Mechanisms Responsible for Intratidal Variations of Stratification in a Coastal Plain Estuary

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Title:
Mechanisms Responsible for Intratidal Variations of Stratification in a Coastal Plain Estuary
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english
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Zwemer,Nicholas Joel
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University of Florida
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Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Coastal and Oceanographic Engineering, Civil and Coastal Engineering
Committee Chair:
Valle-Levinson, Arnoldo
Committee Members:
Thieke, Robert J

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Subjects / Keywords:
estuary -- stratification
Civil and Coastal Engineering -- Dissertations, Academic -- UF
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Coastal and Oceanographic Engineering thesis, M.S.
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Abstract:
Variations in time of vertical density stratification in coastal water bodies can exert significant influence on the function and structure of coastal ecosystems. One such effect is the development of hypoxia from reduced vertical exchange flow with oxygenated waters near the surface. Magnitudes of stratification are quantified through the calculation of the potential energy anomaly, phi, which is the amount of energy needed to fully mix a stratified water column. A dynamic equation for the potential energy anomaly has been rigorously derived in previous studies, and consists of the sum of mechanisms contributing to or destroying stratification. Currently, the calculation of this equation has only been performed with data produced by numerical models, of which only 1-D and 2-D models have simulated estuarine conditions. This thesis uses data from the survey of a coastal plain estuary in the computation of the dynamic equation for the potential energy anomaly in 3-dimensions, and investigates the contributions of mechanisms within the equation. Data were collected at two parallel transects approximately 2 km apart in the James River Estuary, Virginia. Velocity, electrical conductivity and temperature were recorded over a complete semidiurnal tidal cycle. Across and along estuary components of three mechanisms are calculated in this thesis: phi-advection (the advection of a stratified water column), depth-mean straining (tidal straining) and non-mean straining (estuarine circulation). The vertical mixing term is also expected to be a major contributor to variations in stratification, but could not be calculated accurately from the measured data. Previous studies have determined along estuary tidal straining and vertical mixing to be the dominant influences on the development of stratification in an estuary. Yet this thesis has determined that across estuary phi-advection is the dominant term causing stratification locally in the study area. In general, along estuary components of the computed mechanisms were found to be an order of magnitude smaller than their across estuary counterparts. Comparison of the sum of these mechanisms with the measured values of dphi/dt at both transects suggests that vertical mixing terms should contribute to mixing at the study area, with particular influence during maximum ebb and flood velocities.
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Includes vita.
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Statement of Responsibility:
by Nicholas Joel Zwemer.
Thesis:
Thesis (M.S.)--University of Florida, 2011.
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Adviser: Valle-Levinson, Arnoldo.

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1 MECHANISMS RESPONSIBLE FOR INTRATIDAL VARIATIONS OF STRATIFICATION IN A COASTAL PLAIN ESTUARY By NICHOLAS ZWEMER A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2011

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2 2011 Nicholas Zwemer

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3 ACKNOWLEDGMENTS I thank my committee chair and advisor Dr. Arnoldo Valle Levinson for providing encouragement and motivation for the completion of this thesis as well as providing valuable insight on the topic. I would also like to thank Dr. Robert Thieke for sitting on my committee, as well as my parents for their suppo rt throughout my college career Finally I would like to thank the students of Dr. Valle advice and assistance throughout my research.

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4 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 3 LIST OF FIGURES ................................ ................................ ................................ .......... 5 LIST OF ABBREVIATIONS ................................ ................................ ............................. 6 ABSTRACT ................................ ................................ ................................ ..................... 8 CHA PTER 1 INTRODUCTION ................................ ................................ ................................ .... 10 Motivation ................................ ................................ ................................ ............... 10 Estuarine Background ................................ ................................ ............................. 11 Stratificati on ................................ ................................ ................................ ............ 12 A Dynamic Equation for Stratification ................................ ................................ ...... 14 2 METHODS ................................ ................................ ................................ .............. 18 Study Area ................................ ................................ ................................ .............. 18 Data Collection and Pr ocessing ................................ ................................ .............. 20 3 RESULTS ................................ ................................ ................................ ............... 24 Flow Characteristics ................................ ................................ ................................ 24 Stratification Characteristics ................................ ................................ ................... 25 Computed Stratification Components ................................ ................................ ..... 27 4 DISCUSSION ................................ ................................ ................................ ......... 42 Overview ................................ ................................ ................................ ................. 42 Analysis of Mechanisms ................................ ................................ ......................... 45 5 CONCLUSION ................................ ................................ ................................ ........ 48 LIST OF REFERENCES ................................ ................................ ............................... 50 BIOGRAPHICAL SKETCH ................................ ................................ ............................ 52

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5 LIST OF FIGURES Figure page 1 1 A representation of the potential energy anomaly, ................................ ........ 13 2 1 Location of measurement area. ................................ ................................ .......... 22 2 2 Bathymetry of the two transects. ................................ ................................ ........ 23 3 1 Depth mean velocities at transect 1. ................................ ................................ ... 30 3 2 Depth mean velocities at transect 2. ................................ ................................ ... 31 3 3 Transect 1 density profiles of crossings 1 8, with contour units of kg/m 3 ........... 32 3 4 Transect 2 density profiles of crossings 1 12, with contour units of kg/m 3 ......... 33 3 5 Potential energy anomaly values at transect 1. ................................ .................. 34 3 6 Potential energy anomaly values at transect 2. ................................ .................. 35 3 7 Computed lateral mechanisms at transect 1. ................................ ...................... 36 3 8 Computed longitudinal mechanisms at transect 1. ................................ ............. 37 3 9 Computed lateral mechanisms at transect 2. ................................ ...................... 38 3 10 Computed longitudinal mechanisms at transect 2. ................................ ............. 39 3 11 Sum of the computed mechanisms at transect 1. ................................ ............... 40 3 12 Sum of the comput ed mechanisms at transect 2. ................................ ............... 41

