfacevelocitiesreachedtheirmaximumoverthehollow(Figures 3-5 Dand 3-6 D).Depth-averagedvelocitiesexitingtheinletwerestrongerthanoverthehollow,butwerehighlyvariable. 3.4.2Cross-channelStructure Cross-channeltransectsprovidedinformationonthelateralstructureoftheobservedalong-channelcurrentsduringmaximumoodandebbtides.InJuly,theowinthehollowwashorizontallyshearedduringoodwithinowfrom-40to75macrossthehollowwhilereturnow(outow)occurredbetween-75to-45m(Figure 3-7 50

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A).Duringebb,theowacrossthehollowwasthesamedirection.Thealong-channeltransectshowedaverticalshearwithweaklynegativeow(lessthan-0.1m/s)below8mdepth.Duringbothebbandoodtides,velocitiesintheebbandooddirectionwereconcentratedalongtherighthandside(lookinglandward)oftheinlet.LateralvelocitieswerevariableacrosstheinletwithstrongestlateralowsduringoodtowardtheSouthsideoftheinlet.Duringebb,lateralowsweredirectedtowardtheSouthshoreinthesurfaceows,andtowardtheNorthshoreatdepth. InNovember,oodvelocitieswerenotashorizontallyshearedasobservedinJuly(Figure 3-7 A).Outofthesixcross-channelsurveysduringmaximumood,onlytwocapturedasimilarhorizontalshear.Atmaximumood,along-channelcurrentswerecenteredonthenorthernsideofchannel.Duringebb,along-channelvelocitiesacrosstheinletwereconsistentwiththeobservationsfromJulywithaverticallyshearedow.LateralowsweredirectedtowardtheSouthernshoalduringoodandshowedasimilartwodirectionalstructureduringebb. Laterallyshearedowsoccurredmoreoftenduringtheoodtideofthedryseasonsurveys.Thismaybeattributedtothereducedstraticationthatallowedforrecirculationwithinthehollow.Byconservationofpotentialvorticity(),asawatercolumnmovesfromshallowtodeeperdepths,relativevorticity()mustincrease.However,asverticalstratication(@ @z)becomesimportant,theconservationofpotentialvorticityequationchangessuchthatforbaroclinicow =(f+) @ @z(3) asfrom Pedlosky [ 1987 ,eq.2.5.8]wherefistheCoriolisparameter.Therefore,as@ @zincreases,mustdecreasetokeepinvariant.InChacahuaInlet,duringthedryseasonwhenverticalstraticationdecreased,relativevorticityincreasedandbi-directionalowwasobservedacrossthehollowduringmaximumoodtide.During 51

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thewetseasonwhenverticalstraticationincreased,relativevorticitydecreasedandthelateralshearofudecreasedacrossthehollowduringood. Theasymmetricnatureofthealongandcross-channelowduringebbandoodtideslikelyoccurredasaresultofthebathymetryofthehollow.Interestingly,Bernoullidynamicsappliedtodepthaveragedowsduringbothebbandoodtide;however,surfacevelocitiesduringebbtideincreasedfromthelagoonoverthehollow.Todeterminehowtheasymmetriesintheowwerelinkedtohydrodynamics,thetermsofthemomentumequationwerecalculatedalongthechannel. 3.5Along-channelMomentum Previouswork[ ChengandValle-Levinson 2009 ; Salas-MonrealandValle-Levinson 2009 ; Valle-LevinsonandGuo 2009 ]demonstratedthatinlarger,lessboundedsystemsthaninChacahua,owtransitionedfromfrictionaldominancetoadvectivedominancefromtheshoalstothehollow.ToinvestigatewhetherChacahuaInletalsodemonstratedthistransitionofthedynamics,thedominanttermsinthedepth-integratedalong-channelmomentumequation @u @t+u@u @x+v@u @y+w@u @z=)]TJ /F3 11.955 Tf 9.3 0 Td[(g@ @x)]TJ /F3 11.955 Tf 15.26 8.08 Td[(g 0Z@ @xdz+sx 0H)]TJ /F6 11.955 Tf 16.54 8.08 Td[(bx 0H(3) wereinvestigated.Inequation 3 ,u,vandwaredepth-averagedalong-channel,cross-channelandverticalvelocities,x,yandzarethealong-channel,cross-channelandverticaldirections,tistime,gistheaccelerationduetogravity,isthesurfaceelevation,isthedensityofwater,hisdepthandsandbarethesurfaceandbottomstresses,respectively. Localacceleration,lateralandverticaladvectionterms,therst,thirdandfourthtermsinequation 3 ,werefoundtobe<110)]TJ /F4 7.97 Tf 6.58 0 Td[(5ms)]TJ /F4 7.97 Tf 6.59 0 Td[(2overthetidalcycle.Verticaladvectionwascalculatedinthehollowfromthemooreddatausingthescalingof MunchowandGarvine [ 1993 ]wherew@u @z=@ @tu H.Along-channeladvection,bottomfrictionandpressuregradientscouldbecalculatedwiththedata. 52

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3.5.1Along-channelAdvection Thedepth-averagedalong-channeladvection(u@u=@x),sometimesreferredtoastheBernoulliterm[e.g. OttandGarrett 1998 ],wasoforder10)]TJ /F4 7.97 Tf 6.59 0 Td[(4ms)]TJ /F4 7.97 Tf 6.59 0 Td[(2andlargerduringoodthanebb(Figure 3-8 ). DuringmaximumoodinbothJulyandNovembersurveys,thelargestpositivealong-channeladvectionoccurredontheseawardslopeofthehollow(atx=)]TJ /F5 11.955 Tf 9.3 0 Td[(300m)decreasinginmagnitudetowardthebottomofthehollow.Thiswasindicativeofowdecelerationinthealong-channeldirection.Onthelagoonwardslopeofthehollow(betweenx=0and300malongthechannel),negativealong-channeladvectionoccurredasaresultofowaccelerationasthewatercolumnbecameconstricteddownstreamofthehollow.Furtherdownstreamofthehollow,owdeceleratedagain(negativeu@u=@x)fromx=350to650malongthetransect.Thiswaslikelyaresultoftheowenteringthelagoonwhichwasnolongerconstrictedwithintheinletandslowedasaresultofthelargercross-sectionalarea. Duringmaximumebb,along-channeladvectiondiffersbetweenJulyandNovembersurveys.DuringNovember,along-channeladvectionwasconsistentduringbothebbtides(Figure 3-8 B).Negativealong-channeladvectionoccurredontheseawardslopeofthehollow(x=)]TJ /F5 11.955 Tf 9.3 0 Td[(300m),indicatingdecelerationasebbingowsexitedtheinlet.Smallpeaksinacceleration(positiveu@u=@x)occurredatx=400m,consistentwithowaccelerationuponentranceintothehollow. 3.5.2BottomFriction Overthetidalcycle,bottomfrictionvariedacrossandalongtheaxisoftheinlet(Figure 3-9 ).Bottomstressesinthealong-channeldirectionwerecalculatedusingaquadraticfrictionapproximation: bx=CDubjvbj(3) whereCDisaconstantbottomdragcoefcient(0.0025),ubisthealong-channelbottomvelocityandjvbjisthemagnitudeofthebottomvelocity.Asexpected,frictional 53

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effects,bx=H,werestrongerontheshallows,seawardandlagoonwardofthehollowthaninthehollow,itself.Asthevelocityreversedatthebottomofthehollowduringebb,negative(directedintothechannel)bottomstressesoccurredinthehollowovernearlytheentiretidalcycle.Sincethefrictionaltermisinverselyrelatedtodepth,shallowerregionscorrespondtohigherfrictionalaccelerations.However,awayfromtheentrancetotheinlet,bottomstresswasrarelylargerthan110)]TJ /F4 7.97 Tf 6.59 0 Td[(4ms)]TJ /F4 7.97 Tf 6.59 0 Td[(2.Asthebottomstressesweresmallandalong-channelvelocitiesincreasedontheseawardshoal(insteadofdecreasingasaresultoffriction),bottomfrictionwasdeemednotimportanttolowestordertidaldynamics.However,althoughbottomfrictionwasnotimportanttothedynamicsofthissystem,interfacialfrictionmaybelargeinducingmixing,asaresultofwatercolumninstability.Thistopicisinvestigatedinthenextsection. 3.5.3PressureGradients 3.5.3.1Barotropicpressuregradient Thebarotropicpressuregradient,g@=@x,wascalculatedasthedifferenceinwatersurfaceelevationbetweenthemooredcurrentmeterinthehollowandthepressuresensorlocatedintheChacahuaLagoon(Figure 3-1 ).Thebarotropicpressuregradientwas180outofphasewiththesurfacevelocityasmeasuredfromthehollow,withpeaksinthepressuregradientoccurringatthepeakofebborood(Figure 3-10 ).Atthesepeaks,thebarotropicpressuregradientwaslargerthan110)]TJ /F4 7.97 Tf 6.58 0 Td[(4withthelargestbarotropicpressuregradientsoccurringduringthepeakofood(upto210)]TJ /F4 7.97 Tf 6.59 0 Td[(4ms)]TJ /F4 7.97 Tf 6.59 0 Td[(2). Thephaserelationshipbetweenthepressuregradientandvelocitywerelikelyduetothechokednatureofthelagoon[ KjerfveandKnoppers 1991 ].Notonlywerethetidalamplitudesdampedbetweentheoceanandthelagoon,butatmaximumtidalcurrents,thelargestvolumeofwaterattemptedtoenter(orexit)theinlet.However,duetothenarrowinletwidth(120m),wateraccumulatedoneithersideoftheinlet(lagoon-sideduringebbandocean-sideduringood)whileowattemptedtoenterorexittheinlet.Thisresultedinanelevatedbarotropicpressuregradientatmaximumtidalcurrents. 54

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3.5.3.2Baroclinicpressuregradient VerticaldensityvariationsweregreaterduringtheNovembersurveythaninJuly,whichwasattributedtoprecipitationthatoccurredpriortothesurveyinNovember(Figure 3-3 ).DuringNovember,verticaltop-to-bottomdensitydifferenceswereaslargeas4tduringtherstebbtide.Duringthesecondoodtide,theinletwasnotcompletelyusheduntiltheproceedingstrongoodtide(Figure 3-4 C). Thedepth-averagedalong-channelbaroclinicpressuregradient,responsibleformodicationstothealong-channeldynamics,variedbetweenCTDstations(Figure 3-11 ).Weakstraticationduringoodresultedinweakbaroclinicpressuregradientsthatremainedbelow110)]TJ /F4 7.97 Tf 6.58 0 Td[(4ms)]TJ /F4 7.97 Tf 6.58 0 Td[(2duringJulyandNovembersurveys.Thelessstratiedsurveyhadanexpectedloweralong-channelbaroclinicpressuregradient.Duringbothsurveys,thebaroclinicpressuregradientwaspositive,withforcingdirectedoutoftheinletatsurfaceandintotheinletatdepth.ThisoccurredexceptbetweenStations2and3wherethegradientwasnegative.BetweenStations3and4,asemidiurnalcyclewasobservedandthebaroclinicpressuregradientincreasedabove110)]TJ /F4 7.97 Tf 6.59 0 Td[(4ms)]TJ /F4 7.97 Tf 6.59 0 Td[(2duringebb. DuringthelargerstebbinNovember,thebaroclinicpressuregradientdecreasedattheendofebb,andasecondpeakinthebaroclinicpressuregradientoccurredduringthebeginningofoodtide.Apersistentelevatedbaroclinicpressuregradientwasnotedduringthesecondebb,persistingintothesecondoodtide.FromthesamesurveybetweenStations2and3,thebaroclinicpressuregradientincreasednegativelyatthebeginningofoodanddidnotdecreasetopre-ebbvaluesuntiltheendofood.Thisindicatedthatadversebaroclinicpressuregradientsdevelopedoneithersideofthehollow.ThisreversingbaroclinicpressuregradientwillbeinvestigatedinSection 3.6 3.5.4BernoulliEquation Asaresultofthetermscalculatedinthemomentumbalanceinthealong-channeldirection,theimportantdynamictermsreducedthealong-channelmomentumequation 55

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to u@u @x=)]TJ /F3 11.955 Tf 9.3 0 Td[(g@ @x)]TJ /F3 11.955 Tf 15.25 8.08 Td[(g 0Z@ @xdz(3) whichwassimilartotheBernoulliequationthatincorporatesthealong-channelbaroclinicpressuregradient[ ChengandValle-Levinson 2009 ].Theasymmetryintidalvelocitiesobservedhere,however,wasnotinagreementwithobservationsof Salas-MonrealandValle-Levinson [ 2009 ]and ChengandValle-Levinson [ 2009 ],althoughthedynamictermsweresimilar.Thedifferencesintidalvelocitiesbetweenthesystemslikelyoccurredasaresultofdifferencesinstratication. Intheworkof ChengandValle-Levinson [ 2009 ],whenthebaroclinicpressuregradientwasnegative(fresherwaterdownstreamrelativetotheoodow),thistermactedtoincreasealongchannelvelocityinthehollow.Conversely,duringebbswhenthebaroclinicpressuregradientwaspositive(denserwaterdownstreamrelativetoebb),thistermactedtosuppressthealongchannelvelocityinconjunctionwiththetypicalBernoullieffect.Inpreviousworks[ ChengandValle-Levinson 2009 ; Salas-MonrealandValle-Levinson 2009 ; Valle-LevinsonandGuo 2009 ],thebaroclinicpressuregradientactedinthesamedirectionalongthelengthofthehollow,acceleratingowduringoodanddecreasingowduringebb. InChacahuaInlet,thebaroclinicpressuregradienthadopposingsignsoneithersideofthehollowduringtheentiretidalcycle(Figure 3-11 ).Therefore,thedecreaseintidalvelocitiesduringoodlikelyoccurredasaresultofthedifferenceinthebaroclinicpressuregradient.InNovemberduringtherstood,thebaroclinicpressuregradienthadopposingdirectionsoneithersideofthehollow(Figure 3-11 D).AsthebaroclinicpressuregradientbetweenStations3and4wasnegative,itopposedtheincomingoodow,impedingaccelerationinthehollowdespiteapositivebaroclinicpressuregradientbetweenStations3and4.ThisactedinconjunctionwiththeBernoullieffectofslowingthroughanexpansion. 56

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Duringebb,depthaveragedtidalvelocitiesalsodecreaseduponentrancetothehollow.AsthebaroclinicpressuregradientwaspositivebetweenStations4and5aswellasbetweenStations3and4,thistermactedinconjunctionwiththeBernoullieffect,reducingthevelocityinthehollow.However,betweenStations2and3,thebaroclinictermwasnegativewhichwouldacttoincreasethevelocityoftheebbingow.Astheowwasconstrictedontheseawardslope,theaccelerationsproducedbythenegativebaroclinicpressuregradientlikelyincreasedthereturnowatdepth. 3.6MechanismsCausingDensityVariabilityandStratication 3.6.1PotentialEnergyAnomaly Atraditionalmethodofdeterminingstraticationisthroughthepotentialenergyanomaly[ SimpsonandBowers 1981 ].Thepotentialenergyanomaly,(Jm3),isanindexofoverallwatercolumnstabilityrepresentingtheamountofworkpervolumerequiredforcompleteverticalmixing.Todetermine,quantitatively,theenergyrequiredtomixthewatercolumninNovember2009,wascalculatedfromthedensityprolesfollowing SimpsonandBowers [ 1981 ]where =g HZ0)]TJ /F8 7.97 Tf 6.58 0 Td[(h()]TJ /F6 11.955 Tf 11.96 0 Td[()zdz=g HZ0)]TJ /F8 7.97 Tf 6.59 0 Td[(h~zdz(3) and =1 HZ0)]TJ /F8 7.97 Tf 6.59 0 Td[(hdz(3) where~isthedensityanomalywithrespecttothedepth-meanandisthedepthaverageddensity. AtStations2and4,oneithersideofthehollow,increasedduringebb,reachingamaximumduringthemiddleofebbforbothsemidiurnaltidalcycles(Figure 3-12 ).Thepotentialenergyanomalythendecreasedattheendofebb,remaininglowduringoodasthewatercolumnbecamewell-mixed.Inthehollow,followedasimilarpatternwithapeakduringthemiddleofebb.Howeveritwasfollowedbyasecondlargerpeakafterthebeginningofoodinbothsemidiurnalsignals.Themechanismscausingthe 57

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decreaseinstraticationattheendofebbandpeakinstraticationduringearlyoodwereinvestigatedthroughobservationsofdensityalongthechannel. 3.6.2DensityAlongtheChannel Along-channelcontoursofdensitywereplottedfromearlyebbtomid-oodfromNovembertodeterminethevariabilityalongthechannelaswellasthemechanismcausingthechangeinsignofthebaroclinicpressuregradientontheseawardsideofthehollow(Figure 3-13 ). 3.6.2.1Largeebbandmixing Atearlyebb(1inFigure 3-13 ),isopycnalsslopedupwardsfromthelagoontotheocean.Inthehollow,thewatercolumnwaswellmixedbelowthesurface.Atmaximumebb(2inFigure 3-13 ),thetraditionaldensity-drivenslopingisopycnalswerenolongerobservedthroughoutthewatercolumn.Inthesurfacelayers,isopycnalsmaintainedtheirslope,uptowardtheseawardsideoftheinlet.However,inthehollow(x=0),denserwaterdomedinthemiddleofthechannelwithisopycnalsslopingdownontheseawardsideofthehollow.Theoppositeslopeoftheisopycnalsontheseawardsideofthehollowwaslikelyproducedbyenhancedmixingontheseawardslope.Assurfaceoutowreachedtheshallowsillontheseawardsideofthehollow,excessowthatcouldnotexittheinletwasdrivendowntheslope,mixingwithwaterofhigherdensity.Thisactedtoreducethestraticationofthewatercolumnontheseawardsill(atStation2)comparedwiththewatercolumnoverthedeepestpartofthehollow.Astidalvelocitiesinthehollowduringebbwereverticallyshearedwithreturnowinthebottom,thismechanismwaslikelyaresultofinterfacialmixingfromshearinstabilities. Aftermaximumebb(3inFigure 3-13 ),isopycnalsslopeduptoStation4wheretheybegantoslopedown.ThisindicatedfurtherthickeningofthepycnoclineduringebbseawardofStation4asaresultofcontinuousmixingontheseawardslopethatdecreasedthestraticationinthehollow. 58

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Althoughmixingontheseawardslopewaslikelyresponsibleforaportionofthemixinginthehollow,theshearedvelocitystructureobservedduringebbmayhavealsocontributedtomixing.Therelationshipbetweensheargeneratedinstabilitieswillbediscussedinsection 3.6.3 3.6.2.2Smalloodandlaterallyshearedalong-channelvelocity Atthebeginningofood(4inFigure 3-13 ),isopycnalsslopeddowntowardtheseawardsideoftheinletwithanisolatedregionoflowdensitywateratthesurface,overthehollow.Thefresherwaterinthesurfaceoverthehollowwaslikelycausedbyanimpedanceofalongchannelowasaresultofthereversedbaroclinicpressuregradientinthehollowaswellaslaterallyshearedalong-channelvelocity.AcrossTransect3,thealong-channelvelocityatthesurface(between1to3mdepth)waslaterallyshearedwithstrongervelocitiesonthenorthernsideoftheinletontheshoalthanoverthehollow(Figure 3-14 B). Infact,duringJulywhenstraticationwasreduced,uacrossTransect3wasbi-directionalformostofthemaximumebbtide.Increasedstraticationmayhavehinderedthedevelopmentofthebi-directionalalongchannelowduringtheNovembersurvey,however,alateralshearwasstillobserved. AsaresultofthelateralshearinuacrossTransect3,denseoceanicwaterenteredacrossTransect3withstrongestvelocitiesalongthenorthernshoal.Thislikelyactedtoreducetheushingeffectoftheoodtideinthehollow,trappingfresherwaterinthehollow.Denseoceanicwaterthatenteredthehollowlikelysank,mixingwiththefresherwaterinsideofthehollow.Fasterowalongthenorthernshoaladjacenttothehollowtravelledtowardthelagoon(toStation4)withlittleexchangewithwaterinthehollow.Furtherintoood(5inFigure 3-13 ),watercolumnstraticationreducedwhiledepth-averageddensityincreasedthroughtheinputofdenseroceanicwaterintothehollow.Asin4(Figure 3-13 ),thebaroclinicpressuregradient(andisopycnalslopes)wasopposingoneithersideofthehollow. 59

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Atthebeginningofthenextebb(6inFigure 3-13 ),waterwaswell-mixedinsidethehollowbelow5m,abovewhichathinpycnoclinewasobserved.Althoughweakoodalteredstratication,thewatercolumnwasnotcompletelyhomogenizeduntilthenextlargeood.Theweakoodhadshorterdurationthanthelargeood,andasaresult,thedensityvariabilityduringthelargeoodfollowedasimilarpatterntothesmallood,exceptwithfullwatercolumnmixingatthesecondhalfofthelargeood. Therefore,mixingalongtheseawardslopeofthehollowwasanimportantmechanismfordestratifyingthewatercolumntowardtheendofebb.Duringood,lowdensitywaterwasobservedinthesurfaceofthehollowasaresultoflaterallyshearedalong-channelows,areversedbaroclinicpressuregradientinthehollowandupperwatercolumnmixinginthehollow.Duringthewetseason,along-channelgradientsindensitywerefoundtobeimportanttothealong-channeldynamics.Duringthedryseason,theexpectedbalancewassimplybetweenthebarotropicpressuregradientandthealong-channeladvectiveaccelerations. 3.6.3TidalVelocityandWaterColumnStability Intheprevioussection,increasedmixingalongtheseawardslopeofthehollowwasattributedtothereductionofthealong-channelbaroclinicpressuregradientaftermaximumebb.Verticalshearofvelocityinthehollowmayhavealsocontributedtointerfacialmixing.Therefore,watercolumnstabilitywasinvestigatedusingthevelocityanddensityprolesfromeithersideofthehollowatbothmaximumebbandoodtidesfrombothsurveys.Includedintheplotsofvelocityanddensity,thegradientRichardsonnumber(Ri)wascalculatedthroughthewatercolumn.Riisameasureofwatercolumnstabilityandisaratioofthestraticationthatactstostabilizethewatercolumnandthevelocityshearwhichactstodestabilizethewatercolumn,denedby Ri=N2 (@u @z)2(3) 60

