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PAGE 1 1 FRICTION DOMINATED WATER EXCHANGE IN A FLORIDA ESTUARY By KIMBERLY ARNOTT 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 2009 PAGE 2 2 2009 Kimberly Arnott PAGE 3 3 To my f ather PAGE 4 4 ACKNOWLEDGMENTS I thank my advisor and chair, Dr. Arnoldo ValleLevinson, for the guidance and support needed to complete this project. I also thank Dr. Thieke for being on my committee, as well as Dr. Valle Levinsons group of research students, who gave me insightful comments and suggestions throughout this study. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................. 4 TABLE OF CONTENTS .................................................................................................. 5 LIST OF FIGURES .......................................................................................................... 6 LIST OF ABBREVIATIONS ............................................................................................. 8 ABSTRACT ................................................................................................................... 10 CHAPTER 1 INTRODUCTION .................................................................................................... 12 Motivation ............................................................................................................... 12 Estuarine Background ............................................................................................. 12 Circula tion ............................................................................................................... 14 Turbulence .............................................................................................................. 15 Turbulent Kinetic Energy Dissipation Theory .......................................................... 17 2 METHODS .............................................................................................................. 21 Study Area .............................................................................................................. 21 Data Collection ....................................................................................................... 22 Data Processing ..................................................................................................... 23 Tidal Variability ................................................................................................. 24 Subtidal Structure ............................................................................................. 27 3 RESULTS ............................................................................................................... 29 Tidal Variability ....................................................................................................... 30 Exchange Flow ....................................................................................................... 32 Ekman Kelvin Solution ........................................................................................... 32 Hydrographic Variables ........................................................................................... 33 TKE Dissipation ...................................................................................................... 36 4 DISCUSSION ......................................................................................................... 60 5 CONCLUSION ........................................................................................................ 64 LIST OF REFERENCES ............................................................................................... 65 BIOGRAPHICAL SKETCH ............................................................................................ 67 PAGE 6 6 LIST O F FIGURES Figure page 2 1 Map of Hillsborough Bay Estuary, showing transect line and five hydrographic stations. ........................................................................................ 28 3 1 Along Estuary Tidal Flow (cm/s) for February 24. A) Transect 1. B) Transect 2. C) Transect 3. D) Transect 4. E) Transect 5. F) Transect 6. ........................... 38 3 2 Along Estuary Tidal Flow for February 24. A). Transect 7. B) Transect 8. C) Transect 9. D) Transect 10. E) Transect 11. F) Transect 12. ............................. 39 3 4 Across Estuary Tidal Flow for February 24. A) Transect 1. B) Transect 2. C) Transect 3. D) Transect 4. E) Transect 5. F) Transect 6. ................................... 40 3 5 Across Estuary Tidal Flow for February 24. A). Transect 7. B) Transect 8. C) Transect 9. D) Transect 10. E) Transect 11. F) Transect 12. ............................. 41 3 6 Tidal Current Amplitude (cm/s) and Phase (radians) for Along Channel Flow in February 24, as calculated from the least squares fit to the semi diurnal tide .. .................................................................................................. 42 3 7 Tidal Current Amplitude (cm/s) and Phase (radians) for Across Channel Flow in February 24, as calculated from the least squares fit to the semi diurnal tide ....................................................................................................... 43 3 8 Depth Averaged Along Estuary Tidal Flow (cm/s) for Time versus Distance Across for February 24, 2009. ............................................................................ 44 3 9 Residual Along and Across Channel Flow (cm/s) for February 24, as calculated using least squares fit to semi diurnal tidal cycle. .............................. 45 3 10 Results from Ekman Kelvin Model for Along Estuary Residual Flow using low, middle, and high Ekman numbers ............................................................... 