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6 LIST OF ABBREVIATION S Potential Energy Anomaly (J/m 3 ) t Change in the potential energy anomaly over time (W/m 3 ) A advection mechanism (W/m 3 ) B Depth mean straining mechanism (W/m 3 ) C Non mean straining mechanism (W/m 3 ) D Vertical advection mechanism (W/m 3 ) E Vertical mixing mechanism (W/m 3 ) F Surface and bottom density fluxes (W/m 3 ) G Inner sources of density (W/m 3 ) H Horizontal divergence of horizontal turbulent density fluxes (W/m 3 ) ABC Summation of A B and C terms (W/m 3 ) Density (kg/m 3 ) Depth mean density (kg/m 3 ) Variation from depth mean density (kg/m 3 ) ADCP Acoustic Doppler Current Profiler A z Eddy viscosity (m 2 /s) CTD Conductivity, Temperature and Depth Profiler DO Dissolved oxygen (mg/L) LIS Long Island Sound K z Eddy diffusivity (m 2 /s) Ri Richardson number u Along estuary velocity (m/s) u Depth mean along estuary velocity u Variation from depth mean along estuary velocity

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7 v Across estuary velocity v Depth mean across estuary velocity v Variation from depth mean across estuary velocity

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8 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillmen t of the Requirements for the Degree of Master of Science MECHANISMS RESPONSIBLE FOR INTRATIDAL VARIATIONS OF STRATIFICATION IN A COASTAL PLAIN ESTUARY By Nicholas Zwemer August 2011 Chair: Arnoldo Valle Levinson Major: Coastal and Oceanographic Engineering Variations in time of vertical d ensity s tratification in coastal water bodies can exert significant influence on the function and structure of coast al ecosystems One such effect is the development of hypoxia from reduced vertical exchange flo w with oxygenated waters near the surface. Magnitudes of s tratification are quantified through the calculation o f the potential energy anomaly, which is the amount of energy needed to fully mix a stratified water column. A dynamic equation for the poten tial energy anomaly has been rigorously deri ved in previous studies, and consists of t he sum of mechanisms contributing to or destroying stratification. Currently the calculation of this equation has only been performed with data produced by numerical mod els, of which only 1 D and 2 D model s ha ve simulated estuarine conditions This thesis uses data from the surv ey of a coastal plain estuary in the computation of the dynamic equation for the potential energy anomaly in 3 dimensions and investigates the contributions of mechanisms within the equation. Data were collected at two parallel transects approximately 2 km apart in the James River Estuary, Virginia. V elocity, electrical conductivity and temperature were recorded over a comp lete semidiurnal tidal

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9 cycle Across and along estuary components of three mechanisms are calculated in this thesis: advection (the advection of a stratified water column), depth mean straining (tidal straining) and non mean straining (estuarine circulat ion). The vertical mixing term is also expected to be a major contributor to variations in stratification, but could not be calculated accurately from the measured data. Previous studies have determined along estuary tidal straining and vertical mixing to be the dominant influences on the development of stratification in an estuary. Yet this thesis has determined that across estuary advection is the dominant term causing stratification locall y in the study area In general, along estuary components of the computed mechanisms were found to be an order of magnitude smaller than their across estuary counterparts C omparison of the sum of these mechanisms with the measured values of t at both transects suggest s th at vertical mixing terms should contribute to mixing at the study area with particular influence during maximum ebb and flood velocities

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10 CHAPTER 1 INTRODUCTION Motivation Density stratification is observed in many coastal e cosystems with varying degrees of magnitude and duration depending on the forces and physical characteristics of the environment. This study seeks to determine the mechanisms causing tidal variations in stratification through the application of measurements from a c oastal plain estuary to a dynamic equation of stratification develo ped by Burchard and Hofmeister (200 8 ) (see also de Boer et al ., 2008 ). This dynamic equation has been rigorously derived and applied to numerical models but has yet to be applied to real empirical data from a survey estuary The f ield data analyzed in this study was obtained from the lower James River and is used to calculate the mechanisms contributing to stratification and mixing in the estuary These computed mechanisms are then compare d with measured values of stratification in the study area A primary concern related to estuarine stratification is the development of hypoxia or anoxia in near bottom layers which can be induced by restriction of the exchange flow between the near b ottom and near surface layers due to extended periods of vertical density stratification ( Valle Levinson et al ., 1995 ). Hypoxia is the reduction of dissolved oxygen (DO ) to levels below 3 mg/L while anoxia denotes an area depleted of DO An example of the seriousness of hypoxia is elucidated in a publication by the European Geosciences Union, which describes h ypoxia as: a world wide phenomenon in the global ocean [which] causes a deterioration of the structure and functions of ecosystems ( J. Zhang et al., 2010)

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11 The study by Valle Levinson et al. (1995) sought to examine the causes for the persisten ce of large vertical density gradients causing hypox ia and anoxia in the Long Island S ound (LIS) The threat of hypoxia was found to be the preeminent issue regarding the health of the LIS ecosystem and was the result of the development of a strong pycnocline restricting vertical exchange flow and local biological and chemical processes ( Valle Levinson et al. 199 5 ). It was observed that factors such as surfa ce heating and horizontal density gradients caused by freshwa ter inputs, or the lack of freshwater inputs, from the Hudson River caused the persistence of the hypoxia inducing vertical density stratification. While certain mechanisms were found to contribu te to the development of the LIS vertical stratification, the results of this study will provide the basis i n determining the validity of using the dynamic equation for stratification to rigorous ly examine all contributing mechanisms. Estuarine Background Estuaries are diverse coastal environments in which saline ocean water encounters and mixes with the freshwater discharge of a river glacier or land runoff. These region s are also often subject to semi diurnal or diurnal variations in along s hore and ac ross shore current velocities due to tidal forcing mainly from the sun and moon Estuaries are found a round the globe and can range in depth from hundreds of meters in f jords, to averaging just a cou ple of meters in intra coastal waterways. The myriad combinations of physical characteristics such as bathymetry, tidal cycles latitude fresh water input, heating and wind forcing create unique conditions in each estuary. Modern society is deeply reliant on the resources of estuaries as they pr ovide considerable economic and environmental equity to adjacent communities with their diverse ecosystems and strategic locations for commerce With the ceaseless modification of