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Thebuoyancyfrequency(N2)isthefrequencythataverticallydisplacedparcelwilloscillatedenedby N2=)]TJ /F3 11.955 Tf 10.49 8.09 Td[(g z(3) Typically,ifRi<1=4,thewatercolumnisunstableandstraticationisnotstrongenoughtocounteracttheoverturningandmixingasaresultoftheshear[ GeyerandSmith 1987 ; Miles 1961 ].Incaseswhereincreasedmixingoccursasaresultofinternalwaves,alargerRichardsonnumberisused[ NepfandGeyer 1996 ].However,forthiswork,thestandardRiC<1=4isusedasalowerestimateforwatercolumnstability. Prolesofdensity,velocityandregionswhereRi<1=4wereplottedfromCTDstations2,3and4attheendoflargeebbandmaximumood(Figures 3-15 and 3-16 ).Velocityproleswerecalculatedusing30secondaveragesfromthesurveydata.Velocityanddensityprolesweresmoothedtoimprovethestatisticsinthecalculationsofbuoyancyfrequencyandvelocityshearwhilemaintainingthelargerscalevariabilityindensityandvelocityproles. 3.6.3.1Prolesandstability:dryseason(July,2009) Duringebb,velocityproleschangefromweakshearatthesurface(downto3m)upstreamofthehollow(Station4)tointensiedsheardownstreamofthehollow(Station2).Upstreamofthehollow,Riwaslessthan1=4atthesurfaceaconsequenceofturbulentmixing(Figure 3-15 A).Below4m,densityincreasedandstraticationwassufcienttooverwhelmsheardrivenmixing.Inthehollow,outowoccurredinathick,shearedsurfacelayer(downto7m;Figure 3-15 B).Velocityreversedbelow7mwithmaximumvelocityat11m.Thedensityproleincreasedlinearlyfromthesurfaceto8m,coincidentwiththezerocrossingofthevelocityprole.Below10m,thewatercolumnincreasedtoanear-constantdensity.Inthisregion,Ri<1=4andstraticationwaslikelyoverwhelmedbytheshear.Increasedmixinginthebottomofthehollowresultedinconstantdensitybelow10m. 61

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Downstreamofthehollow,Richardsonnumberindicatedanunstableregionatthebottomofthewatercolumn(Figure 3-15 C).Theseresultswereconsistentwithenhancedmixingoccurringonthedownstreamrimofthehollowduringebb.Mixinginthisregionactedtoreducethewatercolumnstratication.Astheseproleswerelessstratied(dryseason),thewatercolumnwasmoreeasilyoverturnedthanduringthewetseason.Duringood,thewatercolumnatStations2to4hadnear-completemixingatallstations(Figure 3-15 D-F).Ateachstation,thedensityprolewasconstantwithdepthwhilethevelocityprolevariedbetweenstations.Therefore,mixinglikelyoccurredeasilyduringood. 3.6.3.2Prolesandstability:wetseason(November,2009) November'sebbtide,upstreamofthehollowwascharacterizedbyastablewatercolumnasRi>1=4atalldepths(Figure 3-16 A).Velocitywasshearedwithlargestsurfaceoutow(27cms)]TJ /F4 7.97 Tf 6.58 0 Td[(1)andclosetozerovelocityatthebottom(-3cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1).Thepycnoclinewasthick,occurringbetween2to4.5m. OutowinthehollowoccurredinathinnerlayerthaninJuly(fromthesurfacedownto5mdepth;Figure 3-16 B).Flowreversedbelowthesurfaceintwopulsesofnegativelydirectedow.Therstlayerwasbetween5and10mandbelow10mowincreasedagain,inthenegativedirection.Maximumnegativeowwasobservedat8m.Thewatercolumnwasunstable(Ri<1=4)at5.5,9.3and11.4m,coincidingwitheachzerocrossingofthevelocityprole. Downstreamofthehollow,thedensityprolehadashallowpycnocline(2m).Althoughbelow2mthewatercolumnincreasedby0.3t,theproleoverturned(lessdensewaterovermoredense)at2.7and3.7m,coincidentwiththeregionswhereRi<1=4.Thisindicatedwatercolumninstability(Ri<0)andenhancedthepossibilityofmixingasaresultofsheargeneratedinstabilities( Tedfordetal. 2009 ;Figure 3-16 C).Althoughthewatercolumnwasstableonexitfromthelagoonasoccursduring 62

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ebbintypicalestuaries,oncetheowencounteredthehollowandsubsequentshallowdownstreamrim,thewatercolumnbecameunstablebelowthesurfaceandmixed. FloodtideswerecharacterizedbyRi<1=4fornearlytheentirewatercolumnupstreamanddownstreamofthehollow(Figure 3-16 D,F).Inthehollow,theupperwatercolumnwasmorestable(above5.5m)buttherewerepatchesofRi<1=4underneath.Asthedensityprolewasconstantwithdepthateachofthesestationsduringood,mixingoccurredmoreeasilydespitethesmallvelocityshear. Duringbothdryandwetseasons,ebbtideswerecharacterizedbyaverticalshearinvelocitydownstreamofthehollowthatwascapableofovercomingthestabilityinducedbystratication,atdepth.ThislikelyresultedinenhancedmixingonthedownstreamrimofthehollowatStation2. 3.6.3.3Transitionfromweakebbtolargeood Asmentionedpreviously,thetransitionfromebbtooodwascharacterizedbystrongeralong-channelowonthenorthsideoftheinlet,actingtotrapfresherwateroverthehollow.ThetransportofdensewaterintothehollowwasinvestigatedusingthevelocityanddensityprolesinconjunctionwithmeasuredbackscatterintensityfromtheADCPonthetransitionfromweakebbtostrongoodinNovember2009.ProlesofdensityfromStations3and4weretaken40minutespriortotheprolefromStation2aswellasmeasurementsofthevelocityandbackscatter.ThesetwosetsofobservationswerecombinedinFigure 3-17 .Backscatterintensityincreasedsignicantlyduringthisportionofthetidalcycle,comparedwithallotherNovembersurveytransectsandthecombinationofthesedataledtoafortuitoussetoftransitionalobservations. Backscatterintensityactedasproxyforvelocitymagnitude.Atthebottomofthehollow,velocity(andbackscatter)waslow(Figure 3-17 D).Comparingdensityprolesfromthistimetothosetakenduringebb,densityinthebottomofthehollowremainedconstant(Figures 3-16 Band 3-17 B).Therefore,therewaslittlemixingandmovementofwateratthebottomofthehollow.FromStation2to3,thedepthofthevelocity 63

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maximumincreasedindepth.Attheentrancetothehollow(x=)]TJ /F5 11.955 Tf 9.3 0 Td[(190),thevelocitywasshearedwithasurfacemaximumwhileatx=)]TJ /F5 11.955 Tf 9.3 0 Td[(100m,maximumtidalvelocitieswereatthebottom.Overthehollow,maximumvelocitieswerebetween4and5m(Figure 3-17 D).ThepycnoclinefromStation3wasthick(surfaceto5m)andwaslikelyaresultofthedenseroceanicwatermixinguponentrancetothehollow.Thewatercolumnwasstable(Ri>1=4)inthehollowexceptatthesurface. Therefore,incomingdensewatersank(downto4to5m)andmixedwithsurroundingwateruponentranceintothehollow.Wateratthebottomofthehollowdidnotinteractwiththeuppermixinglayers,maintainingconstantdensity.Asthemajorityofthewaterwasfoundtofollowthenorthernshoal,thewatercolumninthehollowbecametrapped.Mixingintheupperwatercolumnoccurredbetweensurroundingwateranddenseroceanicwater.Thepycnoclinethickenedcomparedwiththethinnerpycnoclinedownstreamofthehollow(Station4).Notonlywasthelaterallyshearedalong-channelvelocityimportantingeneratingtheopposingbaroclinicpressuregradientsbetweenStations2to4,butmixingisolatedtotheupperlayerofthehollowfurtherincreasedtheopposingbaroclinicpressuregradient. 3.7Conclusions Effectsontidalowsoverahollowwereinvestigatedusingobservationsofcurrentvelocityproles,verticalprolesofdensityandlongtermpressurerecords.Overthewetanddryseasons,tidalvelocitieswereasymmetricbetweenebbandoodtidesbutfollowedBernoullidynamicswithdecreaseddepthaveragedvelocitiesoverthebathymetricdepression.Thealong-channelmomentumincludedbarotropicandbaroclinicpressuregradientsaswellasalong-channeladvection.Thebaroclinicpressuregradientwaspositivealongthechannelexceptontheseawardslopeofthehollow,wherethebaroclinicpressuregradientwasnegativeforbothwetanddryseasonsurveys.Thiswasattributedtoenhancedmixingontheseawardslopeofthehollow.Along-channeloodtidevelocitieswerecharacterizedbyamid-depthmaximumand 64

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unidirectionalowoverthehollow.Acrossthehollow,laterallyshearedalong-channelowwasobserved,withgreatershearduringthedryseasonasaresultofdecreasedverticalstratication.Ebbvelocitieswereverticallyshearedwithaweakreturnowatdepthinthehollow. Enhancedmixing,asaresultofthehollow,causedbothdecreasedstraticationaftermaximumebb,andincreasedstraticationatthebeginningofood.Stratication,quantiedbythepotentialenergyanomaly,showedpeaksatmid-ebbandinearlyoodforbothsemidiurnalsignals.Duringebb,owwastrappedattheseawardsillofthehollowwhichthenmixed.Thisincreasedthethicknessofthepycnoclineontheseawardsideofthehollow.Attheendofebb,thepycnoclinewasdeeperinthehollowasaresultoftheincreasedmixingonthedownstreamrimofthehollow.Atthebeginningofood,denseroceanicwaterenteredtheinlet,withpreferencetothenorthernsideoftheinletduringbothwetanddryseasons.Thelateralshearinthealong-channelowacrossthehollowactedtoisolatethewatercolumninthehollow.Duringearlyood,densewaterenteredthehollow,descendingtomid-depth(4to5m),energeticallymixingwithsurroundingwater.Densityintheupperlayerofthehollowincreasedhowever,bottomwaterinthehollowwasnotdisturbedandmaintainedaconstantdensity.Thismechanismincreasedstraticationcausingthesecondpeakinthepotentialenergyanomalyduringood. 65

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Figure3-1. ChacahuaInlet,Mexico.Bathymetryofthehollowwithintheinletisshownwithgreycontours.Sixhydrographicproles(o)weretakenalongtheaxisoftheinletaswellasvecross-channelandonealong-channeltransectsofcurrentproles.Transect3waslocatedacrossthedeepestpointinthechannel.Temperatureandpressuresensorsweremooredinsideoftheinletandinthelagoon(blackdiamonds)overayearwhileacurrentmeterwasmooredatStation3forthreetidalcyclesinNovember2009. 66

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Figure3-2. Predictedtidalsignal(solidline)duringsurveysamplinginA)JulyandB)November,2009.ADCPandCTDdatafromthesecondportionoftheJulysurveywereaddedtotheendoftherstsetofdata(x's).ADCPdatafromthebeginningoftheNovembersurveywereaddedmid-waythroughthesecondtidalcycle(x's). 67

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Figure3-3. MeteorologicaldatafromChacahuaInlet,2009:A)measuredandlowpasslteredwaterlevel(m),B)lowpasslteredairandwatertemperature(C),C)measuredandlowpasslteredairpressure(kPa),D)precipitation(cm)andE)lowpasslteredwindspeed(m/s).MeteorolgoicaldatafromtheAcapulcoAirportMeteorologicalstationareplottedinthinlinesinpanelsBthroughE.LowpassltereddataareobtainedfromaLanczoslterwithahalfpowerpointof34hours. 68

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Figure3-4. Observationsatthehollow(Station3):A)Surfaceelevation(m)anddepth-averagedvelocity(m/s),B)verticalprolesofalong-channelvelocity(m/s)asmeasuredfromthecurrentmetermooringandC)prolesofdensityoverthesamplingperiod. 69

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Figure3-5. July2009:A,D)depthaveraged(solid)andsurface(dashed)along-channelvelocities(m/s);B,E)along-channelvelocity(vectorsandcontours;m/s);C,F)surfacevelocity(m/s)andtransectrepitionsofthetidalcyclethataveragingistakendenotedbyopencircles.Theoceanisontherightandthelagoonentranceisontheleft.Positivealong-channelvelocitiesaredirectedtowardtheocean. 70

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Figure3-6. November2009:A,D)depthaveraged(solid)andsurface(dashed)along-channelvelocities(m/s);B,E)along-channelvelocity(vectorsandcontours;m/s);C,F)surfacevelocity(m/s)andtransectrepitionsofthetidalcyclethataveragingistakendenotedbyopencircles.Theoceanisontherightandthelagoonentranceisontheleft.Positivealong-channelvelocitiesaredirectedtowardtheocean. 71

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AJuly BNovember Figure3-7. Transectacrossthehollow(Transect3)withalong-channelvelocitycontoursduringmaximumoodandebbtides(m/s)withlateralvelocities(vectors)forA)JulyandB)November2009surveys. 72

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Figure3-8. Depthaveragedadvectiveterm(u@u=@x;ms)]TJ /F4 7.97 Tf 6.58 0 Td[(2)alongtheaxisofthechannelfromA)JulyandB)Novembersurveys.Along-channelbathymetryisshownontheleftandthedepthaveragedvelocity(u)isshownonthetopofeachcontour. 73

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Figure3-9. Contoursofbottomstress(b=H;ms)]TJ /F4 7.97 Tf 6.59 0 Td[(2)fromthealong-channeltransectovertimeduringA)JulyandB)November2009surveys.Along-channelbathymetryisshownontheleftandthedepthaveragedvelocity(u)isshownonthetopofeachcontour. 74

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Figure3-10. Barotropicpressuregradient(ms)]TJ /F4 7.97 Tf 6.59 0 Td[(2)ascalculatedbetweenthemooredcurrentmeteratStation3andapressuresensorlocatedwithinChacahuaLagoon(solidblackline)andthesmoothedsurfacevelocity(ms)]TJ /F4 7.97 Tf 6.58 0 Td[(1)fromthemooredcurrentmeterinthehollow(dashedgreyline).Positivevelocitiesindicateebbwhilenegativeindicateood. 75

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Figure3-11. Depthaveragedvelocity(ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)andalong-channelbaroclinicpressuregradient(ms)]TJ /F4 7.97 Tf 6.59 0 Td[(2)betweenCTDstations2-3,3-4and4-5forA-B)JulyandC-D)November2009surveys. 76

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Figure3-12. Potentialenergyanomaly()ascalculatedfromStation2to4fromNovember2009.Station3aretheprolesfromthehollowandebbtidesaredenotedbythegreyshadedregions. 77

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Figure3-13. Densityvariability(tinkgm)]TJ /F4 7.97 Tf 6.58 0 Td[(3)alongtheinletfromtheNovembersurveys.Theorientationofthealong-channelcontoursissuchthattheoceanisontherightandlagoonisontheleft.Thenumbersineachpanelcorrespondtothepositionduringthetidalcycleasindicatedfromthewaterlevel()anddepthaveragedvelocity(U)fromthemooredcurrentmeter.Positivecurrentvelocitiesareebbingwhilenegativeareooding. 78

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Figure3-14. Surfacevelocity(1to3m)acrosstransect2to4duringA-C)JulyandD-F)November2009surveysoverthediurnaltidalcycle.Dashedlinesrepresentthetimesatwhichthetransectrepetitionoccurred. 79

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Figure3-15. Prolesofdensity(kgm)]TJ /F4 7.97 Tf 6.59 0 Td[(3;thicklines)andvelocity(cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1;thinlines)fromCTDStations4,3and2duringebbandoodtidesinJuly2009.Ebbprolesarefrom18:30to18:35,3July2009andoodprolesarefrom12:51to12:57,4July2009.RegionswheretheRichardsonnumber(Ri)islessthan0.25areshadedgrey. 80

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Figure3-16. Prolesofdensity(kgm)]TJ /F4 7.97 Tf 6.59 0 Td[(3;thicklines)andvelocity(cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1;thinlines)fromCTDStations4,3and2duringebbandoodtidesinNovember2009.Ebbprolesarefrom18:19to18:32,19November2009andoodprolesarefrom11:29to11:44,20November2009.RegionswheretheRichardsonnumber(Ri)islessthan0.25areshadedgrey.Duringood,mostofthewatercolumnisunstableonbothsidesofthehollow,whileduringebb,thewatercolumnisstableupstreamofthehole(Station4)andunstableattwotothreedepthsinthehollowandonthedownstreamrim(Stations3and2). 81

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Figure3-17. (A-C)Prolesofdensity(kgm)]TJ /F4 7.97 Tf 6.59 0 Td[(3;thicklines)andvelocity(cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1;thinlines)fromCTDStations4,3and2atthetransitiontooodtide.Prolesweretakenat8:01,8:08and8:48,20November2009forStations4,3and2,respectively.RegionswheretheRichardsonnumber(Ri)islessthan0.25areshadedgrey.Duringthetransitiontoood,thewatercolumnisunstableatthesurfaceandat4mdepthinthehollow(Station3)anddownstream(Station4).D)Contourofbackscatterandvectors(uandw;black)ofvelocityfromtheADCPmeasuredfrom8:46to8:48,20November2009fromthehollow(x=0)toStation2(x=200).Anintense(78dB)layerfromthebackscatteroverthehollowat4mdepthcorrespondstotheregionofmaximumvelocity. 82

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CHAPTER4TRANSVERSESTRUCTUREOFSUBTIDALFLOWINAWEAKLYSTRATIFIEDSUBTROPICALTIDALINLET 4.1Introduction Subtropicalinletsareuniqueinthattheyarefoundinregionswherethereislittletononetprecipitation;thedynamicsarethereforefreefromthedensity-drivenowcommontotemperateestuaries1.Subtropicalinletshaveonlysporadicfreshwaterinuenceandtheresidualowistypicallydrivenbytidesandwinds[ Valle-Levinsonetal. 2009 ],andmodiedbybathymetry[ Blantonetal. 2003 ; KimandVoulgaris 2008 ; Kjerfve 1978 ; Lietal. 2008 ].Subtropicalestuariesareidealsitesforcomparingobservationsonthespatialstructureoftidalresidualowtotheoreticalresultsasthereislittletonoinuencefromalong-channeldensitygradients. Frequently,naturalbasinsarestronglyaffectedbychannelcurvatureinbothbathymetryandmorphology.Centrifugalaccelerationsproducedbycurvature,forceatransverseowawayfromthechannelbendsatthesurfaceandtowardthechannelbendsatdepth[ KalkwijkandBooij 1986 ].Bydenition,thedepth-averagedtransverseowiszeroeverywherewithintheinlet,andthetransverseequationofmotioninstratiedowreducesto[ Geyer 1993 ; KalkwijkandBooij 1986 ; LacyandMonismith 2001 ; SeimandGregg 1997 ] @un @t+us@un @s)]TJ /F3 11.955 Tf 13.15 8.09 Td[(u2s)]TJ ET q .478 w 145.14 -441.41 m 156.84 -441.41 l S Q BT /F3 11.955 Tf 145.14 -451.77 Td[(u2s R=)]TJ /F3 11.955 Tf 10.5 8.09 Td[(g Zz0@ @ndz0+g o@ @nh+@ @z(Az@un @z)+b,n h(4) whereverticaladvection,depth-averagedlateraladvectionandCoriolisaccelerationsareneglected.Thesubscriptsnandsrepresenttransverseandstreamwisevelocitycomponents,respectively,uisthevelocity,overbarsrepresentdepthaverages,Ristheradiusofcurvature,gistheaccelerationduetogravity,isthewaterdensity,is 1ReprintedwithpermissionfromWaterhouse,A.F.,andA.Valle-Levinson,Subtidalowinaweaklystratiedsubtropicaltidalinlet,Cont.ShelfRes.,30,281-292,2009. 83

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theseasurfaceelevation,zistheverticaldirection,Azistheeddyviscosity,b,nisthebottomshearstressinthetransversedirectionandhisthedepthofthewatercolumn.Theradiusofcurvatureispositivewhenthepositivestreamwisevelocity(ebb,forourstudy)followsaclockwisetrajectoryduetothecurvature;thusRchangessignduringoodow[ LacyandMonismith 2001 ; Nidziekoetal. 2009 ].Thethirdtermonthelefthandsideofequation 4 isthecentrifugalaccelerationterm,whichisgeneratedbythestreamwisevelocity,us.Therstandsecondtermsontherighthandsideoftheequationarethelateralbaroclinicforcingterms.Dependingontheirsign,thesetermsmayacttoopposeorenhancethecurvatureinducedlateralows[ Dronkers 1996 ; Geyer 1993 ; SeimandGregg 1997 ]. Observationsandmodellingofowaroundtidalheadlands[ Geyer 1993 ]andwithincurvedestuarieshaveillustratedtheexistenceofbathymetry-inducedresidualeddies[ Li 2006 ],enhancedverticalmixingduetochannelcurvature[ SeimandGregg 1997 ],theimportanceoflateraldensitygradientsinmodifyingthecurvature-inducedlateralvelocitiesinweaklytostronglystratiedestuaries[ ChantandWilson 1997 ; Dronkers 1996 ; Huijtsetal. 2009 ; LacyandMonismith 2001 ]andchannelsthatexperiencebothwell-mixedandstratiedconditions[ Nidziekoetal. 2009 ].Channelcurvaturehasbeenfoundtoaffecttransportofsedimentandsalt[ Blantonetal. 2003 ; KimandVoulgaris 2008 ]whiletidesandwindsmodifythemagnitudeofthetransverseows[ Chant 2002 ]. Analyticalmodelsofresidualowswithintidallydrivenbasins[ LiandO'Donnell 2005 ; Winant 2008 ],whenadoptedinacurvedchannel,showthatlateraladvectiondominatesinbothlongandshortcurvedchannelswithresidualeddiesformingoneithersideofthechannelbends[ Lietal. 2008 ].In Lietal. [ 2008 ]'smodel,whereacartersiancoordinatesystemisadopted,curvature-inducedowsandresidualeddiesaregeneratedbythenonlinearadvectivetermsofthemomentumequations.Althoughadvectiondominatesincurvedchannels,frictionaleffectsofthetidalwaveenteringthechannelmaystillenhanceordiminishtheadvectivetermsandcannotbecompletely 84