46 3 11 Results from Ekman Kelvin Model for Across Estuary Residual Flow using low, middle, and high Ekman numbers. .............................................................. 47 3 12 Temperatur e (Celsius) for February 24. A) Transect 1. B) Transect 2. C) Transect 3. D) Transect 4. E) Transect 5. F) Transect 6. The x symbols represent the hydrographic stations. .................................................................. 48 3 13 Salinity (ps u) for February 24. A) Transect 1. B) Transect 2. C) Transect 3. D) Transect 4. E) Transect 5. F) Transect 6. The x symbols represent the hydrographic stations. ........................................................................................ 49 PAGE 7 7 3 14 Density Anomaly (kg/m 3) for February 24. A) Transect 1. B) Transect 2. C) Transect 3. D) Transect 4. E) Transect 5. F) Transect 6. The x symbols represent the hydrographic stations. .................................................................. 50 3 15 Mean Temperature (Cel sius), Salinity (psu), and Density Anomaly (kg/m3) Contours for February 24. The x symbol represents the five hydrographic stations. .............................................................................................................. 51 3 16 Potential Energy Anomaly (J/m3). A) Transect 1. B ) Transect 2. C) Transect 3. D) Transect 4. E) Transect 5. F) Transect 6. G I) Bathymetry. ....................... 52 3 17 Potential Energy (J/m3) Contours for Time versus Distance Across for February 24. ....................................................................................................... 53 3 18 Mean Potential Energy Anomaly (J/m3) and Bathymetry for February 24. ......... 54 3 19 Turbulent Kinetic Energy Dissipation (m2/s3) using 128 scans for February 24. A) Transect 1. B) Transect 2. C) Transect 3. D) Transect 4. E) Transect 5. F) Transect 6. The x symbols represent the stations. .................................. 55 3 20 Turbulent Kinetic Energy Dis sipation using 256 scans for February 24. A) Transect 1. B) Transect 2. C) Transect 3. D) Transect 4. E) Transect 5. F) Transect 6. The x symbols represent the hydrographic stations. ..................... 56 3 21 Mean Turbulent Kinetic Energy Dissipation using 128 and 256 scans for February 24. The x symbol represents the five hydrographic stations. ............ 57 3 22 Time series contours for Station 2. A) Ri chardson Number. B) TKE Dissipation using 128 Scans. C) TKE Dissipation using 256 Scans. .................. 58 3 23 Comparison of Friction and Coriolis Momentum Balance Terms. ....................... 59 PAGE 8 8 LIST OF ABBREVIATION S Density (kg/m3) Velocity gradient Vertical eddy viscosity Kinematic viscosity Shear stress B Basin width Bi Body force cics A n O(1) constant cvc C onsta nt related to spectrum in viscous subrange cw A n O(1) constant DT D iffusivity of heat f C oriolis F Fourier transform of F* C omplex conjugate H Water depth (m) k M ax wavenumber K Kelvin number k R ad m1 k W avenumber (rad m1) kB Batchelor wavenumber kk Kolmogorov wavenumber L Length in describing flow PAGE 9 9 q Universal constant rad R adians Re Reynolds Stresses Ri Internal Rossby Radius T T emperature fluctuation To T emperature center of region u S ensor velocity relative to water U Velocity of flow w I nternal waves z V ertical ordinate D imensionless wavenumber A re constants PAGE 10 10 Abstract of Thesi s Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science FRICTION DOMINATED WATER EXCHANGE IN A FLORIDA ESTUARY By Kimberly Arnott December 2009 Chair: Arnoldo ValleLevinson Major: Coastal and Oceanographic Engineering The pattern of net exchange flow typically observed in estuaries consists of a vertically sheared distribution wit h outflow at the surface and inflow at depth. Theoretical results of exchange flows dominated by frictional effects under lateral variations in bathymetry, however, display a laterally sheared distribution with inflow occupying the deepest portion of the c ross section and outflow over the shoals. There is little observational evidence to support those theoretical results. Nonetheless, numerical results in Hillsborough Bay, a branch of Tampa Bay, suggested that the net exchange flow pattern is consistent wit h theoretical results for a flow dominated by friction. The main purpose of this investigation was then to obtain obse rvational evidence that supported theoretical and numerical results. A 12hour field survey was co nducted on February 24, 2009, where cur rent velocity measurements and profiles of temperatur e and electrical conductivity were collected. Observations from Hillsborough Bay were compared to numerical model results and to an analytical solution. The along e stuary tidal currents had amplitudes < 30 cm/s, which were relatively weak when compared to other estuaries. T idal current amplitudes were largest at the sur face of the channel and weak est over the shoals. The isotachs mimicked the bathymetry, indicative of frictional PAGE 11 11 influences f rom the bottom The tidal current phase distributions showed that the currents at the bottom and at depth lead the currents at the surface. The observed residual exchange flow showed a horizontal ly sheared pattern with net volume inflow in the chan nel and outflow over the shoals. This residual exchange flow compared favorably with the numerical model results. Given that the theoretical results indicated a friction dominated flow pattern, t he friction term of the momentum equation was compared against Coriolis accelerat ion and plotted over bathymetry. The friction term was one order of magnitude higher than the Coriolis term, showing that the flow