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12 our surrounding physical environment to enhance our quality of life it is i mportant to fully understand the consequences of these modifications to the environment in order to prevent detrimental results Just as Valle Levinson et al. (1995) elucidated that decreases in freshwater input to the LIS due to upstream withdrawals from the Hudson River may increase the development of stratification induced hypoxia, fully understanding the stratification mechanisms of an estuary will aid in the prevention of potentially harmful results of coastal engineering. Stratification Density strati fication of estuaries and shelf seas has been a topic of extensive study in recent decades, yet many questions still remain concerning causes of its development and dissipation. Early analysis of stratification mechanisms was conducted in areas of negligib le freshwater influence (i.e. the Irish Sea) because these areas provide d the greatest simplicity in calculations. Simpson et al. (1978 ) and Simpson and Bowers (1981 ) computed the competition between surface heating and stirring caused by tidal currents and wind stresses. The investigation of this competition is less challenging due to the relatively uniform and easily quantifiable inputs of heat and wind stress to the surface boundary. Simpson et al. (1990) describes the main difficulty in deriving terms describing tidal straining influence as the discrete sources of fresh water at the lateral boundaries. T o begin analyzing stratification it was recognized that there was a need to represent it in a quantifiable way. An approach to this quantification was proposed by Simpson ( 1981 ) who represented the degree of vertical stratification with the amount of mechanical energy needed to obtain a fully mixed water column from a stratified state. This quantified parameter is the potential energy anomaly, with u nits of J/m 3

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13 Another way to define is the amount of energy needed to transport the center of mass of the water column to the location of the center of mass of its fully mixed state ( F igure 1 1). Figure 1 1 A representation o f the potential energy anomaly, T he S shaped curve represents a stratified water column and the straight line represents the water column in a fully mixed state Density increases in the positive direction, and depth increases in the negative z directio n (Valle Levi nson, 2009). Thus, values of vary in the lateral and longitudinal directions of a water body with a single value representing each vertical column of measurement data in the study area. The calculation of is displayed in E quation 1 1 Variables below a horizontal bar represent a depth averaged value. (1 1) Originally, Simpson and Bowers (1981) analyzed stratification as a function of just the ve rtical direction, assuming horizontal homogeneity. de Ruijter (1983) proposed the contribution of horizontal differential advection, which was incorporated into t by van Aken (1986) (de Boer et al., 2008). The study of stratification was furthered by the investigation of Simpson et al. (1990) who assumed the strat if ying effect of bouncy

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14 inputs ( e.g.: freshwater or surface heating) and mixing from tidal and wind stirring acted independently, and the competition between them determined the existence or abse nce of stratification. Their study of the competition between stratifying mechan isms of the Liverpool Bay found that tidal straining, tidal mixing and estuarine circulation were the main terms determining stratification While also incorporating tidal stra ining, estuarine circulation a nd stirring terms, Simpson et al. (1990) still applied the described mechanisms to a 2 D model, and only compared results to a point location of empirical data in the Liverpool Bay. Prior to this study, tidal straining had not been fully recognized for its importance in producing large values of semi diurnal stratification During periods of large tidal flows, the tidal stirring mechanism dominated stratification development, producing f ully mixed water columns. The estuarine c irculation term is also most influential during periods of low tidal amplitudes such as neap tides which might have significant effects during the slack tides of the estuary analyzed in this study ( Simpson et al ., 1990 ) A Dynamic Equation for Stratifica tion Prior to the studies of Burchard and Hofmeister ( 2008 ) and de Boer et al ( 2008 ) a complete equation describing the mechanisms causing variations in stratification with time had not been developed Burchard and Hofmeister (2008) derived their time de pendent dynamic equation for from dynamic equations for potential temperature and salinity, the continuity equation an d the equation of state for sea water An equation of these terms, as displayed by de Boer et al. (2008), follows (Equation 1 2).

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15 (1 2) The terms develope d in their equation are : advection A ; depth mean straining B ; non mean straining C ; vertical advection D ; vertical mixing E ; surface and bottom density fluxes F ; inner sources of density G ; and horizontal divergence of horizontal turbulent density fluxes H In real estuarine systems, most of the preceding terms will exert some influence, but the processes of stratification and mixing will be dominated by only a few terms locally (Burchard and Hofmeister, 2008) This aspect of the dynamic equation for will be utilized in this investigation, as terms that are not expected to contribute much to stratification will be justifiably omitted from calculation. The terms omitted are : D F G and H D is expected to be negligible due to vertical velocity values on the order of a fraction of a millimeter per second at the measurement area. F and G are omitted under the assumption that buoyancy fluxes due to surface warming, local freshwater input (e.g. springs at the bottom or rain water at the surface) and solar radiation are assumed to be negligible in comparison to the large l ongitudinal density gradients driving tidal straining. H is removed due to its r epresentation of horizontal dispersion terms, which are a fraction of their vertical counterpart, E Equation 1 2 displays the 3 dimensional nature of through the calculation of both along and across estuary components of each stratification mechanism which are themselves dependent on vertical variations of density and velocity In their study of the Rhine region of freshwater influence (ROFI) de Boer et al. ( 2008) use d the terms in this