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neglected,especiallyinlongchannels[ Lietal. 2008 ].Thedynamicsoftidallydrivenresidualowcanbedescribedonthebasisofanon-dimensionallength.Basinswhosenon-dimensionallengthsarelessthan0.6-0.7aredenedasshort,whilethoseabovethisthresholdaredenedaslong[ LiandO'Donnell 1997 2005 ; Winant 2008 ].Basinlengthistheparameterthatdeterminesthefeaturesofresidualcirculationwithinabasin[ LiandO'Donnell 2005 ]. Theoreticalresultshavebeenusedtoexplaintheobservedlateralstructureoftidalresidualowsinlongbasins,bothstraight[ Caceresetal. 2003 ; KjerfveandProehl 1979 ; Lietal. 1998 ]andcurved[ HenchandLuettich 2003 ; Lietal. 2008 ],aswellasinshortstraightbasins[ WinantandGutierrezdeVelasco 2003 ].Lessisknown,however,aboutthesubtidalvariabilityormodulationofthelateralstructureoftidalresidualowsinshortorlongbasinsundertheinuenceofcurvature.Curvature-inducedsecondaryowinastronglystratiedestuaryincreaseswithincreasingtidalrangewhilethethesecondaryowdecreaseswithincreasingriverdischarge[ Chant 2002 ]. Li [ 2006 ]suggeststhatforbathymetricallyinducedresidualeddiesinashort,weaklystratiedbasin(wherecurvaturewasnotincluded),bothwindandtidalrangehavelittleeffectonthestructureorlocationoftheresidualeddiesformedasaresultofthesebathymetricvariations. Thepurposeofthisstudyistodocument,withobservations,thestructureandvariabilityofthealong-channeltidalresidualowsandwhetherthevariabilityofthecross-channelowshelpinthelateralredistributionofmomentuminalong,subtropical,curvedinlet,PoncedeLeonInlet,inEastCentralFlorida.Thisstudyalsoseekstodeterminewhetherthemodulationoftheresidualstructureisproducedbyeithertidesorwinds,orboth.Thesubtropicalnatureoftheinletallowsfordirectobservationsofthetidalresidualowsasalong-channeldensitygradientsarenotinuentialtothedynamics. 85

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4.2StudyArea LocatedontheCentralEastcoastofFloridaat294.5'N,PoncedeLeonInletisashallowsubtropicalinlet(Figure 4-1 ).Flowwithintheinletisforcedbythesemi-diurnal(M2)tidewithameantidalrangeof0.6mandtypicaltidalcurrentsexceeding1ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1.TheinlethasbeendescribedashavingastrongebbchanneladjacenttotheNorthjetty[ MilitelloandHughes 2000 ],whichhasbeenfoundtoberesponsibleforconsiderablescouralongthenorthernsideoftheinlet[ MilitelloandZarillo 2000 ].Freshwaterinputsfromprecipitationvaryseasonally,withthestrongestinuencesduringMaythroughSeptember[ SchwartzandBosart 1979 ]. Theentrancetotheinletis350mwideand12mdeepinachannelthatislessthan100mwide.Thethalwegofthechanneldecreasesto3.5mwithin750minsideoftheinlet.Thisnarrowchannelisanked,asymmetrically,byshoalsthataretypically2to4mdeep.PoncedeLeonInlethastworegionswherethechannelcurvatureislarge(inbothbathymetryandmorphology)withtherstcurvedspitoccurringonthenorthernshore,insidetheinlet(seeFigure 4-1 ),witharadiusofcurvatureRBof500m.Thesecondcurvedspitisseawardoftherst,onthesouthernshoreoftheinlet(seeFigure 4-1 ,RA=420m).Thisspitisaccretingnorthwardonbothebbandoodtidesduetothecurvatureeffectonsandtransport[ MilitelloandZarillo 2000 ].Forebbingows,thecurvatureatRAisclockwiseandRBiscounter-clockwise.Atwo-layercurvature-inducedtransverseowandpossibleformationofresidualeddies,downstreamandupstreamoftheregionofcurvature,areexpected[ Lietal. 2008 ]. PoncedeLeonInletisoneofseveralcoastalinletsconnectingFlorida'sIntracoastalWaterway(IWW)totheAtlanticOcean(Figure 4-1 ).TheIWW,alongandnarrowcoastallagoon,extendsalongtheentireeasterncoastofFloridawithameanwidthof55m,ameandepthof3.5mandamaximumdepthof5m[ KenworthyandFonseca 1996 ; Smith 1983 ].WithintheIWWsignicanttidalattenuationoccurs,50timesgreaterattenuationthanattheinlet[ MilitelloandZarillo 2000 ].DuetotheextentoftheIWW 86

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alongtheEastcoastofFlorida,thelengthofthePoncedeLeonInlet-IWWsystem,asdenedby LiandO'Donnell [ 2005 ]and Winant [ 2008 ],isdifculttodetermineandhence,willbedeterminedbasedontheobservationsofthetidalwavetypeattheentrancetotheinlet[ LiandO'Donnell 2005 ]. Giventheshallowmeandepth(4m),PoncedeLeonInletcanbeclassiedasastronglyfrictionalinletwithafrictionalconstant[ Winant 2008 ]of =r 2Az !H2=0.94(4) whereAzisaconstantverticaleddyviscosity,estimatedtobe0.001m2s)]TJ /F4 7.97 Tf 6.59 0 Td[(1forthiscase,!isthefrequencyofthesemidiurnal(M2)tideandHisthemeandepth.Thisfrictionalconstantcanbecalculatedforaninlettodeterminethefrictionalinuenceonowdynamicswhetherstrong(=1),moderate(=0.5)orweak(=0.1).Therefore,PoncedeLeonInletisahighlyfrictionalinletwithtidallyinducedresidualowsthatmaybedescribedforowsattheupperendofthefrictionallimitasconsideredby Winant [ 2008 ]. 4.3DataCollection Inordertocharacterizethelateralstructureoftidalresidualowsaswellasthetemporalvariabilityofthisstructure,severaltypesofobservationswereobtained.MeasurementsofunderwaycurrentvelocityprolesandwaterdensityproleswerecombinedwithtimeseriesofcurrentprolesattheentrancetoPoncedeLeonInlet. 4.3.1UnderwaySurveys UnderwaysurveyswerecarriedoutattheentrancetoPoncedeLeonInletonSeptember5,2007andonFebruary21,2008(TransectA,Figure 4-1 ).Bothsurveysstretchedfornearlyasemi-diurnalcycle(11.2hours)duringaneaptideinSeptemberandduringaspringtideinFebruary(Figure 4-2 ).Duringbothsurveys,aboat-mounted1200kHzAcousticDopplerCurrentProler(ADCP)withbottom-trackingcapabilitywasusedtomeasurecurrentprolesalongcross-channeltransects.Thetransectswere 87

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sampled15and17timesduringtheSeptemberandFebruarysurveys,respectively.Fullacross-inletcoveragewasensuredbysamplingwithin3moftheinletperimeteroruntilthedepthlimitednavigation.Giventheaccretiononthesouthernspit,depthsonthesouthernsideofthetransectwereveryshallow.Thetemporalcoverageduringeachsurveyallowedfortheseparationoftidalfromnon-tidalsignalsthroughaleast-squaresttothesemi-diurnal(M2)harmonic[ Lwizaetal. 1991 ]afterrotatingthecurrentstotheprincipalaxisofmaximumvarianceconsideringebbandoodtidesseparately.Duringthesurveys,waterdensityprolesweremeasuredwithaSeaBirdSBE19-PlusConductivity-Temperature-Depth(CTD)proleratthedeepestpartofthesurveytransectsduringeveryothertransectrepetition(CTDStationsAandB,Figure 4-1 ).Thisallowedfortheestimationofmeanhorizontaldensitygradientsandtheirinuenceonthemeanows,whichwasfoundtobesmall.Asurfaceconductivityandtemperature(CT)sensor,SeaBirdSBE37,wasmountedonthesurveyboattocapturethelateralsurfacevariabilityinthedensityoverthetidalcycle,recordingat0.2Hz.Lateraldensitygradientsprovedtobelargerandmoreimportantthanthelongitudaldensitygradients. 4.3.2MooredSurvey Timeseriesofcurrentvelocityproleswereobtainedwithbottom-mountedADCPs,equippedwithpressuresensors,deployedatthreelocationsacrossthewidthoftheinlet.Twoinstruments(Stations1and3inFigure 4-1 )weremooredovertheshoalsankingthechannel,andthethirdinstrumentwasinstalledinthechannel(Station2inFigure 4-1 ).Theseinstrumentsrecordeddatafor78daysdistributedintwoperiods,fromJanuary14,2008toFebruary25,2008andfromFebruary25,2008toApril2,2008.Thetwodatasetswerejoinedusingasplinetbetweenthecurrentsandwaterlevel.DuringthesecondperiodtheinstrumentatStation3wasdamagedandtherecordwasunavailable.Instrumentsrecordedtheaverageof400pingsdistributedover10minuteintervalsat0.5mbins.Thecurrentswererotatedtotheprincipalaxisofmaximumvariance[ EmeryandThomson 2004 ]forbothebbandoodtides.Positive 88

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along-channelcurrentsindicatedowoutoftheinlet.AnglesofrotaionforStations1,2and3were17.5and20.0,39.2and38.1,41.9and39.1Tforebbandoodtides,respectively.Positivecross-channelcurrentsweredirected90counter-clockwisefromtheprincipalaxis. Forthepurposesofinvestigatingthesecondaryowsassociatedwithcurvatureeffectsinboththemooredandtowedsurveys,thelateralresidualowwascalculatedastheanomalyoftheverticalprolesrelativetothedepthaveragedvalue[e.g. Geyer 1993 ].Thedeployment-longaveragewascalculatedforeachmooringtocharacterizethelateralstructureofthemeanow.Thesubtidalvariationsweredeterminedusingalow-passLanczos-cosinelterwithhalf-powerof34hourstoeliminatetidalandinertialvariations. 4.3.3AtmosphericData LocalwindobservationswereobtainedfromNewSmyrnaBeachmeteorologicalstation(Station722361fromtheNationalClimaticDataCentre)locatedat2930N,80570W,4kmtotheSouth-WestofPoncedeLeonInlet(Figure 4-1 ).Thedatawerecollectedataheightof3mandthencorrectedto10musingthelog-lawvelocityprole.Thewindvelocities,lteredwitha34-hourLanczoslter,werethenrotatedtobealignedwiththecoast(-40and50Tinthepositivealongandcrossshelfdirections,respectively)givingalongandcross-shorewindsandstresses,calculatedasin LargeandPond [ 1981 ]. 4.4TidalandSubtidalFlow 4.4.1TidalInformation Tidalconstituentsfromthestreamwisevelocity(us)andsurfaceelevation()wereobtainedfromthemooredADCPsusingT TIDE( Pawlowiczetal. 2002 ;Table 4-1 ).Thequarter-diurnalamplitudewasgreaterthanthediurnalamplitudefromthevelocityrecordsatbothshallowmoorings(1and3),consistentwithnon-linearitiesduetothedeptheffectonbottomfriction[ Parker 1991 ].Thecoherencesquaredfroma 89

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Table4-1. Tidalamplitude(A)andphase()andphasedifference()ofthelargestofthediurnal(K1),semi-diurnal(M2)andquarter-diurnal(M4)frequenciesforthethreemooredADCPsacrossPoncedeLeonInletascaculatedfromstreamwisevelocity(us)andsurfaceelevation()usingT TIDE[ Pawlowiczetal. 2002 ].Theaveragephaselagbetweensurfaceelevationandstreamwisevelocityis149. ConsituentA(m)()A(m)())]TJ /F8 7.97 Tf 6.59 0 Td[(us()us Mooring1K10.083530.08211-142M20.591610.5012-149M40.111690.0166-103Mooring2K10.103500.09212-138M20.781630.5112-151M40.051730.0133-140Mooring3K10.083520.09220-132M20.521610.5014-147M40.101770.01120-57 cross-spectralanalysisbetweensealevelandstreamwisecurrentsgaveanaveragephaseof-149atthesemi-diurnaltidalfrequency(1.9cpd)indicatingthattidalcurrentsleadthewaterlevelby1.04hours(Figure 4-3 B).Thisphaselead,conrmedbythephasedifferencefromtheharmonicanalysis(,Table 4-1 ),indicatedthatthetideinPoncedeLeonInletwasclosertoaprogressivethanastandingwave.Duetotheprogressive-likenatureofthewaveatthemouthoftheinlet,thelagoon-inletsystemwaslikelybehavingasalongchannelasdenedby LiandO'Donnell [ 2005 ]. Fromthelargecalculatedinequation 4 andthelargequarter-diurnalconstituent(M4),itfollowsthatfrictionaleffectswerelikelyimportant.Sincethisinlet-lagoonsystemhassmallalongchannelbaroclinicpressuregradients,andthetideisthedominantforcingmechanism,thedynamicsarelikelyrepresentedbythemodelsof LiandO'Donnell [ 2005 ], Lietal. [ 2008 ]and Winant [ 2008 ],fortidallydrivenowthroughahighlyfrictionalchannelofvariabledepth.Whetherthisinletshowedsimilarmeanowsaspredictedbythetheorywasexploredusingbothmooredandsurveydata.Giventhe 90

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stronglycurvingnatureoftheinlet,astreamwiseandstreamnormalcoordinatesystemwasadopted(unliketheanalyticalmodelsabove)inordertofullyisolatethecurvatureinducedsecondaryowsandtodeterminewhethertheselateralowsredistributestreamwisemomentuminthetransversedirection. 4.4.2LongTermMeanFlows Theaveragestreamwiseowovertheentire78dayrecordateachofthemooringstationsindicatedverticallyaveragedoutowinthechannel(Station2)andinowovertheshoalsatStations1and3(Figure 4-4 ).Lateralvelocityshowedverticalshearswithbottomowtowardthenortheast(NE)andsurfaceowtowardtheeast-northeast(ENE)atStation2.Theverticalstructureofthelateralvelocitieswasconsistentwithcurvature-inducedsecondaryowof KalkwijkandBooij [ 1986 ]aroundanegativebendonebb.AsimilarhelicalstructurewasobservedatStation1,withlessshearinthelateralows. Thedifferencesbetweenmeanebbandoodowsillustratedthetidalevolutionofthestreamwiseandlateralows.AtStation2,typicalcurvature-inducedlateralowsoccurredduringebb,withsurfaceowspushedsouthward(away)fromtheinshorebend(RB)andbottomowsdirectedbacktowardthebend.However,duringood,theowwaslikelystillundertheinuenceofRAasthelateralowsshowedsurfaceowsdirectednorthwardatthesurface,andreturnowstowardthespit,RA,atthebottom.Theselateralpatternswereobservedthroughoutnearlytheentiremooredobservationperiodandwillbediscussedfurtherinthenextsection.Toinvestigatetheconsistencyofboththestreamwiseandlateralstructureoftheow,thesurveyacrossthemouthofferedamoredetailedspatialresolutionofthemeanowstructure(wheretheradiusofcurvatureispositiveforebbows). 4.4.3TidalandResidualows Transectsacrossthemouthoftheinletweremeasuredduringonesemi-diurnaltidalcycleatdifferentphaseswithinthefortnightlytidalcycleandunderdistinctwindforcing 91

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conditions(Figure 4-2 ).TheseconditionsinuencedtheresidualowsacrossthemouthoftheinletduringthetwosamplingperiodsinSeptemberandFebruary. 4.4.3.1Tidalows Thetransectsatthemouthoftheinletwereseparatedintomaximumebbandood(Figures 4-5 and 4-6 )todeterminehowthelateralstructureoftheowdiffered,dependingonthephaseofthetide.Theaverageatmaximumebbandoodphasesshowedadistinctlateralstructure,similarbetweenthetwosurveys.Inbothsurveys,maximumoodcurrentsoccurredmid-waythroughthechannelduringoodwhileduringebb,streamwisevelocitieswerestrongestalongthenorthernedgeoftheinlet,asobservedby MilitelloandZarillo [ 2000 ],downtoadepthof6m.Althoughbothsurveysoccurredduringdifferentstagesofthetidalcycle,tidalcurrentsaveragedoverthechannelwidth(from0to110m)weresimilarbetweenthetwosurveys(Figure 4-7 Fand 4-8 F). Lateralowsdifferedbetweenthephasesofthetide.Forbothsurveys,lateralcurrentsduringmaximumebbshowedowawayfromthebend(northward)atthesurfaceandowtowardthebend(southward)closetothebottominthechannel(Figures 4-5 Band 4-6 B).Duringmaximumoodcurrents,bothsurveysshowedtwocounterrotatingcellsofweaklateralowacrosstheinlet.Curvatureeffectslikelyhadlesseffectontheowduringoodastheacrosschanneltransectswerecarriedoutattheentrancetotheinletwhereoodingcurrentshadnotyetencounteredstrongbathymetriccurvature.Theeffectofchannelcurvature,indicatedbytheverticallyshearedlateralowsvisibleduringebbcurrents,wereinvestigatedbycalculatingthecentrifualaccelerationtermfromthestreamwisevelocities,averagedoverthechannelwidth(from0to110m). Centrifugalacceleration(u2s)]TJ ET q .359 w 172.71 -573.22 m 181.29 -573.22 l S Q BT /F8 7.97 Tf 172.71 -580.67 Td[(u2s R)overthetidalcyclewasontheorderof10)]TJ /F4 7.97 Tf 6.58 0 Td[(4ms)]TJ /F4 7.97 Tf 6.59 0 Td[(2forbothsurveyswithpositive(surface)andnegative(nearbottom)componentsoccurringatmaximumebbandood(1300/1900hrs,Figure 4-7 Aand1800/1300hrs, 92

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Figure 4-8 A)asobservedinotherstudies[ KimandVoulgaris 2008 ; LacyandMoni-smith 2001 ; Nidziekoetal. 2009 ].AlthoughtheSeptembersurveyoccurredduringaneaptide,centrifugalaccelerationswerestrongerandmorewellorganizedduringthissurveythanduringtheFebruaryspringtidesurvey.Thiswasattributedtolateralbaroclinicity. Lateralbaroclinicpressuregradientaccelerationswerecalculatedasinthesecondtermontherighthandsideofequation 4 ,g Bh,whereBisthewidthoftheinlet.Giventheoutowalongthenorthernsideoftheinletduringebbtideasobservedby MilitelloandZarillo [ 2000 ]andinFigures 4-5 and 4-6 ,thelocationofthedensityminimumwasaresultofdifferentialstreamwiseadvection[ Dronkers 1996 ; LacyandMonismith 2001 ].Differentialadvectioncausedtheminimumindensitytobelocatedalongthenorthernedgeoftheinlet.Theactualdensityminimumvariedinpositionbetweentowedsurveysfromthenorthensideoftheinlet(80mand60mfromthenorthernedgeoftransectAforSeptemberandFebruarysurveys,respectively).Inbothsurveys,amarkedminimumindensityoccurredattheendofebb(Figures 4-7 Band 4-8 B)andthesurfacebaroclinicpressuregradientwasstrongerduringSeptemberthaninFebruary(Figures 4-7 Cand 4-8 C). Futherinsidetheinlet,thebarocliniceffectonthelateralowswasobservedfromthemooringdataatStation2(Figure 4-9 )whichwasundertheeffectofRBonebbandRAonood.Theverticalshearinthelateralvelocities,un,wascalculatedasthedifferenceinlateralvelocitybetweenthetopandbottombinsoftheADCP.Lowdensitywater,atthemoorings,exitstheinletfollowingthenorthernedgeoftheshore.Asebbprogresses,lateralbaroclinicpressuregradientsdevelop,actinginthesamedirectionasthecentrifugallyforcedow(atthesurfaceatRB)causinganincreaseintheverticalshearinthelateralcurrents(un)frommid-ebbuntilthebeginningofood. Althoughstreamwisefrictionwaslikelyastronginuenceonthestreamwisedynamicswithintheinlet,lateralbottomfrictionwasanorderofmagnitudesmallerthan 93

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streamwisebottomfrictionascalculatedusingCDunjVj=H,wherejVjisthemagnitudeofthevelocityandCDisthedragcoeffcient(CD=0.0025;Figures 4-7 Fand 4-8 F).Modicationstotheowoverthetidalcyclebytheprocessesmentionedabovewerelinkedtotheobservedresidualowsinboththestreamwiseandlateralvelocitiesasexplainednext. 4.4.3.2Streamwiseresidualows Streamwiseresidualvelocitieshadasimilarstructureduringbothsurveys(Figures 4-10 and 4-11 ).Streamwiseandlateralresidualvelocitieswerecalculatedbyremovingthetidalsignalfromtheobserveddatathroughaleast-squaresttothesemi-diurnal(M2)tide[ Lwizaetal. 1991 ].DuringSeptember,weakinowof5cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1waspresentintherst50mofthetransectwithmaximuminowvelocitiesconnedto3mdepth.Southwardof50malongthetransect,thestreamwiseresidualowwasdirectedintotheinletwheremaximuminowcurrentsoccurredovertheshoalsupto20cms)]TJ /F4 7.97 Tf 6.58 0 Td[(1.DuringFebruary,thestreamwiseresidualowshowedoutowonthenorthernsideoftheinlet(0to75macrosstheinlet)withmaximumcurrentsof20cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1constrainedbetween2and6mdepth(Figure 4-11 ).Theshifttowardinow,althoughrelativelyweakat-5cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1,occurredontheslopebetween75and150m.Weak,<6cms)]TJ /F4 7.97 Tf 6.58 0 Td[(1,outowwasobservedsouthoftheslope. Thedifferencesinthestreanwiseowbetweenthetwosurveyswereduetoexternalforcingmechanismssuchaschangesinstratication,thefortnightlytidalcycleandwindeffects.Hydrographicdataobtainedfrombothsurveysshowedthatthewatercolumnwasmixedduringoodandweaklystratiedduringebb.ProlesfromtheendofebbandoodareshowninFigures 4-7 Dand 4-8 D.Attheendofebb,theverticaldensitygradient(@ @z)atthemouthoftheinletwas1.0and0.2kgm)]TJ /F4 7.97 Tf 6.59 0 Td[(4(forSeptemberandFebruarysurveys,respectively)whilefurtherinsidetheinletatStation3,theverticaldensitygradient(@ @z)attheendofebbtidedecreasedto0.7and0.01kgm)]TJ /F4 7.97 Tf 6.59 0 Td[(4(forSeptemberandFebruarytransects,respectively).Thetidallyaveragedaccelerations 94