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16 equation as well as other terms, in the analysis of stratificat ion in a 3 D model furthering the comprehensive understanding of stratification mechanisms. Therefore, the E quation 1 2 as described by de Boer et al. (2008) is the best example to apply to a 3 d imensional investigation. Terms considered to be non dominan t in the estuary were omitted in part due to the lack of detailed measurement data that could be used for their calculation de Boer et al. (2008) were able to calculate these terms with more ease due to the fact that these terms are defined in the model. While the 3 D model of de Boer et al. (2008) is useful in demonstrating the computation of mechanisms in both longitudinal and transverse directions, it is also a model of a coastal system that is wholly different from the James River Estuary The locatio ns of survey data for this investigation lie in a coastal plain estuary con sisting of channels and shoals, with a primary axi s of flow parallel to the estuary banks For this 2 D idealized estuarine model can be expected to better represent dominant mechanisms in th e study area. Their model is an estuarine model from a study by Warner et al. (2005) which was varied by Burchard and Hofmeister (2008) by increasing tidal forcing and depth, and decreasing freshwater inflow. A location near the mouth of the estuar ine simulation displays similar conditions as those seen at the surveyed location of the James River Estuary At this location, the model estuary alternates from a fully mixed state to vertically stratified over the course of a tidal cycle with a local maximum in stratification during the slack after flood and an absolute maximum during the slack after ebb. Near the mouth of the model estuary the depth mean straining and vertical mixing mechanisms dominate the competition

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17 between stratification and mixing, with a smaller contribution from non mean straining near slack water after flood and generally small contributions from advection. One motive of this investigation i s to compare this competition derived from a model to a real estuar ine system consisting of both longitudinal and transverse variability of flow and density gradients

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18 CHAPTER 2 METHODS This chapter will provide a brief overview of the James River Estuary study area, followed by a description of the measurement equipment and techniques used to produce the raw data, and will conclude with an explanation of the processing and analysis of the raw data. Study Area The study area from which me asured data was collected is in the lower portion of the James River located near Newport News, Virginia and is approximately 1.75 km upstream from the James River Bridge (Figure 2 1) Th e estuary is characterized as a drowned river valley resulting from the sea lev el rise due to the melt at the end of the last glaciation nearly 6,000 years ago. The James River is the southern most major tributary to the Chesapeake Bay and is therefore the tributary closest in proximity to the mouth of the bay at the Atlantic Ocean. The proximity to the sea explains the moderate to high salinity values found in the survey area Measurements were obtained simultaneously along two separate parallel transects oriented perpendicular to the banks of the estuary. The study area is located in a relatively straight section of the river, with the nearest flow obstruction located about 1.75 km downstream from transect 1 in the form of the James River Bridge. This obstruction should have no significant effect on the stratification or flow at the study area ( Miller et al ., 1996 ). The estuary is directly forced by the freshwater discharge of the James River and tidal influences from the Atlantic Ocean The period of measurement occurred in the month of August, which corresponds with the yearly minimum discharge of the James River ( Wood and Har gis, 1971 ). Previous studies

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19 have determined that the semidiurnal M 2 tidal period dominates tidal forcing frequency of the estuary ( Browne and Fisher, 1988 ). Therefore, the M 2 tidal period of 12.42 hours is the minimum length of time needed to observe a co mplete cycle of the dominant tidal period Transect 2 is 4 km in length and located approximately 2.3 km upstream and parallel to transect 1 which is 4.8 km in length The area of interest along the transects is a 2.6 km section along both transects that encompasses both channels of the cross section, and the adjacent shoals. The axes of plotted results have been normalized so that the deepes t portion of each transect is located at the same distance from the beginning of the transect (i.e. 2.8 km) along t he x axis (Figure 2 2) F or the purpose of analysis i t was important to align the axe s of both tr ansects for the computations of along estuary density gradients The right side of the tra nsect bathymetry of Figure 2 2 lies towards the north east while the left side lies towards the southwest Although the two transects are located in close proximity to one another, their bathymetries differ moderately. Transect 1 consists of a deep primary channel at 2.8 km and a shallow secondary channel at 1.7 km. A mild ly slop ing bottom, producing non symmetric primary channel side slopes separates the two channels (Figure 2 2A) The n ortheast slope of the primary channel is steep and transit ions into a shallow shoal ~ 4 m in depth. The bathymetry of transect 2 is simila r to transect 1 as it too consists of a deep primary channel at 2.8 km and a shallow secondary channel at 1.7 km (Figure 2 2B). Yet the bathymetries di ffers as transect 2 has a deeper primary channel consisting of nearly symmetric side slopes Transect 2 i s also shallower over the center of the cross section between the primary and secondary channels The differences between

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20 the two bathymetries are expected to be a major factor contributing to variations in the observed and computed results at the two transects. Data Collection and Processing The data analyzed in this thesis w ere ob tained from a previous investigation of the James River Estuary and were already partially processed before receipt. This section will give an overview of the method of data collection by the initial researchers and describe the format in which the data was received for analysis in this report. Data were collected at the two parallel transects in the lower James River Estuary over the 12 hour duration of one semidiur nal tidal cycle on August 20, 2008 Each transect was measured simultaneous ly for comparison between t hem. C rossings across the transects were performed in a manner to provide the best possible temporal resolu tion of the tidal cycle Approximately 40 minut es w ere needed to complete a crossing, which allowed for 14 crossings at transect 1 and 1 3 crossings at transect 2 over the course of the 12 hour measurement period. Data collection consisted of an Acoustic Doppler Current Profiler (ADCP), Conductivity Te mperature and Depth (CTD) casts along transect 1, and an oscillating CTD along transect 2. ADCP data consisted of bins 100 m wide and 0.25 m deep for both along and across estuary velocity compon ents. North South and East West velocity vectors measured by th e ADCP ha ve been rotated to along estua ry and across estuary components The rotati on of the velocity vectors can have a considerable influence on the results of this analysis, as stratification mechanisms are divided into lateral and longit udinal components calculated with the corresponding velocity components. Thus, lateral mechanisms do not necessarily correspond with flow directed

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21 perpendicular to the along channel vector, but merely are a result of the variation of the estuary flow from the along channel direction. Data begins one meter below the water surface, and continues to the bed of the estuary The CTD casts along transect 1 were only made during alternating crossings, thus reducing the number of crossings containing salinity a nd temperature measurements to eight along transect 1. Meanwhile, the oscillating CTD utilized along transect 2 produced continuous conductivity, temperature and depth measurements during all 1 3 crossings Thus, during certain computations where simultaneous values of density are needed along both transects, the temporal resolution is limited to instances where both transects have corresponding density values, thus reducing the number of usable crossing to seven as the first crossing of transect 1 does not co rrespond to any crossings of transect 2 Received data consisted of partially filled cross section s comprised of a grid containing bins from the various measurement s M issing data was interpolated between missing grid points and extrapolated to the surfa ce and bed of the transect where appropriate Velocity profiles were neglected for the bottom 10% of the water column to reduce the influence of measurement error. In addition, bins of velocity data that did not have corresponding values in the same positi on in the cross section for more than 80% of the survey crossings were discarded for the same reason. The equation of state was used to calculate density values of the water column from the measured CTD values of salinity, temperature and depth. A left handed coordinate system was used throughout the investigation, with the horizontal axis represented by x and y while the vertical axis is specified as z The x

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22 axis is aligned with the along estuary component of flow and is positive towards the river mo uth The y axis is aligned with the transverse flow axis and positive towards the southwes t bank The origin along the z axis is specified as the mean water surface and decreases with depth. Figure 2 1 Location of measurement area A e rial view of the James River measurement area, with transects 1 and 2 displayed adjacent to the horizontal coordinate system axes.

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23 Figure 2 2 Bathymetry of the two transects. A) T ransect 1 and B) t ransect 2, where distance along the x axis is measured f rom the beginning of transect 1, which corresponds to the s outhwest bank. Depths of the transects are displayed as the time mean depth over the measurement period.

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24 CHAPTER 3 RESULTS The results of this investigation are presented in the following chapter describing the flow velocities, stratification and computed mechanisms of both transects. Flow Characteristics Depth averaged transect velocities are plotted with respect to distance from the beginning of the transect along the horizontal axis and with respect to time along the vertical axis (Figures 3 1 and 3 2) Positive along estuary velocities represent down estuary flow towards the mouth, while positive across estuary velocities represent flow towards the southwest bank (towards the left in the fig ures). Maximum along estuary depth mean velocities at transect 1 are 60 cm/s up estuary during flood and 60 cm/s down estuary during ebb (Figure 3 1 A) Measurements at transect 1 begin during the slack velocities before flood. Maximum up estuary velocitie s occur in the primary and secondary channels during flood with smaller velocities visible over the shallower regions. Six hours after the onset of flood, velocity directions of the along estuary flow reverse, signaling the onset of ebb near hour 17 and c onfirming a semi diurnal dominated tidal period Maximum depth mean down estuary velocities at transect 1 occur during ebb near the center of the transect over the gently sloping bed between the two channels This location does not co incide with the primary channel and maximum ebb velocities do not occur over the deepest portion of the transect. Maximum magnitudes of the depth mean across channel component of velocity at transect 1 are roughly 10 cm/s, and follow a similar semidiurnal cycle as the along estuary component (Figure 3 1 B) The lateral component of velocity is negative during flood and positive during ebb A divergence of the depth mean flow is seen on the

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25 northeast shoal at 3.4 km during flood and convergence during ebb. In genera l the lateral component of velocity is similar in magnitude across the entire cross section with the exception of the northeast and southwest shoals at transect 1. Similar to transect 1, transect 2 consists of a strongly semi diurnal tidal period of dept h mean along estuary velocities with symmetric magnitudes of 60 cm/s during both ebb and flood (Figure 3 2 A). Measurements at transect 2 begin s just before maximum flood velocity which occur in the primary and secondary channels of the cross section. Tra nsect 2 ebb velocities are similar in magnitude to those of transect 1, yet the maximum velocity values coincide with the secondary and primary channels as opposed to the location of the center of the cross section seen at transect 1. The a cross estuary component of velocity of transect 2 differ s more in magnitude along the cross section than seen at transect 1 (Figure 3 2 B) While a semi diurnal frequency with negative values corresponding with flood and positive values with ebb is observed, the magnitu des of these depth mean across estuary flows are subdued inside the primary channel. These values are also generally smaller during ebb than during flood displaying tidal asymmetry in across estuary velocities Stratification Characteristics Plots of the potential energy anomaly ( ) and its change in time ( t ) display the spatial distribution of vertical density stratification across the transects as well as its variation over the tidal cycle (Figures 3 5 and 3 6 ) Plots of are presented as contours with units of J/m 3 and vary in distance across the transect along the horizontal axis and change in time along the vertical axis. At the beginning of the measurement period, which corresponds with the onset of flood, vertical density s tratification is present in the primary channel of transect 1 while

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26 the shallower portions of the cross sec tion remain mostly well mixed (Figure 3 5 A) Stratification in the channel then disappears near the end of flood at hour 15 leaving a completely mixed cross section With the onset of ebb stratification again develops, with largest values located in the deepest portions of the cross section but also with moderate amounts developing over the shallower regions. During the waning of ebb, the shallow portions of transect 1 again become fully mixed, while the primary channel retains most of its stratification The largest values of stratification are seen during the initial onset of the following flood in the primary channel I n contrast to the onset of ebb, the shallow portions of the transect remain well mixed over this period The plot of t a cross transect 1 quantifies the degree of changes in stratification observed in the plot of (Figure 3 5 B). Positive values of t represent stratification and negative values represent mixing of the water column It can be seen at hour 12 that the mixing o f the primary channel during flood produces large negative values of t while at hour 17 the development of stratification across the tran sect during the onset of ebb produces large positive values. Stratification in the primary channel of transect 2 closely resembles the pattern seen at transect 1 in respect to both magnitude and temporal variation through the tidal cycle (Figure 3 6 A) At the beginning of measurement, near maximum flood, the channel displays stratification from the previous ebb. Similar to transect 1, this stratification disappears with the full development of flood velocities creating a fully mixed primary channel b efore the onset of the following ebb Stratification returns to the primary channel during the onset of ebb, and a local maximum occurs near hour 18. During the remainder of ebb, the stratification of the channel varies little until an