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producedbythebaroclinicpressuregradient,h(gH=)@=@si(whereanglebracketsdenotethetidalaverage),weresmall(O(10)]TJ /F4 7.97 Tf 6.58 0 Td[(6)ms)]TJ /F4 7.97 Tf 6.59 0 Td[(2).Overthetidalcycle,baroclinicpressuregradientsneverexceededO(10)]TJ /F4 7.97 Tf 6.58 0 Td[(5)ms)]TJ /F4 7.97 Tf 6.59 0 Td[(2forbothsurveys.Therefore,thealong-channelbaroclinicpressuregradientwasneglectedasamechanismaffectingthetidalandresidualowdynamicswithintheinlet. Indensity-drivenestuaries,thefortnightlyspring-neapcycleresultsinstrongerresidualowsduringneaptidesduetoreducedverticalmixing[ Haas 1977 ].Converselyintidally-drivensubtropicalestuaries,thefortnightlyspring-neapcycleresultsinstrongerresidualowsduringspringtidesratherthanduringneaptides[ Valle-Levinsonetal. 2009 ]. Lietal. [ 2008 ]suggestedthatthelocationandstrengthofresidualeddiesincurvedtidallydriveninletsvarylittlewithtidalamplitude.TheSeptembersurveyoccurredduringaneaptidewithanincreasingmeanwaterlevelwhiletheFebruarysurveyoccurredduringaspringtidewithadecreasingwaterleveloverthesamplingperiod(Figure 4-2 ).Althoughstreamwisevelocitiesaveragedacrossthechannelweresimilar(Figures 4-7 Fand 4-8 F),theresidualowinSeptembershowedunequalexchangewithsignicantlyweakeroutowthaninowwhichcorrespondedtoanetvolumeowintotheinletinagreementwithincreasingwaterlevel.Similarly,giventhedecreasingwaterlevelduringtheFebruarysurvey,theresidualexchangeowshowedstrongoutowandweakinowresultinginnetvolumeowoutoftheinlet. 4.4.3.3Lateralresidualows Inbothsurveys,transverseresidualowsshoweddepthvariablelateralowwithatwo-layerstructure(averageofeveryotherverticalproleplottedinFigures 4-10 and 4-11 ).Inbothcases,lateralowatthesurfacewasdirectedtowardtheNorth(awayfromthebendRA)whilelateralowbelow4mandbelowthesurfacelayeralongthesouthernshoalwasdirectedsouthward,towardthebend(RA). TidallyaveragedlateralbaroclinicpressuregradientswerestrongerduringtheSeptembersurveywhilelateralresidualvelocitieswerestrongerduringFebruary. 95

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Thiswaslikelyaresultoftherebeingnolateraldensitygradienttocounteractthecentrifugallygeneratedow.WeaklateralresidualowsduringSeptemberwereduetostrongbaroclinicpressuregradientssuppressingcentrifugalaccelerations[ Chant 2002 ; LacyandMonismith 2001 ; Nidziekoetal. 2009 ; SeimandGregg 1997 ]. Therefore,@ @ywaslikelyplayingaroleinmodifyingtheresidualowwithintheinlet,eventhoughthealong-channelbaroclinicpressuregradientwassmall.FreshwaterinputtoPoncedeLeonInletissporadicandowforcedonlybycentrifugalaccelerationswillalsolikelybesporadic,dependingontheexternalfreshwatersources.Giventhestronglateralshear,thepresenceofstronglateralvelocitiesduetoaweakbaroclincpressuregradientmayaffecttheredistributionofmomentumwithintheinletwhichwillbeexploredusingthemooringdata.Alsotoexaminethedetailsofthemodulationofresidualowssuggestedbythesurveys,thetimeseriesmeasurementswereexaminednext. 4.5SubtidalModulation Withtheknowledgethatcurvatureisanimportantdrivingmechanisminthisinlet,thecartersiancoordinatesystemof LiandO'Donnell [ 2005 ]and Winant [ 2008 ]isusedtostudyhowlateralowshelpedintheredistributionofstreamwisemomentum.Thiswasexaminedwiththevariationoftheadvectivetermsinthestreamwisedirection,h v@ u=@yi,whereuandvarealongandcrosschannelvelocities,respectively.SubtidalvariationsofthestreamwiseexchangeowsinsidetheinletconrmedsurveyobservationsthatthepatternofoutowinthechannelandinowovershoalspersistedthroughoutalmosttheentireobservationperiodatalldepthsforStations1and2(Figure 4-12 C).ThesubtidalowatStation3(notshown)oscillatedbetweeninowandoutowalthoughthemeanowovertheentirerecordwasnegative(inow)andsmall.DuetotheverycloseproximityofthismooringsitetoStation2,theresidualcurrentswerelikelyundertheinuenceoftheowinthechannel. 96

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Duringpositivecrossshelfwinds(offshorewindsonFebuary14andMarch8,2008inFigure 4-12 B),thesubtidalowrespondedwithanincreaseinmagnitudeoftheoutowinthechannel(Station2)andacorrespondingdecreaseoftheinowovertheshoals(Station1).Strongnortherlyalong-shorewindpulsesmodulatedtheresidualowintheoppositedirectionwithdecreasedoutowandincreasedinowcorrespondingtoanonshoreEkman(January21,2008inFigure 4-12 BandC). Modulationofmagnitudeoftheresidualowthroughouttheobservationperiodindicatedaresponseoftheresidualcirculationduetowindeffects.Variabilityinthesubtidalwaterlevelwithintheinletwascorrelatedwithalong-channelwindstress(correlationcoefcient,Rc,of0.41),whilecross-channelwindstresseswerelesscorrelated(Rc=0.12).Windeffectscausedwaterlevelset-upduringonshorewindsduetoanettransportofwaterintotheentirecross-sectionoftheinlet.Correspondingly,awaterlevelset-downduringoffshorewindswasrelatedtoanetseawardtransportofwaterthroughoutthecross-sectionoftheinlet.Remotewindeffects,notrelatedtoobservedwinds,wouldcausesimilartransportintotheinlet(outoftheinlet)duringrising(falling)waterlevel. Inadditiontowindeffects,theresidualexchangeowatthemouthoftheinletwasaffectedbyfortnightlytidalforcing.Thestrengthofthenetexchangeow(Figure 4-12 D),asdeterminedbythedifferencebetweenthesubtidaloutowinthechannelandinowovertheshallowstation,wasmodulatedbythefortnightlytidalcycle.ThestrongestexchangeowsoccurredduringthelargestspringtidesofJanuary23andMarch9.OtherlargeexchangeowsdevelopedduringthespringtidesofFebruary9,21andMarch22.Ingeneral,thestrengthofthenetexchangeowdidnotshowevidenceofwindeffectsasthewindvelocitywasnotstronglycorrelatedtothemagnitudeoftheexchangeow(Rc<0.17forbothcross-shoreandalong-shorewindstresscomparedtoaRc=0.63withtidalamplitudevariations).Theobservedmodulationoftheexchangeowwasconsistentwithobservationsfromasinglemooredtime-seriesinasubtropical 97

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inletthatshowedstrongestexchangesduringspringtides[ Valle-Levinsonetal. 2009 ].Thisstudyprovidesmorecompleteobservationsofthelateralstructureandthesourceofthemodulationoftheseresidualexchangeows. Observationsfromeventswheretheowwithintheinletwascompletelyunidirectional(reversedowatStation2)tendedtooccurmorefrequentlyduringneaptideswithsustainedwinds.Duringthethreeneaptides,January31,February29,March30,owreversaloccurredineachcase.Duringspringtides(January23,February9and21,March9and22),windstresseswerenotlargeenoughtoovercomethetidallyinducedresidualow.Asaresult,noreversaloftheowatStation2wasobservedduringspringtides.Therefore,duringneaptideswhenwindstressexceededbottomstress,owreversalinthechannelwaslikelyoverwhelmingthetidallyinducedresidualcirculation. Abasic,verticallyaveraged,dynamicalbalanceinthestreamwisedirectionwithintheinlet,usingtheBoussinesqandhydrostraticapproximations,canbeapproximatedas 0=h)]TJ /F3 11.955 Tf 13.95 0 Td[(g@ @xi)-222(h v@ u @yi+hs Hi)-222(hb Hi(4) wherethersttermisthebarotropicpressuregradientrelatedtosealevelslope,thesecondislateraladvectiveacceleration,andthethirdandfourtharethesurfaceandbottomstresstermsusingparameterizationsforwindandbottomfrictionalstresses.Althoughthesealevelslopewasnotmeasuredduringthisexperiment,itwaslikelyanimportantdynamicalcomponent. Inthestreamwisedirection,tidalcurvature-inducedowswillmodifythestreamwisemomentumequationthroughlateraladvectiveaccelerations.Infact,resultsfromthestraightpartofacurvedestuaryby LacyandMonismith [ 2001 ]showedthatthelateraladvectivetermwashighinregionswherestronglateralgradientsinstreamwiseowscoincidedwithstronglateralvelocities.Althoughthemagnitudeofthestreamwiseshear(@ u=@y)wasdependentonthespringneapcycle,depthaveragedlateralvelocitieswerenotbutweresmallgiventhecurvatureinducedowyieldingaverticalaveragecloseto 98

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zero.Depth-averagedlateraladvectionh v@ u=@yiwasstrongerinthechannelthanontheshoal,asexpected( LiandO'Donnell 2005 ; Winant 2008 ;Figure 4-12 E).However,lateraladvectionwasstrongestatthebeginningoftherecordinconjunctionwithstrongNEwindsfollowedbyapeakinnegativecrossshore(westward)windspriortotherstspringtide.Thepeakinlateraladvectionoccuredasaresultofthewindratherthanfromthespringtide.Othersmallpulsesinthelateraladvectiveterm(inthepositivedirection)correspondedwithstrongpositivecrossshore(ornegativealongshore)windevents.Therefore,althoughstreamwiseexchangeowsincreasedduringspringtides,fortnightlyvariabilityinlateraladvectiveaccelerationsweremaskedbythewindstress(secondandthirdtermsinequation 4 )andwerenotsufcienttolaterallyredistributestreamwisemomentum.Otherwise,thelateralshearsassociatedwithspringtideswouldhavedecreasedasaresultofthelateralredistributionofstreamwisemomentumassociatedwiththeadvectiveaccelerations. Comparingtheaccelerationsduetolateraladvectiontostreamwisefrictionalaccelerations(hCD Uj Vj Hi;Figure 4-12 F),frictionwasthemostdominantmechanismontheshoalwhilebothtermswereimportantinthechannel.Thiswasinagreementwith LiandO'Donnell [ 2005 ]and[ Winant 2008 ]indrivingaresidualowinatidallydominatedchannel.Despitethestronglycurvingnatureofthechannel,residualowsweregeneratedmostlythroughtheinteractionbetweenthetidalwaveanddepthvariations.Frictionalaccelerationswerestrongestduringspringtidesandactedtoreducetheincreaseinstreamwisevelocityproducedbythespringtideows. 4.6Conclusions InthehighlyfrictionalPoncedeLeonInlet,observedresidualowswereconsistentwiththeoreticalresidualowsinatidallydominated,curvedchannel.Residualow,showingmoderatere-circulation,waspersistentattwobendsinthetopography:ontheleeoftheupstreambendoftheinletaswellasonthedownstreambendfurtherinsidetheinlet.Alaterallyshearedpatternofnetoutowinthechannelandnetinowoverthe 99

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shoalsinthestreamwisevelocitypersistedunderdifferenttidalamplitudesandmostwindforcingconditions.Longtermcurrentmeasurements,mooredacrosstheinlet,providednovelobservationalinformationonthevariabilityandmodulationofthelateralowwithinthesesubtropicalcurvedinlets. Observationsindicatedthatstrengthofthecurvature-inducedresidualcirculationwasaffectedbybothwindsandtides.Thestrengthofthestreamwiseexchangeowacrosstheinletwasmodulatedbytidalforcingfromthespring-neapcycle.Unliketemperateestuaries,thestrongestexchangeowsoccurredduringspringtidesconrmingrecentobservationsfromasinglemooredtimeseries[ Valle-Levinsonetal. 2009 ]. Along-channelwindscausedunidirectionalowsthroughouttheinlet.Thedirectionoftheseowswasdependentonwhethercoastalset-uporset-downwasobserved,therebyreducingorincreasingtheinoworoutowcomponentofthetidalresidualcirculation.Underspeciccriteriaofwindspeedduringneaptides,unidirectionalowwasobservedthroughouttheinletwithareversalinthechannel.Inthelateraldirection,centrifugalaccelerationsandlateraldensitygradientwereinuentialinthedynamics.Lateralbaroclinicpressuregradientsactedtoreducelateralowsatthemouthoftheinlet.Advectionofstreamwiseshearbythelateralvelocitieswasfoundtoberelatedtothewind(anditseffectonwaterlevel)maskingthevariabilityduetothespring-neapcycle. 100

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Figure4-1. StudyareaofPoncedeLeonInlet,FloridawhichconnectstheIntracoastalWaterway(IWW)totheAtlanticOcean.ThemooredADCPsitesaredenotedwithdiamonds(Stations1,2and3)andthetowedADCPsurveylineisdenotedbyasolidlineacrosstheinlet(TransectA).TheCTDlocationsaredenotedwitho's(StationsAandB).ThethalwegoftheinletfollowsfromCTDStationA,ADCPStation2andCTDStationB.ThetworegionsofcurvatureareNorthofCTDStationB(RB=500m)andSouthofCTDStationA(RA=420m).Themeteorologicalstation(NewSmyrnaBeach,Station722361)isdenotedbytheblacksquare,4kmtotheSouth-WestofPoncedeLeonInlet. 101

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Figure4-2. Tidalamplitude(m;dashedline)andsubtidalwaterlevel(m;solidline)asmeasuredbytheADCPinmetersatStation2.PeriodofthetowedADCPtransectsare()September5,2007and(2)February21,2008.SubtidalwaterlevelwasobtainedfromNOAATideStation8721147(293.8'N,8054.9'W)andlteredusingalowpassLanczos-cosinelterwithhalf-powerof60hours. 102

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Figure4-3. A)CoherencesquaredandB)phaseofthestreamwisevelocityandwatersurfaceelevationfromStation1(thickline,o's)andfromStation2(thinline,x's)fromthebottombinsofeachADCP.Condenceinterval(95%)is0.26forbothcurrentmetersandisrepresentedbydashedlineinA.Phaseat1.9cpdindicatesa-147phaselagbetweenstreamwisecurrentsandseasurfaceelevation. 103

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Figure4-4. A)DeploymentlongmeanowvectorsatthethreeADCPmooringsitesinPoncedeLeonInlet,Florida.Stations1and2showtransverseshearwithdepthwherethethicksolidarrowsrepresentthesurfaceowandthethickdashedarrowsrepresentthebottomowindicatingtheimportanceofchannelcurvature.ForStation3(withonlyonebindepth),themeanowisrepresentedbyasinglevector.Meanowsduringmaximumoodandebbmeans(BandC)showthedifferenceinlateralvelocitiesbetweenthetwophasesofthetide.Astrongerlateralshearisosbervedduringebbshowingtheclassicalhelicalstructureofcurvatureinducedows. 104

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Figure4-5. Streamwiseandlateralcurrents(cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)duringA)maximumoodandB)maximumebbacrossTransectAfromPoncedeLeonInletonSeptember5,2007.Asymmetryoverthetidalcycleisnotedbythechangeinpositionofthevelocitymaximabetweenoodandebbtides.Northisonthelefthandsideofthegure,andpositivevelocityisoutoftheinlet(inthestreamwisedirection)andtowardthenorth(inthelateraldirection). 105

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Figure4-6. Streamwiseandlateralcurrents(cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)duringA)maximumoodandB)maximumebbacrosstransectAfromPoncedeLeonInletonFebruary21,2008.Asymmetryoverthetidalcycleisnotedbythechangeinpositionofthevelocitymaximabetweenoodandebbtides.Northisonthelefthandsideofthegure,andpositivevelocityisoutoftheinlet(inthestreamwisedirection)andtowardthenorth(inthelateraldirection). 106

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Figure4-7. Centrifugalacceleration(u2s)]TJ /F4 7.97 Tf 8.66 2.43 Td[(u2s R)A)variabilityoverthetidalcycleandB)averageoverthetidalcycle;C)surfacet(20m,60mand360mfromnorthernedgeoftransectA,respectively);D)prolesofdensityatendofebb(dotted)andood(solid)atA(thick)andB(thin);E)lateralbaroclinicpressuregradientcalculatedatthesurfaceacrosstransectAfrom60mto360mandstreamwise(dashed-dot)andstreamnormal(dotted)bottomfrictionparameterizations;andF)streamwisetidalvelocity,averagedoverthechannelwidth(0to110m),acrosstransectAfromPoncedeLeonInletonSeptember5,2007. 107

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Figure4-8. Centrifugalacceleration(u2s)]TJ /F4 7.97 Tf 8.66 2.43 Td[(u2s R)A)variabilityoverthetidalcycleandB)averageoverthetidalcycle;C)surfacet(20m,60mand360mfromnorthernedgeoftransectA,respectively);D)prolesofdensityatendofebb(dotted)andood(solid)atA(thick)andB(thin);E)lateralbaroclinicpressuregradientcalculatedatthesurfaceacrosstransectAfrom60mto360mandstreamwise(dashed-dot)andstreamnormal(dotted)bottomfrictionparameterizations;andF)streamwisetidalvelocity,averagedoverthechannelwidth(0to110m),acrosstransectAfromPoncedeLeonInletonFebruary21,2008. 108

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Figure4-9. A)Lateralvelocities,un(m/s),fromthesurface(solid)andbottom(dotted;positivenorthward)fromStation2;B)Verticalshearinthelateralvelocities(vnsurface)]TJ /F3 11.955 Tf 11.95 0 Td[(unbottom)fromStation2(m/s).Negativelateralshearmeanscentrifugallyforcedowforebbowsaroundtheinshorebend(RB),andpositivelateralshearmeanscentrifugaltypeowfromRAwithweaksurfacelateralows.Shadingalongthezerolineindicatesood(grey)andebb(black). 109

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Figure4-10. Contoursofresidualstreamwiseow(cms)]TJ /F4 7.97 Tf 6.58 0 Td[(1)ascalculatedfromtheleastsquaresttothesemi-diurnaltidalconstituentacrossTransectAfromPoncedeLeonInletonSeptember5,2007.Lateralvelocities(arrows)aretheanomalyoftheverticalprolesrelativetothedepthaveragedproleandtheaverageofeveryotherproleisshown.Northisonthelefthandsideofthegure,andpositivevelocityisoutoftheinlet(inthestreamwisedirection)andtowardtheNorth(inthelateraldirection). Figure4-11. Contoursofresidualstreamwiseow(cms)]TJ /F4 7.97 Tf 6.58 0 Td[(1)ascalculatedfromtheleastsquaresttothesemi-diurnaltidalconstituentacrosstransectAfromPoncedeLeonInletonFebruary21,2008.Lateralvelocities(arrows)aretheanomalyoftheverticalprolesrelativetothedepthaveragedproleandtheaverageofeveryotherproleisshown.Northisonthelefthandsideofthegure,andpositivevelocityisoutoftheinlet(inthestreamwisedirection)andtowardtheNorth(inthelateraldirection). 110

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Figure4-12. A)Tidalamplitudeandlow-passedwaterlevelduringmooredobservations,(2)timeofFebruary21,2008towedsurvey;B)lowpassedalongshelf(solid;positivenorthward)andcrossshelf(dotted;positiveeastward)windstress(Pa);C)subtidalstreamwisecurrents(positiveseaward)fromalldepthsatStations1(dotted)and2(solid),D)lateralshearbetweenthesubtidalstreamwisecurrents(bottom)betweenStations1and2;E)streamwiselateraladvectiveterm;F)bottomfrictionparameterizationusingCD=0.0025.SolidverticallinesdenotetimesoflargealongorcrossshorewindsasdiscussedinSection 4.5 andverticaldashedlinesdenotespringtides. 111

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CHAPTER5RESPONSEOFRESIDUALFLOWSTOTWOTROPICALSTORMSINASUBTROPICALTIDALINLET 5.1Introduction Residualcirculationintidallydominatedinletshasbeenfoundtodependonlateralvariationsinlength,bathymetricshape,frictionandrotation[ HenchandLuettich 2003 ; LiandO'Donnell 1997 2005 ; Winant 2008 ].Forashallow,sinuous,frictionalbasinwithachannelandshoalsoneitherside,nonlinearadvectiontermsbecomeimportanttosupplementthepressuregradientandfrictionalbalancewhilerotationaleffectsarenegligible[ Lietal. 2008 ; Winant 2008 ].Subtropicalinletsfeatureaperiodicprecipitationandbaroclinicpressuregradientsareoftenweak,withsmalltonegligibleinuenceonthetidallydominatedresidualcirculationduringmostoftheyear.Thisattributeofweakbaroclinicityallowsfordirectobservationsonthemodulationoftidallygeneratedresidualowsduetoexternalforcingmechanismsastidalowsarenottypicallyinuencedbybarocliniceffects. Residualcirculationinsubtropicalinletsismodied,indifferentways,byexternalforcingmechanismssuchastidalvariabilityandwinds.Laterallyshearedresidualcurrentsexhibitfortnightlymodulationwithincreasingmagnitudeofexchangeowduringspringtides[ Valle-Levinsonetal. 2009 ; WaterhouseandValle-Levinson 2009 ].Residualcurrentsaremostsensitivetochangesinwaterlevelcomparedwithvariationsintidalamplitude[ LiuandAubrey 1993 ].Variationsinwaterlevelcausedbyatmosphericforcingonthecontinentalshelfcauseunidirectionalresidualows[ Smith 1977 ; Wong 1987 ].Elevatedmeanwaterlevelshavebeenfoundtoalsooccurinsideabay(abovethemeansealevel),asaresultofriverdischarge,groundwaterorsurfacerunoffthatmodulatetheresidualtransportwithincoastalinlets[ Mehta 1990 ].LowfrequencymodulationofresidualmasstransportduetochangesinwaterlevelintwoFloridainlets(SebastianInlet[ Liu 1992 ]andFortPierce[ Smith 1983 ])showedthatmasstransportincreasedaswaterlevelincreased.Residualexchangethroughan 112