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27 absolute maximum is obser ved at the onset of the following flood. Unlike transect 1 which displayed small yet measurable stratification across the shallower portions of the cross section transect 2 displayed no such effects and remained fully mixed everywhere outs ide the primar y channel. Magnitudes of t at transect 2 see location s of rapid stratification in the primary channel in addition to having larger values (Figure 3 6 B) Recall also that density values of transect 2 ha ve better temporal resolution than transect 1 due to salinity and temperature data collected over 13 crossings, as opposed to eight at transect 1. Computed Stratification Components The stratifying mechanisms of the two transects were calculated for both along and across estuary components The stratification terms of advection A ; depth mean st raining, B ; and non mean straining, C ; are plotted as contours with units of W/m 3 (Figures 3 7 3 8 3 9 and 3 10 ) The computed across estuary (lateral) mecha nisms A B and C for transect 1 are the same order of magnitude as measured t values (Figure 3 7 ) Largest values at transect 1 are seen mostly in the pri mary channel The advection term contributes the most to stratification of the three computed mechanisms Large stratifying values are not observed in the computations of depth mean and non mean straining terms yet they exert considerable influence in the de stratification of the transect. Values of the across estuary mechanisms are lower in magnitude over shallow er portion s of transect 1 The computed along estuary mechanisms at transect 1 range in magnitude from 5.0e 4 to 3.0e 4 W/m 3 and are an order of magnitude smaller than across estuary components (Figure 3 8 ) Stratification values are largest for the depth mean straining

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28 term and occur at th e end of the measurement period during the onset of flood. Near hour s 13.5 and 19.5 advection cont ributes significantly to mixing with respect to magnitudes of other along estuary mechanisms. Non mean strain ing in the along estuary direction contributes little to either stratification or de stratification of the transect. The sum of the computed mechanisms, ABC, at transect 1 produces a result that is similar in some aspects to measured t values (Figure 3 11 A ). The difference between the summed components and measured values of t is displa yed in the plot of residual t (Figure 3 11 B) Near the beginning of the measurement period (hour 13), the summed me chanisms closely resemble the measured t data and predict de stratification to occur, although the magnitude is over predicted by nearly a factor of 2. The summed mechanisms also differ from measured values in the predict ion of stratification to occur around hour 18, which can be seen in the residual mech anism plot to be over predicting stratification at that time. The computed across estuary mechanisms A B and C for transect 2 display similar characteristics as those of transect 1 (Figure 3 9 ) The largest magnitudes of stratification and de stratifi cation occur inside the primary channel, with advection contributing the largest magnitudes to stratification. Transect 2 along estuary components also agree with results of transect 1 and are an order of magnitude smaller than across estuary co mponents (Figure 3 10 ) The main difference between the computed mechanisms of both transects is the location of large stratification and mixing values. This is most notably seen in the large stratification predicted by the advection

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29 term at transect 2 near the b eginning of the measurement period when the same mechanism of transect 1 predicts mixing at that location Of note from the sum of the computed mechanisms at transect 2 is the over prediction of stratification occurring at the beginning of the measurement period by the advection term. This dominates the summed components at that location and correspond to measured data at that location and time. Also, the sum of the mechanisms at transect 2 produce a very large ar ea of mixing between hours 18 and 22 which does not correspond with measured data.

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30 Figure 3 1 Depth mean velocities at t ransect 1 A) D epth mean along channel and B) depth mean across channel flow velocities

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31 Figure 3 2 Depth mean velocities at t ransect 2 A) D epth mean along channel and B) depth mean across channel flow velocities

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32 Figure 3 3 Transect 1 density profiles of crossings 1 8, with contour units of kg/m 3 Crossing 1 is displayed in row 1, column 1 and increase down column 1 and continues to progress in time down column 2.

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33 Figure 3 4 Transect 2 density profiles of crossings 1 12, with contour units of kg/m 3 Crossing 1 is displayed in row 1, column 1 and increase down column 1 and continue s to progress in time down column 2.

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34 Figure 3 5 Potential energy anomaly values at t ransect 1 A) P otential energy representing changes in stratification through the tidal cycle.

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35 Figure 3 6 Potential energy anomaly values at t ransect 2 A) P otential energy representing changes in stratification through the tidal cycle.

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36 Figure 3 7 Computed lateral mechanisms at t ransect 1 L ateral A) advection of a mean magnitudes.

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37 Figure 3 8 Computed longitudinal mechanisms at t ransect 1 A long channel A) terms displayed with identical color scales to display relative magnitudes.

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38 Figure 3 9 Computed lateral mechanisms at t ransect 2 Lateral depth with identical color scales to display relative magnitudes.

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39 Figure 3 10 Computed longitudinal mechanisms at t rans ect 2 A long channel A) terms displayed with identical color scales to display relative magnitudes.

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40 Figure 3 11 Sum of the computed mechanisms at t ransect 1 A) S um of the co mputed stratification mechanisms and B) the difference between the summed mechanisms and the measured values of the change in phi with time.

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41 Figure 3 12 Sum of the computed mechanisms at t ransect 2 A) S um of the computed stratification mechanisms and B) the difference between the summed mechanisms and the measured values of the change in phi with time

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42 CHAPTER 4 DISCUSSION Overview The two survey transects of this investigation are geographically close, ye t differ slightly in bathymetry, caus ing the competition between stratification and mixing com ponents to differ between them. Transect 1 is about 2.5 kilometers nearer to the mouth of the estuary than t ransect 2, and is about 4 m shallower at its deepest point. Furthermore, t ransect 2 has well defined symmetric channels unlike transect 1, which consists of asymmetric channels separated by a mildly sloping bottom The differences between channel depth and shape are t he dominating bathymetric effect s distinguishing transect 1 from transect 2 The depth mean velocities of the study area demonstrate a semidiurnal tidal period with near symmetric ebb and flood velocity magnitudes. Conventional coastal plain estuaries have maximum velocities over the deepest portions of the flow cross section due to the balance between the horizontal pressure gradient and friction, y et maximum ebb flow at transect 1 does not coincide with the primary channel Instead maximum ebb flow occurs over the shallower gently sloping bed adjacent to the channel. This is likely d ue to the asymmetry of the channel slopes, where an absence of a steep slope on the southwest side of the channel does not balance friction from the steep northeast slope Flows of t ransect 2 however, have largest depth mean velocity magnitudes o f both ebb and flood located in the primary and secondary channels likely due to the opposing frictional effects of the symmetric channel slopes The s hallow fully mixed portions of transect 2 experience large across estuary velocities while the deeper portions that become stratified experiencing only small

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43 across estuary velocities. The inverse correlation between lateral velocities and stratification at transect 2 suggest that the across estuary components of the stratification mechanisms will likely have significant influence There is a clear correlation between stratification and depth, as the deepest portions of the study area correspond with the largest magnitudes of stratification at both transects From the results of previous studies by Simpson et al. (1990) in the Liverpool B ay and Burchard and Hofmeister (2008) in 1 D and 2 D numerical models, the mechanisms dominating the competition between stratification and mixing should occur between along estuary tidal straining and vertical mixing cause d by tidal and wind stirring. However, the results of this investigation suggest the dominant influence is produced by across estuary components with a large contribution from the advection term in particular From the results of both transects, it can be seen that across estuary advection is the dominant term in producing or destroying the local stratification in the estuary. An analysis of the processed data reveals that this is due to large values of across estuary density gradients, most specifical ly the gradient of the deviation of density from depth mean values in the across estuary direction Recall that, in part, the computation of mechanisms A B and C consisted of the multiplication of u v or u v / x / y or / x / y respectively. Therefore, because across e stuary density gradients are an o rder of magnitude larger than along estuary values across estuary stratification mechanisms are larger than their along estuary counterpar ts despite having smaller velocities. From the studies of Burchard and Hofmeister (2008) and de Boer et a. (2008), t he mechanism of vertical mixing, E is expected to be a major component determining the

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44 development of stratification in the measurement area. This mechanism was defined by Burchard and Hofmeister (2008) as a function of vertical eddy diffusivity ( E quation 4 1). (4 1) Three methods were employed in the attempt to determine eddy diffusivity values, K z Two methods attempted to determine K z as a function of the Richardson N umber Ri (4 2) The equations defining K z as a function of Ri were obtained from Munk and Anderson ( 1948 ) and Pacanowski and Philander ( 1981 ) ( E quations 4 2 and 4 3, respectively). (4 3) (4 4) The third method assumed a value of 1 x 10 3 for K z which was constant with depth. Substitution of computed values of K z from the three methods into E quation 4 1 produced values of E orders of magnitude larger than measured data. These results have therefor e been discarded, as the accuracy of their computation is cannot be confirmed through comparisons to expected values Further examination is needed to

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45 determine the cause of this discrepancy, and the accurate calculation of this term will greatly enhance the findings of this investigation. Yet, the influence of E can be inferred from the d ifference between measure values of t and ABC These residual values of t displayed in the results indicate locations and times during the tidal cycle where large contributions to mixing can be expected fr om vertical mixing Analysis of Mechanisms This section describes the contributions from the various computed stratification mechanisms, the sum of their components and the causes for their variation from measured values of t The best correlation between the sum of the computed mechanisms and measured values of t appears in the primary channel of transect 1 near the beginning of the measurement period, hour 1 2 .5. While overestimating the magnitude of mixing by a factor of 2, the shape of the contours of ABC from hour 12.5 to 15 is almost identical to that of the measured values of t at tra n sect 1. Large contributions to this area of m ixing are observed from both along and across estuary advection and across estuary depth mean and non mean straining In co ntrast ABC values at the same time and location at transect 2 show little correlation with measured values of t In contrast ABC predicts stratification at transect 2 will increase rather than decrease at this location, with the across estuary advec tion term the largest contributor to this discrepancy. It i s therefore very likely that vertical mixing compensates for the stratification produced by advection Maximum flood velocities also correspond with this period of measurement, and the large amount of vertical mixing needed to overpower stratification agrees with the findings of Simpson et al. (1990) in which large tidal velocities creat ing significant amounts of tidal stirring caused the influence of vertical mixing to rise during the se tidal periods. Friction from the steep

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46 channel slopes of transect 2 could be another factor contributing to vertical mixing which is not seen at transect 1. Also of note at this time and location in the results is the absence of influence from depth me an and non mean straining terms at transect 2, most likely due to the small across estuary velocities of the primary channel. Another area of interest is hour 19 at transect 1, where ABC over predicts stratification, and is another possible location of in fluence from vertical mixing due to the strong ebb flows at that time. Also recall that not all components of the t equation were cal culated from the survey data from lack of necessary measurements and predi ction of minimal influence. Yet comparisons betw een ABC and t at transect 1 show not only areas of over predicting stratification, for which the vertical mixing term might compensate, but also for an under prediction of stratification This is ob served between hours 16 and 18 (mid day in August) occurring during slack flow between flood and ebb, and also mostly over shallower regions of the transect. These factors suggest density fluxes due to surface heating could cause stratification not accounted for in the other terms. This assumption is supp orted by f inding by Simpson et al. (1990) and de Boer et al. (2008), explaining that during periods of minimal influence from other terms due to slack velocities or small density gradients, other buoyancy forcing mechanisms can exert dominance. Finally, ABC values at t ransect 2 produce a large discrepancy with t near the end of the measurement period on the northeast slope of the primary channel Her e ABC greatly over predict s mixing. Towards the end of the measurement period, the grid of raw data covered a smaller percentage of the transect than obtained f rom other