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inlettoLakePontchartrainoccurredduringlarge-scaleeventscharacterizedbyvolumeuxesuptosixtimesgreaterthanthenormaltidalprism[ SwensonandChuang 1983 ],highlightingtheimportanceofunderstandingtheeffectofsubtidalforcingmechanismstoresidualcurrents. Wind-drivenowhasbeenfoundtobeofequalorgreaterimportancethantidalorgravitationalcirculationinbays[ WeisbergandSturges 1976 ].Windshavebeenseparatedintoremoteandlocalwindsduetothedifferingresponsesofthewinddrivenow.RemoteeffectsarecausedbychangesinwaterlevelasaresultofEkmantransport[e.g. WangandElliott 1978 ],drivingexchangebetweeninletsandoffshorewaterbodies[ Smith 1977 ]. WongandWilson [ 1984 ]foundstrongcouplingbetweenwaterlevelinsideofbaysandthoseontheshelf.Incontrast,localwindeffectsmodifytheresidualcurrentsasaresultofanalong-estuarywindstresses.Surfacewaterisfrictionallycoupledtothelocalwindstresswhilethebottomwaterrespondstothewind-generatedsurfaceslope(inoppositedirection; Wang 1979 ).Localwindeffectstendtovarywithstraticationandfrequencyofwindevents[ WongandValle-Levinson 2002 ].Bi-directionalsubtidalcurrentsinDelawareBay,asaresultoflocalwindeffects[ WongandMoses-Hall 1998 ],werefoundtodominatetheremote(along-shore)winddrivencirculation.Thelocalwindeffectenhancedthebi-directionalsubtidalvelocitydrivenbythelocalwindeffect,anddiminishedtheunidirectionalremoteeffect[ Garvine 1991 ; JanzenandWong 2002 ; Wang 1979 ].Whenbathymetryofthebasinvaries,theresidualwind-drivenowhasbeenfoundtobeinthesamedirectionasthewindovershallowswithareturnowinthechannel[ Csanady 1973 ; Winant 2004 ; Wong 1994 ]. Duringextremeevents,suchashurricanesandtropicalstorms,residualcirculationpatternsaredisruptedandmodiedbythelargechangesinwaterlevel,highwindsandprecipitationoversmalltimescales.Instratiedestuaries,hurricanesarecapableofmixingthewatercolumnthroughincreasedvelocityshear[ Lietal. 2007 ].IntheChesapeakeBay,residualowsduringahurricaneweredrivenbyanunequal 113

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combinationofwindforcingandbuoyancyforcing[ Valle-Levinsonetal. 2002 ].ObservationsfromSebastianInlet,onFlorida'sEastcoast,indicatedthatsuper-elevatedwaterlevelsinsidethelagoon,andshort-livedpulsesoffreshwateroutowinterruptedthetypicalresidualcirculationinconjunctionwithlongertermsealevelchangesduetoremotewindeffects[ Liu 1992 ].Inthisstudy,theresidualcirculationisstudiedinSt.AugustineInletontheEastcoastofFlorida,wherethebackgroundalong-channelbaroclinicpressuregradientistypicallyweak.Theobjectiveofthisstudyistodeterminehowlaterallyshearedresidualowsinasubtropicalinletaremodiedbythepassageoftropicalstorms. 5.2StudyArea St.AugustineInletisanarrow,dredged,coastalinletconnectingFlorida'sIntracoastalwaterwaytotheAtlanticocean.Thebathymetryacrosstheinlethasashallowbank(6m)onthenorthside,followedbyadeepchannel(15m;Figure 5-1 ).Insideoftheinlet,thebasinexpandsandsplitsintothreebranches:SaltRunandthetwobranchesoftheIntracoastalWaterway(MatanzasrivertotheSouthandtheTolomatorivertotheNorth).Florida'sIntracoastalwaterwayisaninlandwaterwayrunningthelengthofFlorida'sEastcoast.SaltRunisashort(4500minlength)semi-enclosedbasinlocatedsouthoftheentrancetoSt.AugustineInlet. Theregionisaffectedbyaperiodicprecipitation,mostnotablybetweenJuneandNovember(2008recordinFigure 5-2 ).ThesalinitydistributionalongtheinlandwaterwaybetweenPellicerCreek,SanSebastianRiverandPineIslandshowsacorrelationbetweensalinityandprecipitationwithlargergradientsinsalinityinthelocalriver(PellicerCreek)andsmallergradientsclosesttotheinletwithinthetheinlandwaterway(SanSebastianRiver). Onthesouth-eastcoastoftheUnitedStates,thesummersof2007and2008wereactiveyearsforhurricaneandtropicalstorms,while2006wasrelativelyinactive,withnomajorhurricanesmakinglandfallonthecontinentalUnitedStates.During2008, 114

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twotropicalstormspassedinthevicinityofSt.AugustineInletalongtheEastcoastofFlorida:tropicalstormsFay(15Augustto26August,2008)andHanna(28Augustto7September,2008;Figure 5-3 ).TropicalstormFaywasaslowermovingstormcomparedwithHanna,remaininginalocalizedregionoffshoreoftheeastcoastofcentralFloridaforover36hours.Precedingthesestorms,precipitationwasfrequentbeginninginJunewithpulsesoflargerprecipitation(>5mm/day;Figure 5-2 ).Waterlevel,windsandprecipitationincreasedasaresultofthearrivalofthestormsandtheirinuenceontheresidualowisdiscussedinSection4. 5.3FieldObservations Datacollectionconsistedoffoursurveysbetween2006and2008aswellasaperiodofmooredRDInstrumentsacousticDopplercurrentproler(ADCP)measurementsin2008.Thesurveysconsistedoftowed1200kHzADCPtransectsaswellashydrographicprolesusingaSeabirdSBE19PlusConductivity-Temperature-Depth(CTD)proler.Resultsfromthe2006surveyarediscussedindetailin Webbetal. [ 2007 ]andcomparedtoresultsfromathree-dimensionalmodeloftheGuanaTolomatoMatanzasNationalEstuarineResearchReserve(GTMNERR)systemin Shengetal. [ 2008 ]. TowedADCPmeasurements,takenoverasemi-diurnal(M2)tidalcycle,followedvariousrepeatedpathswithinSt.AugustineInletwithaconsistenttransectacrossthemouthoftheinlet.Transectsthatcrossedthemouthoftheinlethadsmallvariationsinposition(<100m)andbearingbetweensurveys.Thetransectsacrossthemouthoftheinletwereusedtodeterminehowtheresidualexchangeatthemouthoftheinletchanged,dependingondifferingforcingconditions.Surveydatawereinterpolatedontosectionsofequallengthwith10mgridcellsinthehorizontaland0.5mintheverticalforacross-channeltransects.Auniquegridwasestablishedforeachofthefourtowedsurveysduetothevariationinpositionofthecross-inlettransect.AttotheM2tidalconstituent,usingthedatawithinaparticulargridcell,wasappliedusingaleast 115

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squarestmethodtoremovethetidalsignal[ Lwizaetal. 1991 ].Consequently,residualvelocitieswereobtainedforeachgridcellalongthetransectlineofthesurveyacrossthemouthoftheinlet. AswiththetowedADCPtransects,locationsofthehydrographicproleswereatdifferentlocationseverysurvey(2006to2008;Figure 5-1 ).However,lateralandverticaldensitygradientswerecalculated,whenpossible,usingthehydrographicdatatodeterminethevariabilityinstratication. Longtermmeteorologicaldata(precipitation,airtemperatureandpressure)wereobtainedfromtheGTMNERRPellicerCreekmeteorologicalstation(Figures 5-1 and 5-2 ).WinddatawereobtainedfromSt.AugustineBeachWindstation(NationalClimaticDataCenterStation994410)at29.867N,-81.267W.Winddatawerecorrectedtoanelevationof10mandwererotatedtobealignedwiththecoastline(8counterclockwise).Thealongandcross-shorecomponentsofthewindstresseswerecalculatedusing LargeandPond [ 1981 ]oftheform (sx,sy)=Cair(uw,vw)jVwj(5) wheresxandsyarethecrossandalong-shorewindstresses,Cisthedragcoefcient(afunctionofwindspeed),uwandvwarethewindvelocities,jVwjisthemagnitudeofthewindspeedandairisthedensityofair.Lowfrequencyvariationsofmeteorologicaldataincludingwindstresscalculationsandwaterlevel,temperatureandsalinitydatawereobtainedusingaLanczoslterwithahalf-powerpointof34hours. Waterlevel,surfacesalinityandtemperaturerecordswerealsoobtainedfromtheGTMNERRstationsatPellicerCreek,SanSebastianRiverandPineIsland.AlthoughtheGTMNERRandmooredADCPpressurerecordswerenotreferencedtoaparticulardatum,waterlevelvariationsateachstationwereobtainedbyremovingthemeandepthovertherecordlength(oneyearfortheGTMNERRrecords;e.g. WongandValle-Levinson 2002 ). 116

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ThewaterlevelsensorfromtheGTMNERRstationatPineIslandsufferedfromdepthvariations(1to10cm)afterinstrumentre-deploymentsduring2008.Thissensorwasmoored21kmNorthfromthemouthofSt.AugustineInletandnoothermeasuredwaterleveldatafromtheIntracoastalwaterwaywereavailableatthisdistance.Therefore,waterlevelmeasurementsfromthisstationprovidedimportantinformationonthebarotropicpressuregradientbetweenthemouthoftheinletandalongtheIntracoastalWaterway.TocorrectforthedepthvariationsvemanualadjustmentsweremadetothewaterleveldataonAugust1(+0.01m),August22(-0.02m),August23(-0.02m),September4(+0.03m)andSeptember9(+0.11m),2008.Despitetheseadjustments,adriftremainedinthesubtidalpressurerecordafterthetropicalstorms,whichcouldnotbecorrected.Therefore,waterleveldatafromPineIslandwasused(withcaution)tocalculatethebarotropicpressuregradientforcomparisontotheothertermsinthealong-basinmomentumequation.Thesubtidalwaterlevelfromthissensorwasobtainedfromalow-passedde-meaned(depthmeanminustheannualcycleofthewaterlevel)record. A600kHzbottommountedADCP(Figure 5-1 )wasmooredattheentrancetoSt.AugustineInletinthechannelrecordingprolesofcurrentvelocity,sealevelpressureandwatertemperature.Currentsweremeasuredin0.5mbinsatapingrateof1.5s,averaging400samplesperensemble.TheADCPwasmooredat15mdepthandrecordedcontinuouslyfromJuly18,2008untilSeptember18,2008.Currentvelocitieswererotatedtotheangleofmaximumvariancefortheentirerecord(8counter-clockwise)suchthatthealong-channelvelocity,u,wasalignedwiththeprincipalaxisoftheinlet,withpositivevaluesdirectedseaward. 5.4ResidualFlows 5.4.1LateralStructureofResidualExchange ThelateralstructureofresidualowsatthemouthoftheinletwasconsistentforallfourtowedADCPsurveys(Figure 5-4 ).Sinceeachofthefoursurveysfollowed 117

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adistincttransectbearingacrossthemouthoftheinlet,theacross-inletbathymetryshowninFigure 5-4 wasvariable,eachcontainingadeepchannelwithashoaloneitheroneorbothsides.Asin Webbetal. [ 2007 ],thealong-channelexchangewaslaterallyshearedwithinowinthedeepchannelandoutowoccurringovertheshoals.LateralvelocitiesalongtheNorthandSouthshoalswerestronglyconvergenttowardthemiddleofthechannel.Theobservedresidualstructurewasduetooodowsenteringalongthestraightchannelaxis,whiletheebbowswereconstrictedonexitfromtheinlet,resultinginameanconvergingoutowintotheinlet[ Webbetal. 2007 ].Theresidualowreectstheasymmetricpatternoftheood-ebbows. Newinformationgarneredfromthefoursurveysincludedthevariabilityandpersistenceoftheresidualowstructureobservedinitiallyin2006by Webbetal. [ 2007 ].During2007,surveyswereconductedduringbothaneap(18October2007)andaspringtide(26October2007)inaperiodwherelowfrequencywaterlevelchangewassmall.Whileinowremainedofrelativelyequalsize,outowincreasedduringspringtidesandreducedduringtheneaptides.Thiswasconsistenttothemodulationofresidualvelocitiesobservedinothersubtropicalinlets[ Valle-Levinsonetal. 2009 ]includinginPoncedeLeonInlet,100kmtotheSouth[ WaterhouseandValle-Levinson 2009 ].PoncedeLeonInlet,alsoconnectedtoFlorida'sIntracoastalWaterway,isatidallydominatedinletthathassimilarlateralvariationsinbathymetryasSt.AugustineInletwithashallowerchannel(12m). Longtermvariabilityofthenon-tidalowinthechannelfromthemooredADCPshowedthatovertwomonths,consistentinow(ofvaryingmagnitude)wasobserved,exceptduringthetwotropicalstorms(Figure 5-5 ).Beforetheinuencefromthetropicalstorms,depth-averagedalongandcross-channelvelocitiesdecreasedduringneaptidesandtendedtobestrongerduringspringtides.Theselongtermobservationswereinagreementwiththetowedsurveystakenoverasingletidalcycleshowingweakerlateral 118

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convergencetowardthechannelduringtheneaptidesurvey(October18,2007;Figure 5-4 ). 5.4.2Baroclinicity Along-andcross-channelbaroclinicitywerefoundtobeweakduringthesurveys.Prolesoftwereplottedasthetidalmeanaswellasduringmaximumebbandoodforeachsurvey(Figure 5-6 ).Prolesduringoodwerewell-mixedandinallbuttheOctober18,2007survey,ebbproleswerealsowellmixed.DespitethelargeebbstraticationonOctober18,2007,therewaslittlenoticeablechangetothemeanresidualvelocityinthechannelasaresultofasmallmeanverticaldensitygradient(=z=0.1kgm)]TJ /F4 7.97 Tf 6.59 0 Td[(4whereisthedensityofwaterandzistheverticalcoordinate;Figure 5-4 ).Althoughverticalstraticationmaynothavebeenplayingaroleinthedynamicsoftheinletduringthetowedsurveys,thealong-basindensitygradient(=x)likelyinuencedtheresidualow.Fortheremainderofthisstudy,along-basincharacteristicswillbeusedtodescribethestreamwisecoordinatesystemthatencompassesboththeinletandtheIntracoastalWaterway.AstheIntracoastalWaterwayisperpendiculartotheinlet,along-basingradientsdescribedynamicsvaryingalongtheprincipalaxisoftheIntracoastalwaterway(North-South)andtheinlet(East-West). Longtermvariationin=xduring2008wasobtainedusingtwoGTMNERRwaterqualitystationsfromwithintheIntracoastalWaterway:PineIslandandSanSebastianRiver.AlthoughbothstationsarelocatedwithintheIntracoastalWaterway(andnotattheinletmouth),thebackgroundbaroclinicpressuregradientaffectingtheinletcanbeobtainedfromthebaroclinicpressuregradientbetweenthesetwopointsduetothecloseproximityofSanSebastianRivertotheSt.AugustineInlet(4.5kmtotheSouth).Thedepth-averagedalong-basinbaroclinicpressuregradientwascalculatedusing g xH(5) 119

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wherethedepthHistakenasameanbetweenthetwostations(3m),gistheaccelerationcausedbygravity,thealong-basindistancebetweenthetwostationsisx=21kmanddensitywascalculatedfromtheequationofstatedusingobservedsalinity,temperatureandpressure. Duringearly2008,thealong-basinbaroclinicpressuregradientwasweakwithvaluesbelow110)]TJ /F4 7.97 Tf 6.59 0 Td[(5ms)]TJ /F4 7.97 Tf 6.58 0 Td[(2(Figure 5-7 ).PulsesofanincreasedbaroclinicpressuregradienttermcoincidedwithprecipitationeventsinlateFebruaryandearlyMarch.Inlate2008,thebaroclinicpressuregradientincreasedatthebeginningoftropicalstormFaytogreaterthan110)]TJ /F4 7.97 Tf 6.58 0 Td[(5ms)]TJ /F4 7.97 Tf 6.59 0 Td[(2andremainedelevatedduringthepassageoftropicalstormHanna.Theeffectofastrengthenedbaroclinicpressuregradientinthechanneloftheinletwilltendtoreducesurfaceinowandincreaseinowatdepth.DuringthesurveyonSeptember19,2008,thebaroclinicpressuregradientwas1.310)]TJ /F4 7.97 Tf 6.59 0 Td[(5ms)]TJ /F4 7.97 Tf 6.58 0 Td[(2.Theinuenceofthebaroclinicpressuregradientwillbefurtherexploredusingthemooredcurrentprolerresults.Otherinuencesontheverticalstructureandevolutionofthesubtidalowwasthroughwindeffectswhichwillbediscussednext. 5.4.3RemoteandLocalWindEvents Windandwaterlevelactinconjunctiontomodifytheowinalocalandremotesense.Locally,windsblowingonshorewilldriveatwolayercirculationwithsurfaceowinthedirectionofthewindandbottomreturnowasaresultofthewaterlevelsetupinsidethebasin.Remotewindeffectsmaycauseanincreaseinwaterlevelfromanoffshorehighinwaterlevel,inturnresultingfromanalongshorewinddrivenonshoreEkmanux.Thisremoteforceactsintheentirewatercolumninaunidirectionalsense.Whenwaterlevelrisesinsidetheinlet,owisdrivenintotheinletandaswaterleveldecreases,owisdrivenoutoftheinlet.Giventhelateralstructureoftheresidualcirculationobservedfromthetowedsurveys,theunidirectionalremotewindeffectscausedbycoastalset-downwilldecreaseinowinthechannel,whileincreasingthe 120

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outowovertheshoals,asobservedinPoncedeLeonInlet[ WaterhouseandValle-Levinson 2009 ]. TheresponseofSt.AugustineInlettowindstressesonwaterlevelandcurrentswascomplexastheinletisorientedperpendicularlytotheIntracoastalwaterway.Thecorrelationcoefcients(RC)betweenwind,waterlevelanddepth-averagedalong-channelcurrents( u,wheretheoverbarrepresentsadepth-averagedquantity)wereinvestigatedtodeterminethewinddirectioncausingthemajorityoftheforcingonthesystem. WaterlevelatPineIslandandfromthemouthoftheinletwerewellcorrelated(Rc=0.97),indicativethatforcingatthecoastaffectstheentiresystemequallyoverthetwomonthrecord.Thiscorrelationwaslargerthanfoundinadynamicallylongandwidetemperateestuary(e.g.DelawareBay, JanzenandWong 2002 ).Cross-shorewindstresses(paralleltotheinletandperpendiculartotheIntracoastalWaterway)weremostcorrelatedwithwaterlevelchangesatthemouthoftheinletandatPineIsland(Rc=)]TJ /F5 11.955 Tf 9.3 0 Td[(0.8forboth).Atthemouthoftheinlet,cross-shorewindsarealignedwiththeaxisoftheinlet.Positivewindstresses(outoftheinlet)willgenerateanegativechange(decrease)inthewaterlevelasthewindpusheswateroutoftheinlet.Thiswillacttoemptytheinlet,andbyconservationofvolume,thewaterlevelatPineIslandalsodecreases. Along-shorewindstresseswerecorrelatedwithwaterlevelsetupbetweenthemouthoftheinletandPineIsland(=x;RC=0.55).Givenapositivealong-shorewindstress(windsblowingtowardtheNorth),waterlevelset-upsatPineIslandcomparedwithatthemouthoftheinlet,drivingapositivechangein=x.Therefore,thealong-shorewindstressmodiedthebarotropicpressuregradientalongthebasin.Correspondingly,depth-averagedalong-basinvelocityattheinlet( u)wasbettercorrelatedwiththealong-shorewindstress(Rc=0.54)thanthecross-shorewindstress(Rc=)]TJ /F5 11.955 Tf 9.3 0 Td[(0.37). 121

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Frommasscontinuity,remotelyforcedalong-basinvelocityinaninletisproportionaltothetimerateofchangeofthewaterlevelatthemouthoftheinlet(=t; Garvine 1991 ; JanzenandWong 2002 ).Asthedepth-averagedvelocitywasnegativelycorrelatedto=t(Rc=)]TJ /F5 11.955 Tf 9.3 0 Td[(0.63),aportionofthesignalinthedepth-averagedvelocitywasdrivenbytheremoteforcingonthesystemaswellasbythealong-shorewindstress,asfoundabove.Althoughstatisticalcorrelationsareusefulfordeterminingsignicantrelationshipsbetweenvariables,theyoftendonothighlightvariabilityinforcingdynamicsofasystem.Therefore,furtherobservationsonthevariationsofthesubtidalvelocityasaresultofthesechangesinlocalwindandremoteforcingsweremadeusingtheprolesofcurrentvelocityfromthemooredADCPdata. 5.4.4WindsandAlong-basinVelocityAnomaly Variationsinthesubtidalvelocitystructureasaresultofthelocalandremoteforcingontheinletcanbedistinguishedwiththevelocityanomaly,u(z,t))]TJ ET q .478 w 399.63 -292.16 m 406.39 -292.16 l S Q BT /F3 11.955 Tf 399.63 -299.47 Td[(u(t).Theamplitudeanddirectionof u(t)isneededinconjunctionwiththevelocityanomalytounderstandtheeffectofthewind.AstheowatthemooredADCPisgenerallyinowingwithalogarithmicshape,followingthelawofthewall[e.g. Monismith 2010 ],thetypicalvelocityanomalywillexhibitatwo-layerstructure:negativeatthesurfaceandpositiveatthebottom(Figure 5-9 ).Remoteforcingswillnotaffectthetwolayerstructureoftheanomalybutwillmodify u(t).Givenanoffshorewindstress,surfaceinowwillbereducedandbottominowwillincreaseresultingina3layeranomaly(Figure 5-9 B).Onshorewindswillstrengthenthenegativeandpositiveshapeoftheanomaly(Figure 5-9 C). 5.4.4.1Pre-stormvelocities Beforethearrivalofthetropicalstormsinthesummerof2008,localwindeffectsonthevelocityanomalywereobservedduringthreeconspicuousevents(Figure 5-10 ).Notethatallwinddirectionsarereferencedtothealong-shorecoordinatesystemwhichisrotated8counterclockwisefromNorth.Ingeneral,windswereweak(<5ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)and 122

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variedbetweenalongshore(from180;towardthenorth)andoffshorewinds(from270)overthreeperiods(Figure 5-10 A).Waterlevel()andthechangeinwaterlevel(=t)wererelativelyconstantexceptbetweenAugust3andAugust7,2008(Figure 5-10 B).Asthewindschangeddirectionfromalongshoretooffshore,inowvelocitywasreducedatthesurface(enhancednegativeanomalyatthesurface)beginningonJuly21,July31andAugust7,2008(Figure 5-10 D).Betweenthesecondandthirdperiod(August3toAugust7,2008),thelargest=toccursduringthispre-stormperiodasaresultofanincreaseandsubsequentdecreaseinwaterlevel.Thedepthaveragedvelocity, u(t),decreasedaswaterleveldecreasedbutshowedlittlechangewithwaterlevelincrease(Figure 5-10 C). Asimilarremoteeffectwasobservedduringaweakchangeinwaterlevelduringtherstoffshorewindevent(July21,2008).Althoughthewaterlevelchangewassmall(10)]TJ /F4 7.97 Tf 6.58 0 Td[(6ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1),theresponsecausedowtobemoredepth-uniformthatoverwhelmedthelocalwindresponseoverashortperiod.Thisresultedinaweakeningofthethree-layervelocityanomalyonJuly22,2008(Figure 5-10 D).Therefore,theresponseofthesubtidalvelocitytolocalwindeffectswasareducedsurfaceinowwhenwindsblewoffshore.Thiswindblewintheoppositedirectiontothevelocityinthechannelandresultedinreducedinowdownto4.5mdepth.Anexpectedstrengtheningofthenear-bottomvelocityanomalywithoffshorewindswasnotconsistentlyobservedinrelationtothelocalwindeffect. 5.4.4.2Stormvelocities DuringtropicalstormsFayandHanna,thevelocityanomalywasmorecomplexthanbeforethetropicalstormsduetothestrongwindsandwaterlevelchangesaswellasanincreasedbaroclinicpressuregradientoverpartofthestormperiod(Figure 5-11 ).AfterthepeakofFay(August22,2008asdeterminedfromthepeakinatmosphericpressure,Figure 5-4 ), u(t)reversedtooutowfor2days(Figure 5-11 C).Assoonas u(t)reversedtopre-stormconditions(negativevelocity),gravitationalcirculation(positive 123

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surfaceandnegativebottomvelocityanomaly)wasobservedforapproximately4.5dayswhenwindswereweak(<4ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)andvaryingindirectionfromalongshoretooffshore(Figure 5-11 AandD).Thevelocityanomalywaslikelycausedbyacombinedresponsetotheenhancedbaroclinicpressuregradient(observedfromstationsalongtheIntracoastalWaterway,Figure 5-7 B)aswellasapeakinoffshorewindsmidwaythroughtheassumedgravitationalexchange(Figure 5-11 D).Thistwo-layeranomalyweakenedwithtimeandbecamethree-layeredinconjunctionwiththeweakeningbaroclinicpressuregradientandasmallpeakofoffshorewinds.ThisresponsedidnotpersistnoroccurinthecompletewatercolumnduringHanna. AfterHanna(September7,2008),athree-layeredresponseinthevelocityanomalywasobservedsimilarlytothatobservedasaresultofanoffshorewindeventwheresurfaceandbottomvelocitieswerepositivewhilethemiddleofthewatercolumnwasnegative(Figure 5-11 D).However,sincewindswereveeringfromoffshoretoalongshore,thiswaslikelyaresponseduetoaweakbarocliniceffectaswellasalocalwindeffect. Largechangesinwaterlevel(=t210)]TJ /F4 7.97 Tf 6.59 0 Td[(6ms)]TJ /F4 7.97 Tf 6.58 0 Td[(1)weremostoftenassociatedwithincreasedwindspeedcoincidingwithanappropriatewinddirection.Eachpeakin=thadanassociatedpeakin u(t).Therstpeakwasassociatedwithincreasedwaterlevel(justprecedingAugust15,2008),thatdevelopedaswindspeedsdecreasedbutveeringfromoffshoretoalongshore(Figure 5-11 BandC).Thesecondpeak(August21,2008)alsooccurredafterthemaximumwindspeedsbutwithwindsdirectedfrom72(onshore).Theeffecton u(t)wasweakasthedepthaveragedvelocityonlyincreasedbyasmallamountcomparedwiththechangein=t.Thethirdpeakin=toccurredwiththemaximumwindspeedsobservedduringFay(14.5ms)]TJ /F4 7.97 Tf 6.58 0 Td[(1from135)with u(t)reversingdirection.DuringHanna,therewerethreepeaksin=t,twonegative(decreasingwaterlevel)andonepositive(increasingwaterlevel).Therstnegativepeakwasaresultoftemporaryweakeningonshorewinds(decreasing 124

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waterlevel).Thewindspeedthenincreased(onshore)andwaterlevelincreased.Asthewindveeredtowardalongshore(towardtheNorth),waterlevelreachedamaximum.Windspeedthendecreased,waterleveldecreased,and=twaslargeandnegative.Depth-averagedvelocityfollowedthepatternof=twithdecreasingandincreasingmagnitude. Thelocalwindresponseonthevelocityanomalywasobservedtwice.TherstwasbeforethearrivalofFayandoccurredwhensurfacevelocitywasreduced(twopulses)duetooffshorewinds.Thisresultedinpositivesurfacevelocityanomaliesandweakenedbottomvelocities(Figure 5-11 D).ThesecondinstanceoflocaleffectswasafterFayandbeforeHanna,whenwaterlevelchangedlittle,thewinddirectionwasconstant(from130)]TJ /F5 11.955 Tf 11.49 0 Td[(90;onshore)andwindvelocityhadtwopulsesofincreasedspeed.Thewatervelocityanomalyrespondedwithtwopulsesofincreasedsurfaceinowandbottomoutow.Althoughthiswasalocaleffect,onshorewindsreinforcedthevelocitystructurewithinthechannel.Duringthetropicalstorms,theincreasinginuenceofthealong-basinbaroclinicityandsurfacewindstressesmodiedthealong-basinmomentumbalance.Todeterminetheirsize,thetermsinthealong-basinmomentumbalancearecalculatedanddiscussednext. 5.4.5Along-basinMomentumBalance Intidallydominatedinlets,frictionaleffectsarebalancedbypressuregradientsandadvection[ LiandO'Donnell 1997 2005 ; Winant 2008 ].Inthisinlet,lateraladvectionhasbeendeterminedtobeinuentialtotheresidualowsatthemouthoftheinlet[ Webbetal. 2007 ].Asextremeeventsoccur,thisbalanceismodiedwitheffectsfromalong-basinbaroclinicityandwindeffectsbecomingimportantinthebalance.Asnotedpreviously,atwo-layeredexchangeinthevelocityanomalywasobservedafterthetropicalstorms.Thevertically-averaged,subtidalalong-basinmomentumbalancecan 125

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beapproximatedas @ u @t+ u@ u @x+ v@ u @y+ w@ u @z)]TJ /F3 11.955 Tf 11.96 0 Td[(f v=)]TJ /F3 11.955 Tf 9.29 0 Td[(g@ @x)]TJ /F3 11.955 Tf 13.15 8.09 Td[(g @ @xH+s H)]TJ /F6 11.955 Tf 13.68 8.09 Td[(bx H(5) wherethersttermislocalacceleration(ofdepthaveraged,subtidalalong-basinvelocity)followedbythethreenonlinearadvectiveterms,whereoverbarsrepresentdepthaveragedquantities,andtheaccelerationsduetoCoriolisdeection.Ontherighthandsideoftheequationarethebarotropicandbaroclinicpressuregradients,followedbythesurfaceandbottomstresses.Thethirdnon-linearadvectivetermcanbescaled[ MunchowandGarvine 1993 ]suchthat w@ u @z@ @t u H(5) aswisrelatedto@=@t.Bottomstressesinthealong-basindirectionwerecalculatedusingaquadraticfrictionapproximationwhere bx=CDubjVbj(5) whereCDisaconstantbottomdragcoefcient(0.0025),ubisthealong-basinbottomvelocityandjVbjisthemagnitudeofthebottomvelocity. FromthemooredADCPandthesensorsofGTMNERR,allofthetermsinthedepth-averagedmomentumequationwerecalculatedoverthesubtidalperiodexceptforthealong-basinandlateralnon-linearadvectivetermsastherewasnosuitablevelocitydatainthealongandcross-basindirection.Bottomandsurfacestresses,verticalnon-linearadvectionandbaroclinicpressuregradientswerecalculatedusingabasin-averageddepth,H,of3m.As u(t)variedaccordingtothealong-shorewindstress(sy;Section 5.4.3 ),accelerationsduetoalong-shorewindstresseswereinputintothealong-basinmomentumequation,insteadofthecross-shorewindstress. LocalandCoriolisaccelerationswereanorderofmagnitudesmallerthantheothertermsinthemomentumequation(barotropicandbaroclinicpressuregradientterms 126

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andaccelerationsduetowindstressandbottomfriction;Figure 5-12 ).Theverticaladvectiveaccelerationtermwassmallvaryingbetween-1and-210)]TJ /F4 7.97 Tf 6.59 0 Td[(5ms)]TJ /F4 7.97 Tf 6.58 0 Td[(2withthespring-neapcycle(Figure 5-12 A).Peaksgreaterthan510)]TJ /F4 7.97 Tf 6.59 0 Td[(5occurredinboththebarotropicpressuregradientandthesurfacewindstressduringtropicalstormFay(Figure 5-12 B).Bottomstresswasweakerthanthesurfacestressduringthetropicalstorms,whilebottomstresswasstrongerprecedingthestorms(Figure 5-12 C).ThestrengtheningofthebaroclinicpressuregradientwasseenastwopulsesassociatedwithtropicalstormsFayandHanna,largerinmagnitudethantheaccelerationsduetosurfaceandbottomstresses.Theaccelerationsassociatedwiththecross-shorewindstressfollowedthesameuctuationsasobservedinthebarotropicpressuregradientaftertropicalstormFaywhilebeforethestorm,thevariabilitydidnotfollowthepressuregradientterms(Figure 5-12 C). Thealong-basinbarotropicpressuregradient(g@=@x)wascomparedwiththesumoftheothercalculatedtermstohighlighttheimportanceofeachtermintheoverallbalance.Along-shorewindstresswasusedinthecalculations.Precedingthetropicalstorms,thepatternofthebarotropicpressuregradientwaswellreproducedbythethewindandbottomstresses(Figure 5-13 ).Whenalltheothertermswereadded,thebarotropicpressuregradientwassmallerthanthesummation.Thisindicatedthatthenon-linearterms(along-andcross-basinadvection)werelikelyinuencingtheowandwererequiredtomakethecompletebalanceinthealong-basindirection.Themagnitudeandvariabilityofthesemissingadvectivestermswerelikelysimilartothedifference(Figure 5-13 C)calculatedbetweenthebarotropicpressuregradient(Figure 5-13 A)andthenothertermsinthemomentumequation(Figure 5-13 Bi).Asdiscussedabovebyobservationsfromthevelocityanomalyattheinlet,accelerationsassociatedwiththealong-basinbaroclinicityandsurfacewindstressbecomemoreimportantuponthearrivaloftropicalstormFay. 127

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AfterFay,thesumofthealong-shorewindstresswithbottomstressonceagainhasasimilarshapetothebarotropicpressuregradient(Figure 5-13 ).However,thefullbalance(includingallthetermscalculated)wasmuchlargerthanthebarotropicpressuregradientwithanotableinuenceasaresultofthebaroclinicpressuregradient.Afterthetropicalstorms,thenon-linearadvectivetermswerelikelycontributingtothedynamicswithintheinlet,asfoundby[ Webbetal. 2007 ]andlikelyactedtoredistributeincreasedmomentumwithintheinlet[ WaterhouseandValle-Levinson 2009 ].Theinclusionofthesetermswouldprovideabetterclosuretothebalancewithintheinlet. Theinuenceofthebaroclinicandwindstresstermsduringandafterthetropicalstormsshowedaninuencetoalong-basindynamics.Thiswasobservedbyvariabilityinthesubtidalvelocitiesaswellasthesubtidalvelocityanomaly.Althoughtypicallytidalinletsarecontrolledbythebalancebetweenbarotropicpressuregradient,frictionandadvection,tropicalstormsmodiedthedynamicsmostimportantlybyincreasedprecipitation,windsandwaterlevel. 5.5Conclusions Residualcirculationinasubtropicalinletisconsistentovermanyobservationsperiodsandmodicationstothelateralstructureandmagnitudeofthispatternvariesdependingonthespring-neapcycle,localandremotewindeffectsandalong-basinbaroclinicity.Towedsurveys,conductedoverfourtidalcyclesduringbothspringandneaptides,determinedthatthelateralstructureofinowinthechannelandoutowovertheshoalswasconsistentexceptduringtropicalstorms.Beforethetropicalstorms,themagnitudeofthealong-basindepth-averagedvelocityfollowedthespring-neapcyclewithstrongeralong-andcross-basinowsoccurringduringspringtides.Residualvelocitiesalongtheaxisoftheinletreversedonlyduringalargeset-upasaresultofthetropicalstorms.ChangeinwaterlevelbothatthemouthandinsidetheIntracoastalwaterwaywerewellcorrelatedtothecrossshelfwindstress.However,thechangeinseasurfaceelevationbetweentheinletandwithintheIntracoastalWaterwayas 128

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wellasthedepth-averagedvelocityalongtheaxisoftheinletwasbettercorrelatedtothealong-shorewindstress.Offshorewindeffectswereseenasareductioninthesurfaceinowalongtheaxisoftheinlet(inthevelocityanomaly)whileonshorewindsincreasedthemagnitudeofthesurfaceinow.Remotewindeffectsmodiedthewatercolumninaunidirectionalsense,increasingordecreasingthemagnitudeofthedepthaveragedvelocitydependingonthemagnitudeofthewaterlevelvariation.Althoughthealong-basinbaroclinicpressuregradienthadlittleeffectduringtowedobservations,thistermincreasedduringtropicalstormsasaresultofincreasedprecipitationgeneratingtransitionalgravitationalcirculation,aidedbyoffshorewinds.Therstorderbalanceinthealong-basindynamicswithintheinletwasbetweenthebarotropicpressuregradient,surfaceandbottomstressesandthenonlinearadvectiveterms.Accelerationsproducedbythebaroclinicpressuregradientwerelargerthanboththewindandbottomstressaccelerationsafterthersttropicalstorm,andshouldbeincludedinthebalanceofthealong-basinmomentumequationduringtropicalstorms. 129

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Figure5-1. A)Studyarea,St.AugustineInlet,ontheEastcoastofFlorida.Meteorological(squares)andphysicalwaterproperties(diamond)wereobtainedfromGuanaTolomatoMatanzasEstuarineResearchReserve(GTMNERR)andSt.AugustineWindstations.B)TowedADCPtransectacrossthemouthoftheinletfrom2006-2008denotedbytheorangelineandmooredcurrentmeterdenotedbycircles.LocationsofCTDprolesaremarkedbysquares.C)Depthprolesacrossthemouthoftheinlet(acrossorangeline)andapproximatelocationofmooredADCP(greencircle),whereNorthisonthelefthandsideofthegure. 130

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Figure5-2. MeteorologicalconditionsforSt.AugustineInletfrom2008:A)lowpassedwinddatafromSt.Augustinemeteorologicalstation,B)measured(grey)andlowpassed(black)waterlevelfromSanSebastianRiver,C)measured(grey)andlowpassed(black)salinityfromSanSebastianRiver,PellicerCreekandPineIsland,D)precipitationfromGTMNERRPellicerCreekmeteorologicalstation. 131

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Figure5-3. TracksoftropicalStormsFayandHannafromAugustandSeptember,2008.Dotsonthestormtracksrepresentthelocationofthecentreofthetropicalstormat6hourintervalsasthestormspropagatefromSouthtoNorth. 132

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Figure5-4. ResidualvelocitiesacrossthemouthofSt.Augustineinletfrom2006to2008(cm/s).Contoursareofalong-channelvelocity,withathickwhitelinedenotingthezerovelocity.Arrowsindicateacross-channelvelocities.TransectisfromNorth(left)toSouth(right).Thetimeofthesurveywithinthefortnightlytidalcycleisnotedinthesmallerguresontheright.Eachcross-inlettransectfollowedauniquepathacrosstheinletresultinginthevariablebathymetrydisplayedineachcontour. 133

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Figure5-5. A)Lowfrequencywaterlevel(m)andatmosphericpressure(hPa).B)Tidalamplitude(m)anddepthaveragedvelocities(uandv;cm/s)C)Residualalong-channel,u,andD)cross-channel,v,velocitiesfromthemooredADCPinthechannelofSt.AugustineinletfromJulytoSeptember2008(cm/s).Thickwhitecontourlinedenotesthezerovelocity.PassageoftropicalstormsFayandHannaaremarkedinA. 134

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Figure5-6. Meanprolesofdensity(t(kgm)]TJ /F4 7.97 Tf 6.59 0 Td[(3);solidblacklines)averagedoverthesemi-diurnaltidalcycleofeachsurveyasmeasuredfromtheCTDstationatthemouthoftheinlet,inthechannel.Meanprolesoftduringebb(dashed)andood(solid;grey)arealsoshown. 135

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Figure5-7. A)Density(t)asmeasuredatPineIslandandSanSebastienRiverandprecipitationfrom2008;B)HorizontalbaroclinicpressuregradientfromNorthtoSouthwithintheIntracoastalWaterwaybetweenPineIslandandSanSebastianRiver,separatedbyadistanceof21kminameandepthof3m. 136

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Figure5-8. VariationsinA)depthaveragedvelocity( u)andwaterlevel(adcp)atthemouthoftheinlet,B)thechangeinwaterlevelwithtimeatthemouthoftheinlet(=t),andthealong-channelchangeinwaterlevelbetweenthemouthoftheinletand20kminsidetheIntracoastalWaterway(atPineIsland)andC)windstresses(sx,sy).CorrelationsbetweeneachofthesecomponentsareshowninTable??. 137

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Figure5-9. A)Velocityprolefromthecenterofthechannel(u(z,t);thickblackline),meanvelocityprole(u(t);thinblackline)andresultingvelocityanomaly(u(z,t))]TJ /F5 11.955 Tf 19.81 3.32 Td[(u(t);thickblackline).VariationinvelocityanomalygivenlocalB)offshoreandC)onshorewindsandD)baroclinic(gravitational)effects. 138

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Figure5-10. ObservationsbeforethetropicalstormsofA)windspeedanddirection(inmeteorologicalconvention),B)watersurfaceelevationandchangeinwatersurfaceelevation(=t),C)depthaveragedalong-channelvelocitywherenegativeisowintotheinlet(m/s),D)along-channelvelocityanomaly(u(z,t))]TJ /F5 11.955 Tf 19.81 3.32 Td[(u(t);m/s). 139

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Figure5-11. ObservationsduringTropicalstormsFayandHannaofA)windspeedanddirection(inmeteorologicalconvention),B)watersurfaceelevationandchangeinwatersurfaceelevation(=t),C)depthaveragedalong-channelvelocitywherenegativeisowintotheinlet(m/s),D)along-channelvelocityanomaly(u(z,t))]TJ /F5 11.955 Tf 19.8 3.32 Td[(u(t);m/s). 140

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Figure5-12. Accelerationsfromthealong-basindepth-averagedmomentumequationfromJuly21toSeptember19,2008.TermscalculatedincludeA)localaccelerations,Coriolisandverticaladvectiveaccelerations,B)thebarotropicpressuregradientandC)bottomandwindstressesandthealong-basinbaroclinicpressuregradient.Bothalongandcross-shorewindstressesareplottedtohighlighttheirrelativeimportance. 141

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Figure5-13. ComparisonoftheA)barotropicpressuregradienttoB)theothertermsinthealong-basinmomentumequation.Linesitoivindicatetheinclusionofdifferenttermsinthemomentumequation.C)Thedifferencebetweenthebarotropicpressuregradient(A)andtheothertermsinthemomentumequation(Bi).Accelerationsproducedbythealong-basinbaroclinicpressuregradientbecomemoreimportantafterthetropicalstormsthroughtheincreasedfreshwaterinputtothesystem. 142

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CHAPTER6SUBTIDALFLOWANDITSVARIABILITYATTHEENTRANCETOASUBTROPICALLAGOON 6.1Introduction Theforcingmechanismsofsubtropicalcoastallagoonsmaydifferfromthoseoftypicaltemperateestuaries1.Whereasdensitygradientsnormallyplayamajorroleinforcingtemperateestuaries,theytendtobeofsecondaryimportanceinsubtropicallagoons.Generalcharacteristicsinherenttosubtropicallagoonsincludemicrotides,shallowdepths,smallwatersheds,andnarrowinlets.Consequently,theamountoffreshwaterinput[ Leeetal. 1990 ; Lippetal. 2001 ; MillerandMcPherson 1991 ; Poulakisetal. 2004 ; Schroederetal. 1990 ; SylaiosandTheocharis 2002 ],meteorologicalforcing[ Liu 1992 ; Smith 1977 1979 ; SwensonandChuang 1983 ; Wang 1998 ],andthestrengthoftidalcurrents[ Ianniello 1979 ; Seimetal. 2006 ; Sepulvedaetal. 2004 ; Smith 1993 ; Valle-Levinsonetal. 2000a ; WeisbergandZheng 2003 ]arecrucialindeterminingwhethersubtropicalestuariesaredrivenbydensitygradients,tides,orwinds. Narrowinletsatthelagoon/oceanboundaryaretypicallyformedasaresultofactivelittoraldrift,waveenergy,andmicrotides[ Kjerfve 1986 ].Previousstudieshaveexaminedthecirculationoneithersideofsubtropicallagoons[ BlumbergandNicholasKim 2000 ; Molleretal. 2007 ; MurphyandValle-Levinson 2008 ; Webbetal. 2007 ]whiletheowstrictlywithintheinlethasbeenlessstudied.Theowstructureofaninletdeterminestheestuary/oceanexchangeandisresponsiblefordispersionofnutrientsandpollutants,forlarvaltransport,andsedimentdynamics[ Brownetal. 2000 ; GuyondetandKoutitonsky 2008 ; Hill 1995 ; Lyczkowski-Shultzetal. 1990 ]. 1ReprintedwithpermissionfromMurphy,P.,A.F.Waterhouse,T.Hesser,A.Penko,andA.Valle-Levinson,Subtidalowanditsvariabilityattheentrancetoasubtropicallagoon,Cont.ShelfRes.,29(20),2318-2332,2009. 143