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47 crossing s This meant extrapolation to the extents of the cross section boundaries might have produce d slightly larger error than seen at other locations

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48 CHAPTER 5 CONCLUSION The ultimate objective of this paper was to determine the major components causing stratification an d mixing at the James River estuary survey site. In pursuit of this objective, measurement data from the estuary was applied the calculation of advection, depth mean straining and non mean straining in both the along and across estuary directions from the dynamic equation of the potential energy anomaly derived by Burchard and Hofmeister (2008) and de Boer et al. (2008). An attempt was also made to calculate the vertical mixing term, which produced unsatisfactory results. S imilar trends were seen between ABC and measured t values at certain locations in the study area However, summed components of t ransect 1 displayed a better correlation between the computed and measured data The inability to accurately compute a vertical mixing term from measurements is expected to be a significant cause of the difference between computed and measured terms. De Boer et al ( 2008 ) al so states in their findings of the dynamic equation for that many of the computed mechanisms cancel one another but are still important in developing the overall picture of stratification Even with the difference s between the summed mechanisms and mea sured t valuable and unexpected conclusions can be drawn from the results of the investigation. Across estuary terms, specifically advection, exert much more influence in the competition determining stratification than was hypothesized in earlier studi es While globally the longitudinal density gradient of the fresh water source at the head of the James River and the high salinity seawater at its mouth produce the stratification observed in the estuary as a whole. Locally lateral velocities and density gradients

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49 contribute significantly to the development of stratification. This knowledge is of great importance for analysis of land development along or in the James River A s modification of the estuary cross section espec ially on the shallow portions adjacent to the channels may signi ficantly alter the development or destruction of stratification. This was demonstrated in the apparent influence of bathymetry in determining the balance bet ween stratification mechanisms.

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50 LIST OF REFERENCES Bro wne, D.R. Fisher, C.W., 1988. Tide and tidal currents in the Chesapea ke Bay. NOA A Tech. Rep. NOS OMA, U.S. Department of Commerce, Rockville, Md., 3, pp. 143 Burchard, H., Hofmeister, R., 2008. A dynamic equation for the po tential energy anomaly for analyzing mixing and stratification in estuaries and coastal seas. Estuarine Coastal and Shelf Science 77, 679 687. de Boer, G.J., Pietrzak, J.D., Winterwerp, J.C., 2008. Using the potential energy anomaly equation to investigate the roles of tidal straining and advection in river plumes. Ocean Modelling 22, 1 11. de Ruijter, W.P.M., 1983. Effects of velocity shear in advective mixed layer models. Journal of Physical Oceanography 13 (September), 1589 1599. Miller, J.L., Valle Levi nson, A., 1996. Effects of Chesapeake Bay Bridge Tunnel pilings on destratification in the lower Chesapeake Bay. Estuaries 9 (6), 526 539. Rabalais, N.N., Gilbert, D., 2009. Distribution and consequences of hypoxia, Watersheds, Bays, and Bounded Seas, Isla nd Press, Washington DC, pp. 209 225. Simpson, J.H., 1981. The shelf sea fronts: Implications of their existence and behavior. Philosophical Transactions of the Royal Society London Series A 302, 531 546. Simpson, J.H., Allen C.M., Morris, N.C.G., 1978. Fr onts on the continental shelf. Journal of Geophysical Research 83, 4607 4614. Simpson, J.H., Bowers, D., 1981. Models of stratification and frontal movement in shelf seas. Deep Sea Research 28, 727 738. Simpson, J.H., Brown, J., Matthew, J., Allen G., 1990 Tidal straining, density currents, and stirring in the control of estuarine stratification. Estuaries 26, 1579 1590. Valle Levinson, A., 2009. Turbulence and mixing lecture notes. University of Florida 3 Valle Levinson, A., Wilson, R.E., Swanson, R.L., 1995. Physical mechanisms leading to hypoxia and anoxia in western long island sound. Environmental International 21, 657 666. Valle Levinson, A., Wong, K.C., Lwiza, K.M.M., 2000. Fortnightly variability in the transverse dynamics of a coastal plain estua ry. Journal of Geophysical Research 105, 3413 3424.

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51 van Aken, H., 1986. The onset of seasonal stratification in shelf seas due to differential advection in the presence of a salinity gradient. Continental Shelf Research 5 (4), 475 485. Warner, J.C., Sherwood, C.R., Arango, H.G., Signell, R.P., 2005. Performance of four turbulence closure models implemented using a generic length scale method. Ocean Modelling 8, 81 113. Wood, L., Hargis, W.J., 1971. Transport of bivalve larvae in a tidal estuary. Proceedings 4th European Marine Biology Symposium, Cambridge University London pp. 29 44. Zhang, J., Gilbert, D., Gooday, A.J., Levin, L., Naqvi, S.W.A., Middelburg, J.J., Scranton, M., Ekay, W., Pe a, A., Dewitte, B., Oguz, T., Monteiro, P.M.S., Urban, E., Rabalais, N.N., Ittekkot, V., Kemp, W.M., Ulloa, O.M., Elmegren, R., Escobar Briones, E., Van der Plas, A.K., 2010. Natural and human induced hypoxia and consequences for coastal areas: synthesis and future development. Biogeosciences 7, 1443 14 67.

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52 BIOGRAPHICAL SKETCH Nick was enrolled at the University of Florida from 2005 to 2011 He achieved a Bachelor of Science degree in c ivil e ngineering with an emphasis on water resources in 2010. He then pursued a M aster of Science degree in the field of c oastal and o ceanographic e ngineering at the University of Florida receiving the degree in the summer of 2011