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Thepurposeofthisstudyistodeterminethespatialandtemporalvariabilityofowattheentrancetoasubtropicallagoon,St.AndrewBay,Florida.Thisuniquesubtropicalinlethasmarkedfreshwaterinuenceandmoreresemblesatemperatedensity-drivenestuarythanatidallydrivensystem,typicalofsubtropicalareas.Theinuenceofdifferentforcingmechanismsincausingspatialandtemporalvariabilityandindrivingtheinletshydrodynamicsisexaminedoverdifferenttemporalscales.Surveyandmooredobservationscombinedwiththeoreticalresultsareusedtoaddresstheseobjectives. 6.2StudyArea 6.2.1St.AndrewBaySystem NorthwestFlorida'sSt.AndrewBaysystemisadrownedrivervalley,coastalplainestuaryconsistingoffoursubestuaries:NorthBay,WestBay,EastBay,andSt.AndrewBay(Figure 6-1 ).ThelatteristheonlybaywithadirectconnectiontotheGulfofMexico,whileWestBayandEastBayconnecttotheGulfIntracoastalWaterway.Thisestuaryisecologicallyimportantbutsurroundedbyaregionwithgrowinganthropogenicactivity.St.AndrewBaycontainsthemostdiversemarinepopulationofanyestuaryonthenorthernGulfofMexicocoast[ OgrenandBrusher 1977 ]duetolowturbiditydespitefreshwaterinow,extensivesandats,widespreadsubmergedaquaticvegetationandadeepbasincontainingbothcoarseandnesediments[ BrusherandOgren 1976 ]. Tidesintheentireestuaryarediurnalwithameantidalrangeof0.5mandalongerebbtidethanoodtide[ IchiyeandJones 1961 ; McNultyetal. 1972 ].Thesystemhasasurfaceareaof243km2,drainingawatershedofapproximately2800km2[ USEPA 1999 ],whichislocatedentirelyinthestateofFlorida[ NWFWMD 2001 ].ThelargestfreshwatersourceforthesystemisspilloverfromtheDeerPointReservoirlocatedattheheadofNorthBay(Figure 6-1 ). 6.2.2WestPassandEastPass WestPassisa150mwidechannel,originallydredgedin1934,thatprovidesadirectlinkfromSt.AndrewBaytotheGulfofMexico.Thisinletisarmoredwithjetties 144

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attheentrance,maintainingaminimumdepthof9mfromWestPasstothePortofPanamaCity(St.AndrewBay)andtoEastBay.WestPassistheinletstudiedinthepresentwork. EastPass,theoriginalentrancetoSt.AndrewBay,wasanatural,shallowinletsoutheastofSt.AndrewBay.EastPassclosednaturallyin1998,wasre-openedin2001,andagainclosednaturallyby2004.TheoreticallyEastPasswillnotnaturallystabilizewhilethepresentdepthofWestPassismaintainedbydredging[ Jainetal. 2004 ]. 6.3DataCollectionandMethods 6.3.1MeteorologicalForcingandWaterLevels MeteorologicaldatafortheSt.AndrewBaysystemwereobtainedfromPanamaCity-BayCountyInternationalAirport(PFN),located7kmnorthofthestudyarea(Figure 6-1 ).WaterheightmeasurementsfromNOAAtidestation8729108(PanamaCity,FL),located6.5kmfromWestPass,wereusedtoidentifysubtidalvariabilityandforcing.MeandailywaterowfromtheDeerPointReservoirwascalculatedfromdailywaterlevelmeasurementsattheWilliamsBayouPumpingStationadjacenttotheDeerPointReservoirDam.WaterlevelheightsatthereservoirwerecorrelatedwithvaluesofwaterowoverthedamusingatablelookupmethodcalculatedbytheBayCountyWaterDivision. 6.3.2ProlesofPhysicalParameters Conductivity-temperature-depth(CTD)proleswerecollectedusingaSeaBirdSBE19CTDattwolocationsalongthesurveyroute.SamplingsiteB0waslocatedinsideWestPasswhilesamplingsiteD0wasattheouterendofWestPass,adjacenttotheGulfofMexico(Figure 6-1 ).Atotaloffteenproleswereobtainedovertheobservationperiodateachsitetodeterminethetemporalvariabilityofwatercolumnstraticationandtheeffectsoftidalstrainingonsuchvariationsinstratication.Tidalstrainingistheresultofvelocityshearactingonahorizontaldensitygradientcreatingoscillationsin 145

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thestraticationofthewatercolumn.Ingeneral,tidalstrainingcreatesastratiedwatercolumnduringebbtideandamixedwatercolumnduringoodtide[ deBoeretal. 2008 ; Simpsonetal. 1990 ].Todeterminetheinuenceoftidalstrainingonwatercolumnstratication,thepotentialenergyanomaly,(Jm)]TJ /F4 7.97 Tf 6.59 0 Td[(3),ofthewatercolumnforeachCTDcastwascalculated.Followingtheapproachof[ Simpsonetal. 1978 ],thepotentialenergyanomalyistheamountofworknecessarytocompletelymixthewatercolumnwhichcanbecalculatedfrom =1 hZ(^)]TJ /F6 11.955 Tf 11.96 0 Td[()gzdz(6) where^istheverticallyaveragedwaterdensity, ^=1 hZ0)]TJ /F8 7.97 Tf 6.59 0 Td[(h(z)dz(6) andhisthetotaldepth,isthedensityofwater,zistheverticaldepthcoordinateandgistheaccelerationduetogravity(9.8ms)]TJ /F4 7.97 Tf 6.59 0 Td[(2).Temporalvariationsofwatercolumnstraticationcausedbytidalstrainingcanbequantiedby (d dt)ts=g@^ @xZ0)]TJ /F8 7.97 Tf 6.59 0 Td[(h(up)]TJ /F5 11.955 Tf 14.48 0 Td[(^up)zdz,(6) whereupisthealong-estuaryverticalvelocityand^upistheverticallyaveragedvelocity,bothatapointneartheCTDsamplingsites[ Simpsonetal. 1990 ].Thehorizontalgradient,@^ @x,isdeterminedbycalculatingtheaveragedensitybetweenthetwosamplingsites(B0andD0)foreachtime.Comparisonofd dtasderivedfrominequation 6 and(d dt)tsfromequation 6 ,determinestherelativecontributionoftidalstrainingtoestuarinestratication.Anexactmatchbetweenthetwoquantitieswouldindicatethattidalstrainingistheonlymechanismcausingstraticationvariations. 6.3.3TowedADCPData InordertodescribethespatialstructureofthesubtidalcirculationinWestPass,asurveywasconductedaboardtheR/VHaroldBbetweenFebruary14and15,2008.Thevesseltowedadownwardpointing1200kHzbroadbandADCP(RDInstruments, 146

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Poway,CA)mountedona1.2msledalongaclosedhourglassshapedtrajectoryinsideWestPass(Figure 6-1 ).Thetransectlinesatthegulfandbayextremesofthechannelwereperpendiculartothethalweg. TheADCPwastowedatapproximately2ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1for23.98hours,collecting1spingsaveragedover10ensembles,yieldingahorizontalresolutionof20mandaverticalresolutionof0.5m.Thesurfacebinwasat1.5mdepth.Datainthelower15%ofthewatercolumnwerediscardedduetointerferencefromsidelobeeffects(RDInstruments,1996).Datawerecompass-calibratedandcorrectedbythemethodof[ Joyce 1989 ]usingaGlobalPositioningSystem.Atotalofthirtytransectrepetitionswereexecuted. 6.3.4GriddedRawMeasurements RawvelocitiesmeasuredbytheADCP(uobs,vobs)wereplottedontoagridof1030pointscoveringtheentireareaofWestPassresultingin48mby54mgridsquares(Figure 6-2 ).Squarescontaininglessthan75%ofthemeasureddataandcontainingoutliers(columnsabandrows1to2and27to30inFigure 6-2 )wereeliminated,leaving90gridsquaresforfurtheranalysis.Residualcomponentsofthevelocity(u0,v0)wereobtainedfromttingtheobservedcurrentsineachgridsquaretothedominantdiurnal(K1=23.92hours)andsemidiurnal(M2=12.42hours)harmonicsusingaleastsquaresmethod[ Lwizaetal. 1991 ].GiventherecordlengthandtheRayleighcriterion,completeresolutionofalldiurnalandsemidiurnalconstituentswasnotpossible[ EmeryandThomson 2004 ]. Predictedcurrents(upred,vpred)calculatedfromtheleastsquarestwerecomparedtotheobservedcurrentsusingagoodnessoftparameter,R2, R2=P()]TJ /F3 11.955 Tf 9.3 0 Td[(upred)2 P()]TJ /F3 11.955 Tf 9.3 0 Td[(uobs)2(6) whereangledbracketsrepresenttemporalaverages.Furtheranalysiseliminated18gridsquareswheretheleastsquarestdidnotrepresentthediurnalnatureofthetide 147

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despiteahighR2value,leaving72gridsquaresfornalanalysis.Individualtransectswerealsostudiedforinformationonthedepthandspatialpatternofresidualowacrosstheinlet. 6.3.5ResidualFlowandAnalyticalModel TimeseriesofobservationsalongtransectAtoB(Transect1)andtransectCtoD(Transect2)werealsoexamined(Figure 6-1 ).Observedcurrentswererotatedtotheangleofmaximumvariance[ EmeryandThomson 2004 ]andttedtoK1andM2harmonicsalsousingtheleastsquarestmethod.Thespatialcontoursofresidualvelocitiesacrosseachtransectwerethencomparedtoananalyticalmodel[ Valle-Levinson 2008 ]thatconsidersthenontidalmomentumbalanceamongpressuregradient,Earth'srotationandbottomfriction.ResultsfrombothobservedandmodeledresidualowswerecastintermsoftheKelvinandEkmannumbers.TheKelvinnumber,Ke=b=Ri,indicateswhethertheEarth'srotationaffectstheexchangeowinachannelbycomparingthecross-sectionalwidthofthebasin,b,totheinternalRossbyradius,Ri.TheEkmannumber,Ek=Az=(fH2),isameasureoffrictionalforcestoCoriolisforceswhereAzistheverticaleddyviscosity,Histhemaximumwaterdepth,andfistheCoriolisparameter. 6.3.6MooredADCPData Abottom-mountedADCP,equippedwithapressuresensor,wasdeployedattheentrancetoWestPass(3017.30600N,85143.78300W;Figure 6-1 ).TheADCPwasmooredinthedeepestsectionofthechannelatadepthof12.1mfromJanuary10,2008toMarch7,2008,measuringa57-daytimeseriesofcurrentvelocityproles.TheADCPaveraged120pingsdistributedovera6-minuteintervalin1mbins.Currentswererotated45totheprincipalaxisofmaximumvariancesuchthatpositivealongchannelvelocitiesrepresentedowintotheinlet,whilenegativevelocitiesindicateowoutoftheinlet,towardtheGulfofMexico.Subtidalvariationofthecurrentswas 148

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determinedusingalow-passLanczoslterwithhalf-powerof34hours[ EmeryandThomson 2004 ]. 6.4ResultsandDiscussion 6.4.1ExternalForcing WinterwindsinSt.AndrewBayduringthebeginningof2008werecharacterizedbyfrontalsystemswithaperiodicityof46days(Figure 6-3 ).Twenty-fourhoursbeforethetowedADCPsurvey,moderatenorthwestwinds(reachingamaximumof6.5ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)wereobserved.Twohoursaftertheinitiationofthesurvey,windspeedsdecreased,andrangedfrom0to3.5ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1for30hours.WaterlevelattheDeerPointReservoirwas1.52mthroughoutthetowedsurveyresultinginahigherthannormalfreshwaterdischargeofapproximately22m3s)]TJ /F4 7.97 Tf 6.59 0 Td[(1intoNorthBay. 6.4.2TidalWaveandEllipses Thephasederivedfromcross-spectralanalysisbetweensurfaceelevationandalongchannelcurrentsfromthemooredADCPindicatedthatcurrentsintheinletleadsurfaceelevationby4.5hours(67;Figure 6-4 B).Consequently,thetidalwaveattheWestPassentrancehadcharacteristicsmoresuggestiveofastandingwaveratherthanaperfectlyprogressivewave(whichhasanexpectedphaselagof0).Thephaselagbetweensurfaceelevationandalongchannelvelocitycorrespondedwithmeasuredsectionallyaveragedvelocitiesandwaterlevelobservationsobtainedduringthesurveyatthelocaltidegauge(Figure 6-4 C). TidalellipsescalculatedfromthetowedADCPindicatedadiurnalvariation(K1)withstrongestowsmidwaybetweentidalheightextremes(Figure 6-5 ).Orientationoftheellipseswassimilaratalldepths.MajoraxesoftheK1tidewere100cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1andminoraxeswere10cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1atalldepths.EllipsesinWestPassforboththeK1andM2tideswererectilinear,orientedinthedirectionofthechannel.TheK1ellipsesbecamelessrectilinearapproachingtheGulfofMexicofrominsideWestPassaswellastowardtheshalloweastsideofWestPassoutsideofthemainshippingchannel. 149

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Thisisindicativeofbottomfrictioneffectsontidalowsimilartotheresultsfoundby[ Valle-LevinsonandLwiza 1995 ].Inthissystem,theoodtideentersSt.AndrewBayasajet,encountersthenorthernboundary,andbifurcatesupEastorWestBay[ MurphyandValle-Levinson 2008 ].TheorientationoftidalellipsesadjacenttotheconnectionofWestPasswithSt.AndrewBayillustratesthesource-sinkmodelof[ StommelandFarmer 1952 ]workingontheoppositesideoftheinlet,whereebbtideactsasasinkofwaterfromthebayandtheoodtideactsasajetenteringthebay. ThephaseoftheK1tideincreasedfrom0ontheeastsideofWestPassto15onthewestsideofWestPasscorrespondingtoatimedifferenceof1hour.Thesurfacetidalphasesweresimilartothoseobservedby[ Uncles 1988 ]intheBristolChannelandtheSevernEstuarywheretheowatthecoastlineleddeeperpartsofthechannel.Inoursurvey,co-phaselinesatdepthexhibitedthesameacrosschanneldifference,butledthesurfacephasesatthesamelocation. 6.4.3DensityField Duringthetowedsurvey,densewaterfromtheGulfofMexico(=1026kgm)]TJ /F4 7.97 Tf 6.59 0 Td[(3)enteredWestPassduringoodtidecreatingawell-mixedwatercolumn(Figure 6-6 ).Thedensityprolestratiedasthetideprogressedtowardebb(14.9days).Straticationbecamestrongerthroughebbtidewithlowestdensitiesobservedbetween15.3and15.5daysforB0,andat15.5daysforD0,towardtheendofebb. Asaresultofdensityvariations,increasedat15.0days(Figure 6-7 )coincidingwiththeinitiationofebbtideatbothstations(Figure 6-6 ).atStationB0reachedamaximumafter15.4days.Followingthispeak,straticationdecreasedasoodtidebegan.AslessdensewaterpushedthehigherdensitywateroutofWestPass,graduallyincreased,reachingamaximumattheendofthesamplingperiod.Comparisonsbetweenthechangeinwithtime(asobservedfromthedensityeld)andthechangeinpredictedbytidalstrainingatStationB(Figure 6-7 )showedaconsistentpatterndespitesmallerscaleuctuations.Consistenciesbetweenthesame 150

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parametersatStationD0werenotasevident,implyingthatotherforcingmechanisms,suchastheadvectionofaverticalgradient,werelikelyaffectingstraticationofthewatercolumn.Bothparameterswereconsistent,exceptat15.1dayswhenpeaked.Thetidalasymmetriesintidalstrainingareexpectedtoinuencetheobservedresidualexchangeowwithintheinlet[e.g. Staceyetal. 2008 ]. 6.4.4ResidualFlow Thecross-sectionsofTransects1and2showedatwo-layerexchangeowwithowenteringthebottomandexitingatthesurface.TheisotachsassociatedwiththeresidualowsacrossTransects1and2hadapositivelateralslope(lookingintoSt.AndrewBay,Figures 6-8 and 6-9 ).Theslopeoftheinterfacebetweenoutowsandinows,thezeroisotach,was0.02forTransect1(5mdepthdifferencein250macrosstheinlet)and0.05forTransect2.ThesignoftheseslopeswasconsistentwithCoriolisaccelerations.Asarstdiagnosticofdetermininghowmuchofthisisotachslopewasproducedbyageostrophicbalanceacrosstheinlet,theMargulesslopewasdeterminedas[ Gill 1982 ] =)]TJ /F3 11.955 Tf 10.49 8.09 Td[(f(u11)]TJ /F3 11.955 Tf 11.95 0 Td[(u22) g(2)]TJ /F6 11.955 Tf 11.96 0 Td[(1)(6) wherefis7.3x10)]TJ /F4 7.97 Tf 6.59 0 Td[(5s)]TJ /F4 7.97 Tf 6.59 0 Td[(1,gis9.8ms)]TJ /F4 7.97 Tf 6.59 0 Td[(2,u1,1andu2,2aretheupperandlowerlayerowsanddensities,respectively.InTransect1,takingnominalvaluesforu1of0.08ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1,1of1025kgm)]TJ /F4 7.97 Tf 6.59 0 Td[(3,u2of0.05ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1,and2of1026kgm)]TJ /F4 7.97 Tf 6.59 0 Td[(3yieldedavalueofof0.001,whichwasoneorderofmagnitudesmallerthantheobservedslope.Similarly,takingthesame2and1of1025.5kgm)]TJ /F4 7.97 Tf 6.58 0 Td[(3forTransect2plusu1of0.15ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1andu2of0.02ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1,resultedinof0.003.Theseestimatesofthegeostrophicslopebeingmuchsmallerthantheobservedslopeindicatedthatfrictionandadvectioncouldhavecontributedtoshapingtheexchangeowsattheinlet[e.g. Valle-LevinsonandLwiza 1995 ].ThiswillbeexploredfurtherwithanalyticalsolutionsinSection 6.4.5 ItisnoteworthythatthemaximumalongchannelvelocitiesinTransect2were50%largerthanthoseinTransect1.Thiswasnotreallyanincreaseinvolumeoutow 151

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fromTransect1toTransect2,butratheritwastheresultoftheowsbeingmorechannelizedinTransect2.AtTransect1themainorientationoftheowswastowardthewesternsideofthechannel(Figure 6-8 )andbetweenthetwotransectsthemeanowwasaffectedbyrecirculationcausedbythecomplicatedmorphologyoftheinlet[e.g. Lietal. 2006 ].Infact,theanalyticalmodelresultspresentedinthefollowingsectionrequiredtheprescriptionofthesamevolumeinow(riverdischargeof40m3s)]TJ /F4 7.97 Tf 6.58 0 Td[(1)forbothtransects,whichindicatedvolumeconservationfromTransect1to2intheobservations.TheanalyticalmodelallowedacomparisonofthecombinedeffectsofCoriolisandfrictiononthemeanows.Thediscrepanciesbetweenanalyticalresultsandobservationscouldthenbeattributedtoadvectiveeffects,asexplainednext. 6.4.5FrictionandCoriolisImportanceattheInlet Theanalyticalsolutions(asin Valle-Levinson [ 2008 ])werecalculatedintermsoftheKelvinandEkmannumbersforthebathymetriesofTransects1and2.ForTransect1,atthenorthernendoftheinlet,areasonablematchbetweenobservedowsandanalyticalsolutions(Figure 6-8 )wasobtainedforanEkmannumberof0.01andaKelvinnumberof0.8.ThevalueoftheEkmannumbercorrespondedtoaverticalkinematiceddyviscositycoefcientof210)]TJ /F4 7.97 Tf 6.59 0 Td[(4m2s)]TJ /F4 7.97 Tf 6.59 0 Td[(1.Thesevaluesindicatedthatatthenorthernendoftheinlet,bothrotationandfrictionwereinuentialtotheexchangehydrodynamicsandtheinternalradiusofdeformationwasoftheorderoftheinlet'swidth.Thebathymetryhadmildlateralvariationsthatwerenotinuentialintheoverallwaterexchangepattern.Notonlytheshapeoftheexchangeowsbutalsothemagnitudeoftheobservedmeanowscomparedwellwiththeanalyticalresults,includingthedepthatwhichtheowreversed. ForTransect2,atthesouthernendoftheinletandthetransitionwiththeGulfofMexico,areasonablematchwasobtainedbetweentheanalyticalsolutionandtheobservedmeanows(Figure 6-9 ).ThismatchwasattainedwithanEkmannumberof0.03,correspondingtoaneddyviscosityof1103m2s)]TJ /F4 7.97 Tf 6.59 0 Td[(1,andaKelvinnumberof1.8. 152

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TheincreasedvaluesofEkmanandKelvinnumbers,relativetothevaluesatTransect1,producetheincreasedslopeintheisotachs.ItisevidentthatfrictionaleffectswerestrongeratTransect2thanatTransect1asshownbydecreasedstraticationandstrongertidalcurrentsatthesouthernendoftheinlet(Figure 6-6 ).TheanalyticalsolutionforTransect2comparesfavorablywiththemagnitudeoftheexchangeowsandthelateralslopeoftheisotachs.ThedynamicsatWestPasscouldthenbecharacterizedbyweaktomoderatefrictionalandCorioliseffects.TheroleoffrictionbecomesmoresignicantatTransect2thanatTransect1.WhichisconsistentwiththedynamicsdescribedinthemainpartofSt.AndrewBay[ MurphyandValle-Levinson 2008 ]. Discrepanciesbetweenobservationsandtheanalyticalsolutioncanbeattributedtocurvatureeffects(oradvection),whichareneglectedintheanalyticalmodel'smomentumbalance.Recentstudies[e.g. Chant 2002 ; Li 2006 ; Webbetal. 2007 ]haveshownthatadvectionmaybesignicantincomplexestuarinesystems.InWestPass,lateraladvectionenhancestheowstructureandshouldcontributetotherecirculationobservedintheresidualow(Figure 6-10 ).ThediscrepanciesbetweentheowobservationsandtheanalyticalmodelimplythatadvectionisarelevantmechanismatWestPass.Theresidualowdepictedhereoverasinglediurnaltidalcycleisonlyasnapshotwithinavarietyofpatternsthatwillresultfromwindforcingandspring-neaptidalforcing.Thesemechanismsarefurtherexploredwithcurrentproles(mooredADCP)recordedover57days. 6.4.6TemporalVariationsinExchangeFlow MooredADCPmeasurementsinWestPasswereusedtodeterminetheverticalstructureofthenetowaswellasitstemporalvariability(Figure 6-11 ).Theverticallyaveragedowwaswellcorrelatedwithwindforcing.Thecorrelationcoefcientbetweenalongshelfwindsandalongchannelcurrentswas0.72.Visually,thedepth-averagedcurrentsweremostnoticeablycorrelatedwiththewindafterJanuary27,2008indicating 153

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thatthevariabilityofthealongchannelsubtidalowswasdominatedbywindforcing.Subtidalalongchannelcurrentshadmaximumoutowsof37.3cms)]TJ /F4 7.97 Tf 6.58 0 Td[(1andinowsof19.8cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1whereasacrosschannelcurrentsrangedbetween9.0cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1and7.7cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1(Figure 6-11 ).Throughouttheperiodofobservation,alongchannelsubtidalowsweremostoftenunidirectionalwithdepthandwellrepresentedbytheverticalaverage.However,thisverticalstructurechangedbetweenunidirectionaltolessfrequentexchangeowwithaperiodicityrelatedtoboththefortnightlymodulationofthetideandalong-shelfwindstress.DuringthesurveyofFebruary14to15,thealongchannelsubtidalowbasicallyshowednetoutow,consistentwithFigure 6-9 Cross-channel(secondary)subtidalowshadadistincttwo-layerstructurewithsurfaceowtowardtheNorthwest(positive)anddeeperowtowardtheSoutheast(negative),indicativeofcurvatureinducedtwo-layerlateralow(Figure 6-11 ).Thistwo-layerowwasinagreementwiththelateralowfromthesurveytransects(Figures 6-8 and 6-9 ).Thetwo-layerstructurewasprevalentovernearlytheentireobservationperiodexceptforJanuary20,2008andseveraleventsinthelast2weeksofthedeployment.Alongchannelwindswerenegativelycorrelated(correlationcoefcientof0.80)totheacrosschannelcurrents. Toexaminetherelationshipbetweenalongchannelvelocitiesandforcingbywindsandtides,thevariationofthealongchannelvelocitieswasgroupedaccordingtotidalamplitudeandalongchannelwinddirection(Figure 6-12 ).Thealongchannelowasafunctionofwinddirectionwassortedforlow-passwinds42.5ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1,whichisthespeedatwhichwindforcingoverwhelmsthedensity-drivenforcing.Unidirectionalowoccurredattheweakestneaptides(<0.125m)andstrongestspringtides(>0.375m)whileexchangeowoccurredatallothertidalamplitudes.AlongchannelcurrentsshowedoutowforwindstowardtheSouth-Southeast(90to200)correspondingwiththeeffectsofanoffshoreEkmantransport.Thesubtidalsealevelshowedasimilar 154

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decreaseforsouthwardtosouthsoutheastwardwinds(Figure 6-12 ).Theoppositeresponsewasillustratedforwindsbetweennorthwestwardandnortheastward. Themagnitudeofthelateralowsvariedapproximatelywiththetidalamplitude(Figure 6-13 A).Strongestlateralowsdevelopedduringspringtides(i.e.tideswithlargestamplitude)becauseofstrongestcentrifugalaccelerations,consistentwith Chant [ 2002 ].However,thedepthoflateralexchangevariedwithwinddirection(Figure 6-13 B;calculatedusingaminimumwindspeedcutoffof2.5ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1).Windsalignedwithoutowinthechannel(toward45to225)resultedinanincreaseinthedepthofpenetrationofthenorthwestwardlateralows.Thispenetrationwaslikelyduetoanincreasedwindinducedoutowatthesurfacewithintheinlet,whichcorrespondinglyincreasedthelateralstructureatthesurface.Conversely,windsheadingtowardthesouthwesttonortheast(toward225to45)resultedinincreasedbottomlayerthickness. Tofurtherexaminetheverticalstructureofthealongandcrosschannelowandtheirtemporalvariability,anempiricalorthogonalfunction(EOF)analysiswascarriedoutonthetimeseries.TheEOFanalysisshowedthattherstmodeportrayedunidirectionalnetows.Thismodeexplained93%ofthevariabilityofthealongchannelcurrentswithinWestPass(Figure 6-14 B)andwaswellcharacterizedbythealong-shelfwindstress(Figure 6-14 A).ThesecondEOFmodehadatwo-layerstructurewithowintotheinletatthesurface,andoutowbelow5mdepth(Figure 6-14 D).Thismoderepresented6%ofthevariabilityandwaswellcharacterizedbythetidalamplitude(Figure 6-14 ).Similarly,thelateralcurrentsshowedatwo-layerstructureintherstEOFmode(Figure 6-15 ),whichrepresented65%ofthevariabilityoftheow,andcorrelatedwiththetidalamplitude(Figure 6-15 A).ThesecondEOFmoderepresented30%ofthevariabilityandhadaunidirectionalverticalstructurewithstrongersurfaceowthanatdepth(Figure 6-15 D).Thealongshelfwindstresswasofsecondaryimportanceindrivingthelateralsubtidalow(Figure 6-15 C). 155

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Furtheranalysisrevealedthatthetemporalevolutionofthealongchannelsubtidalowstructureshowedepisodiceventsofincreasedverticalshearbetweenthenear-surfaceandnear-bottomrecords(Figure 6-11 andFigure 6-16 ).Themagnitudeofverticalshearshowedpeakscoincidingwithneaptidesandhada0.70correlationtothespring-neapcycle.Exchangeowswithintemperateestuaries,mostlydrivenbyalongchanneldensitygradients,aretypicallystrongerduringneaptides[ GrifnandLeBlond 1990 ; Haas 1977 ; LindenandSimpson 1988 ].UnlikeseveralinletsinthesubtropicalregionofFlorida[ Valle-Levinsonetal. 2009 ],WestPassbehavedinasimilarmannertotemperateestuariesduetotheinuenceofdensity-drivenows.Severalpluvialprecipitationpulses,occurringinconjunctionwithalongshelfwindstresses,increasedthedensity-drivenowsandtheverticalshear(February18,19and23;Figure 6-16 ).Inparticular,therainpulseonFebruary23coincidedwithneaptidesandcausedthelargestverticalshears. ThespatialcoverageofthesurveyallowedanevaluationofthesubtidalexchangeowattwotransectsofWestPass,includinganassessmentoftheimportanceoffrictionalandCoriolisforcingonthedynamicsoftheexchangeow.However,theresultsfromthesurveyandfromthemooredrecordshowedthattheobservedexchangeowwasinfrequent.Thesubtidalowattheinletwasmainlydependentonthealong-shelfwindstressandsecondlyonthetidalamplitude. 6.5Conclusion WestPassintheSt.AndrewBaysystemisauniquesubtropicalinletforthestudyofsubtidalowsbecauseofitsmarkedfreshwaterinuence.Thedensitygradientarisingfromthefreshwaterinuencecausedtidalstrainingandtidalasymmetriesinwatercolumnstratication.Theseasymmetriesshapedthespatialstructureofthealongchannelresidualow,whichshowedatwo-layerexchangewithoutowatthesurfaceandinowatdepth,asinatypicaltemperateestuary.However,thisexchangepatternwasinfrequentlyobservedbecausethenetowwasoftenunidirectionalthroughout 156

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thewatercolumnandmainlymodulatedbywindforcing.Also,asfoundintemperateestuaries,theshearinthealongchannelowwasinverselyrelatedtotidalforcingwithstrongestshearsoccurringduringneaptides.Thelateralowsoverthetimeseriesshowedadistincttwo-layerstructure,whosemagnitudewasmodulatedpredominantlybythespringneaptidalcycle.TheresultsofthisstudyindicatethattheexchangehydrodynamicsattheWestPassareessentiallydeterminedbypressuregradientandfrictionwithnon-negligibleinuencefromCoriolisandadvective(centrifugal)accelerations. 157

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Figure6-1. StudyareaofSt.Andrew'sBayInlet:B0andD0arelocationsofCTDproles.ThethicksolidblacklineconnectingpointsA-DinthelowergureindicatesthesurveyrouteofthetowedADCP.Thejaggedsymbolatthesurveymid-pointdenotesthepositionofthemooredADCP.Isobathsarerepresentedbythinsolidlines,withdepthsindicated.LineA-BisTransect1andLineC-DisTransect2. 158

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Figure6-2. GridsuperimposedonFebruary14-15,2008surveyroute.Opencircledenotegridsquaresusedfordataanalysis.Columnsa)]TJ /F3 11.955 Tf 11.96 0 Td[(bandi)]TJ /F3 11.955 Tf 11.96 0 Td[(jwereremovedalongwithrows1-2and27-30toensureaccuracyofinterpolation. Figure6-3. A)Tidalheight(m),B)windspeed(ms)]TJ /F4 7.97 Tf 6.58 0 Td[(1),C)sealevelpressure(mbar),andrainfall(cm)duringthestudyperiod. 159

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Figure6-4. A)CoherencesquaredandB)phasebetweenalong-channelvelocityandseasurfaceovertheentireobservationperiodofthemooredADCPwiththe95%condenceinterval(dashed-dottedline);C)Observedalongchannel(dashed)andseasurfaceelevation(solid)duringthetowedADCPsurveyfromFebruary14-15,2008. 160

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Figure6-5. Surface(1.86m)K1tidalellipsesoverlaidoncontoursofK1tidalphaseforFebruary14-15,2008 161

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Figure6-6. ObservedtvaluesandtidallyaveragedtateachtransectthroughthetowedADCPsamplingperiodatA)StationB0andC)StationD0.CorrespondingtidalvelocityandtidalaveragenearCTDsamplingpointsareshowninBandD(cms)]TJ /F4 7.97 Tf 6.58 0 Td[(1).Notethelowesttforbothtransectsoccurwhenvelocityisapproachingzerosignifyingtidalstraininginuence. 162

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Figure6-7. A)ThepotentialenergyanomalycalculatedfromtheobserveddensityprolesatstationsB0andD0.ComparisonsbetweenpotentialenergyanomalychangesandtheforcingfromtidalstrainingatB)Transect1andC)Transect2. 163

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Figure6-8. A)Contoursrepresenttheobservedresidualmeanow(cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)inTransect1rotatedtotheangleofmaximumvariance.Arrowsdenoteobservedtransverseresidualow.B)Contoursrepresenttheanalyticalsolutionofthemeanow(cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)withthebathymetryofTransect1(Ke=0.8andEk=0.01).Arrowsdenotetransverseresidualowcalculatedfromtheanalyticalsolution.Negativecontours(shaded)areowoutoftheinlet,positiveisintotheinlet,fromtheGulfofMexico. 164

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Figure6-9. SameasFigure 6-8 butforTransect2(Ke=1.82andEk=0.03). 165

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Figure6-10. Bi-harmonicsplineinterpolationofsurface(1.36m)subtidalcirculationresultingfromremovalofdiurnalandsemidiurnaltidalsignalsduringFebruary14-15,2008survey.Arrowswithdotsatbasedenoteobservationusedforinterpolation. 166

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Figure6-11. A)Wind(ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)andtidalamplitude(m),B)depthaveragedsubtidalalongchannelcurrents,subtidalC)alongandD)cross-channelcurrentsofthemooredADCPlocatedattheentranceofWestPass(cms)]TJ /F4 7.97 Tf 6.58 0 Td[(1).Windspeedanddirectionareplottedinoceanographicconvention.Depthisshowninmeters(m).Positive(negative)along-channelresidualcurrentsindicatesowinto(outof)theinletfrom(to)theGulfofMexico.Positivecross-channelcurrentsindicateowtowardtheNorthwest. 167

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Figure6-12. Variationinsubtidalalongchannelvelocities(cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)withA)tidalamplitudeandB)winddirection.C)Thevariationinthesubtidalmeansealevelheightwithwinddirection.Winddirectionisinoceanographicconvention.Aminimumwindcutoffof2.5s)]TJ /F4 7.97 Tf 6.59 0 Td[(1wasusedincalculatingtheobservedvariationswithwinddirection. 168

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Figure6-13. Variationinsubtidalcross-channelvelocities(cms)]TJ /F4 7.97 Tf 6.58 0 Td[(1)withA)tidalamplitudeandB)winddirection.Winddirectionisinoceanographicconvention.Aminimumwindcutoffof2.5ms)]TJ /F4 7.97 Tf 6.59 0 Td[(1wasusedincalculatingtheobservedvariationswithwinddirection. 169

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Figure6-14. EOFofthealongchannelsubtidalvelocity.A)Therstmodeofvariability(solid)withthealong-shelfwindstress(dashed),B)theverticalstructureoftherstmode,C)thesecondmodeofvariability(solid)withthetidalamplitude(dashed),andD)theverticalstructureofthesecondmode. 170

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Figure6-15. EOFofthecrosschannelsubtidalvelocity.A)Therstmodeofvariability(solid)withthetidalamplitude(dashed),B)theverticalstructureoftherstmode,C)thesecondmodeofvariability(solid)withthealong-shelfwindstress(dashed),andD)theverticalstructureofthesecondmode. 171

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Figure6-16. TemporalevolutionofthealongchannelsubtidalverticalshearcalculatedbetweensurfaceandbottombinsofthemooredADCPlocatedattheentranceofWestPass(solid).Thetidalamplitude(dotted),thealong-shelfwindstress(dashed)andtherain(opencircles)overthesamplingperiodareshown. 172

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CHAPTER7CONCLUSION Inthiswork,vechapterswerepresenteddealingwiththedynamicsofinletsattidalandsubtidaltimescales.Eachchaptertackledadifferentthemerelatedtoinlethydrodynamics.Afterabriefintroductorychapter,thesecondandthirdchaptersdealtwithtidaldynamics.Inparticular,Chapter 2 examinedthetidalpropagationthroughafrictionalinterconnectedbasinandshowedthatthetidalsignal,asseenthroughseasurfaceelevationandvelocity,wasstronglydampeduponentranceintothebasin.BathymetriceffectsontidalprocesseswerepresentedinChapter 3 ,whichcharacterizedtheunusualvariabilityinstraticationatatidalchannelthatfeaturedahollow.Theremainderofthethesisdiscussedsubtidalprocesses.Chapter 4 investigatedhowtidalprocesses,andinparticular,curvatureinducedows,modiedtheobservedlateralstructureofthesubtidalowsthroughaninlet.Chapter 5 determinedhowsubtidalowsweremodiedbyextremeforcing,suchastropicalstorms,ndingthatunidirectionalinowswerefollowedbyunidirectionaloutows,whichcompetewiththecustomarylaterallyshearedresidualvelocitystructure.Finally,Chapter 6 delvedintosubtidalowsinasubtropicalinletthatweredriven,predominantly,bydensity-drivencirculation. Section 7.1 unitesthepreviouschaptersbasedonthemainthemesofthedissertation.Thisisfollowedbyrecommendationsforfutureworkbasedontheseresults(Section 7.2 ). 7.1Summary Thethemeunifyingthisworkisthatthatinlethydrodynamics,attidalandsubtidaltemporalscales,area)dominatedbythebalancebetweenpressuregradient,frictionandadvection;andb)greatlyinuencedbybathymetriceffectsthatprovidearichspatialvariability.Threegeneralresearchlinesrelatedtotidalinletsarestudiedinthisworkandarehighlightedbelow. 173

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7.1.1TidesinanInter-connectedEstuary Thisworkprovidesanewandrelativelysimpletheoreticalframeworkforthepropagationoftidesthroughasystemoftwoconnectedinlets.Previousmodelsstudyingtidalpropagationthroughhighlyfrictionalenclosedbasinsusedthediffusionequation[ FriedrichsandMadsen 1992 ; LeBlond 1978 ]andstudiesonthetide-inducedmasstransportthroughhighlyfrictionalinterconnectedbasinsusedaone-dimensionallinearizedmomentumequation(withquadraticfriction; vandeKreekeandDean 1975 ).Themodelusedinthisworkuseslinearizedmomentumequations(inxandy),whichincludelateralvariationsinbathymetryandtheeffectoftheearth'srotation.Themodelpredictedtheobservedcurrentandseasurfaceelevationchangesinarealbasin(Florida'sIntracoastalWaterway).Thismodelallowedforthequanticationofthephaserelationshipbetweensurfaceelevationandvelocitygivendifferentnon-dimensionalfrictionalparameters,whichpreviouslydependedoncomplexequationsanddimensions[ Friedrichs 2010 ].Thismodelhighlightedtheimportanceoffrictionindampeningtidalvelocitiesawayfromthemouthoftheinlets.Fromtheobservationsofalong-andcross-channelvelocities,increasedushinglikelyoccurredatthemouthsoftheseinlets.Thestagnanttidesattheregioninlandofthemouthsiscrucialwhenconsideringhowthesubtidalowsaffectthissystem. 7.1.2ObservationsofTidalandResidualFlows Thisinvestigationprovidesobservationalevidencefortheoreticalresultsontidal,wind-drivenanddensity-drivenowsinsemienclosedbodiesofwaterwithlateralvariationsinbathymetry.Thelateralstructureofowsonbothtidalandsubtidaltimescaleshasbeenwelldocumentedthroughobservationsinthreesubtropicalinlets.Althoughmodelsandsinglepointmooringshavebeenusedtocharacterizeresidualvelocities,thisworkdeterminedthemechanismsresponsibleforthelateralorverticalvariabilityoftheexchangeows.Thespring-neapcyclemodulatedtheexchangeininletswhereresidualowswerelaterallyshearedwhileremoteeffects 174

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hadaunidirectionaleffectonthelateralexchange.AsobservedatPoncedeLeonandSt.AugustineInlets,subtidalowsatthemouthoftheinletshadaconsistentlateralstructure.Non-linearprocess,drivingalateraladvectionofcurrentsareobservedatthemouthsofbothinlets.Bathymetriccurvatureinducedhelicalowaroundthebendsleadingtovariabilityinresidualows,particularlywhenstraticationincreases.St.AugustineInlet,withaconsiderablylargermouthareaandcurvature,wasfoundtobeinaregionofresidualeddies,alsoinducinglateralvelocities.Althoughthespring-neapcyclemodulatedthelateralexchangeintheseinlets,remoteandlocalwindeffectswerefoundtoberesponsibleformostofthesubtidalvolumeuxinandoutofthesebasins. 7.1.3StratiedFlowOverHollows Thisinvestigationprovidesobservationsonmechanisms,notpreviouslydescribed,associatedwithstratiedtidalowsinteractingwithhollows.Comprehensivemeasurementsofcurrentvelocities(surveyedandmoored)andhydrographicproleswereconducted,forthersttime,overtwodiurnaltidalcyclesinChacahuaInlet,Oaxaca,Mexico.Theinletrespondedtotheuniquebathymetricshapebytidalvariabilityinstraticationduetoincreasedmixinginthehollowonebbtides.Thepotentialenergyanomaly,ameasureofwatercolumnstratication,increasedduringebbtideandhadtwopeaks,oneduringmaximumebbcurrentsandthesecondduringearlyood.Althoughthesetwopeaksinpotentialenergyanomalyhavebeennotedinotherestuaries(e.g.DeeRiverEstuary),thisisanatypicalfeature.Decreasedstraticationattheendofebbwasfoundtobeduetoincreasedmixingontheseawardrimofthehollowduringebb,asowwasconstrictedthroughtheshallowinletentrance.Thiswillalsoaffectnutrientandushingwithinthelagoon,likelyperiodicallyreducinglagoonalushingduringthewetseason.Documentingandunderstandingtheprocessesimportantinthedevelopmentofreducedstraticationattheendofebbhasfurtheredtheunderstandingofmixingprocessesandthevariabilityinthepotentialenergyanomalyinnaturalsystems. 175

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7.2FutureResearch Theanalyticalmodeldeterminedtheeffectofabasinwithtwoopenings.Florida'sIntracoastalwaterwayhas19inletsalongtheEastcoastandthemodelshouldbeextendedtoencompasstheinuenceofseveralinlets,withvariableseparationdistances.Thiswillelucidateregionsalongthewaterwaywhereushingislow(orhigh)andmayhelpindevelopmentandengineeringpracticesintheinletandwaterway,asawhole.Althoughthetidewillmaintainitsstrongattenuationaftertheentranceintoaninlet,dynamicswillvarydependingontheseparationdistancebetweeninlets. Residualowsacrossthreeinletmouthshavebeenstudiedthroughobservationsinthisthesis.Combiningtheresultsofbasininterconnectivityandresidualowsisalogicalnextstep.Thiswillfullycaptureallaspectsofthesystem.AsimilaranalyticalmodelasdescribedinChapter 2 [ Winant 2008 ]canbemodiedformultipleconnectedinlets.Essentialforthisinvestigationaremeasurementsofresidualvelocitieswithinthebasin,intheabsenceofwinddrivenows.Thismaybeachievedthroughtheuseofdriftersreleasedatvariouslocationswithinthewaterwayandinletmouths. Althoughtowedandmooredcurrentsobservationsandperiodicprolesofwatercolumnstraticationrevealedthetidaldynamicsoverahollow,thisinletislikelygeneratinginterfacialinstabilitiesduringebbtideswhenprecipitationishigh.Naturallyoccurringinstancesofshearinstabilitiesaretypicallyfoundinlargersystems,however,asthissystemisverysmallitisaperfectnaturallaboratory.UsingmooredhighfrequencyADCPmeasurements(1second)andechosoundingsovertheebb,furtherinvestigationsintothemixingprocessesalongtheslopeofthehollowwilllikelyrevealinterestingndings. 176

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BIOGRAPHICALSKETCH AmyWaterhousegrewupinVancouver,BritishColumbia.Shespentherchildhoodon,inandaroundthePacicOcean.ShestartedherstudiesinhonoursphysicsattheUniversityofBritishColumbiaandsawthelightinherlastyearofherundergradandswitchedtoacombinedhonoursinphysicsandoceanography.ShegraduatedwithherB.Sc.in2001withanhonoursthesissupervisedbyDr.RichPawlowicz.AfterworkingasaresearchassistantfortwophysicaloceanographersattheUniversityofBritishColumbia,shewentontopursuehermaster'sinphysicaloceanographywithDr.SusanAllen.ShecompletedherM.Sc.in2005studyingtheowdynamicsaroundsubmarinecanyons.Afterworkingfor3yearsinVancouverasaconsultant,shemovedtoGainesville,FloridainthehopesofstudyingoceanographyinwarmerclimatesinSeptember2007. 187