is dominated by friction. The density distribution showed that the greatest str atification was in the channel and more mixed conditions were over the shoals. The mixed water conditions over the shoals are caused by friction from the bottom affecting the entire water column. Due to the depth of the channel, frictional influences do not affect the entire water column, allowing for stratification to occur The distribution of turbulent kinetic energy dissipation showed that the highest values were in the channel and near the bottom The strongest current s and greatest stratification took place in the channel. Even though this estuar y has we ak tidal currents, observational evidence showed that there can still be considerable frictional effects, resulting in a frictionally dominated exchange flow. PAGE 12 12 CHAPTER 1 INTRODUCTION Motivation Pritchard (1956) proposed that the hydrodynamics of a c oastal plain estuary is a balance between pressure gradient and friction. Utilizing a flat bathymetry, this analysis resulted in a two layer vertically sheared estuarine exchange flow This exchange pattern is characterized by inflow of denser ocean water at depth and outflow of less dense water at the surface. Wong (1994) revisited this concept using a triangular bathymetry. This variation in bathymetry created an exchange flow pattern of inf low in the middle and outflow over the shallow sides The exchange flow t ypically observed in estuaries i s a combined vertically and laterally sheared distribution with inflow at depth and outflow at the surface and on the sides Numerical results in Hillsborough Bay ( Meyers et al., 2007) showed that t he exchange flow pattern was horizontal ly sheared: inflow in the entire water column of the channel and outflow over the shoals. This laterally sheared exchange flow patter n is a highly frictional theoretical condition. There is little observational evidence that supports this pattern, which motivated an investigation at the Hillsborough Bay Estuary. The p urpose of this analysis is to compare field observations from Hillsborough Bay with the results of the numerical model as well as with Valle Levinson (2008)s analytical solution Estuarine Background The region encompassing the meeting point between the ocean and river is loosely defined as an estuary. Typically c omposed of brackish water, estuaries can be classified by their circulation and can be categorized into four g roups: highly stratified, fjords, partially mixed, and homogen e ous. Estuaries are typically described in along  PAGE 13 13 and across estuary components of momentum where the along estuary component runs parallel to the main motion of flow, while the across component runs perpendicular to the principal axis. Equation 11 describes the full momentum equation for the along estuary component. (1 1 ) This equation is comprised of a balance of local acceleration (first term on the l eft hand side l.h.s of the equation), advection (second, third and fourth terms on the l.h.s.) Coriolis forcing (fifth term on the l.h.s), barotropic (first term on the right hand side r.h.s of the equation) and baroclinic pressure gradient s (second term on the r.h.s.) and horizontal and vertical mixing (third, fourth, and fifth terms on the r.h.s.) ( Valle Levinson, 2009a) The parameters u, v, and w represent the along, across, and v ertical components of velocity, while f, g, and Ax, y, z stand for the Coriolis acceleration, gravity, density, and vertical eddy viscosity in the x, y, and z components. In a partially mixed estuary, the following assumptions can be made: steady state, linear motion, no rotation with friction only occurring in the vertical with a constant AZ ( Valle Levinson, 2009a). With these assumpt ions, Equation 11 reduces to Equation 12. (1 2 ) Equation 12 dem onstrates a balance between pressu re gradient and friction. Equation 1 3 represents the mean dynamical balance for the across estuary component of momentum. (1 3 ) PAGE 14 14 This equation consist s of local acceleration (first term on the l.h.s), advection (second, third and fourth terms on the l.h.s.), C oriolis forcing (fifth term on the l.h.s.) total pressure gradient (first term on the r.h.s.), and horizontal and vertical mixing in the lateral direction(second, third, and fourth ter ms on the r.h.s.) Equation 14 demonstrates becomes a geostrophic balance between C oriolis and pressure gradient (1 4 ) This is the reduction of Equation 13, utilizing the following assumptions: steady state, fr ictionless, and linear motion. This is the dynamical framework established by Pritchard (1956) to study estuaries. The water circulation occurring in estuaries is the next concept to be discussed. Circulation Estuarine circulation is the residual movement of w ater, after the tidal effects have been removed. T ypical estuarine circulation is a density driven flow, characteriz ed by denser ocean water entering the estuary along the bottom and less dense freshwater moving at the surface, toward the ocean. However, circulation can differ depending on parameters such as basin width, friction, and the effect of C oriolis ( Valle Levinson, 2008) Estuarine circulation can be characterized as vertically or horizontally sheared. Vertical shearing is defined as outfl ow of the less dense water at the surface and the inflow of denser water below. Horizontally sheared exchange flow is described as inflow occurring in the channel and outflow over the shoals. The transition from vertically sheared to horizontally sheared exchange has been explained by ValleLevinson (2008). Valle Levinson (2008)s model is a semi analytical solution that solves dens ity driven exchange flows in terms of Ekman, Ek, and Kelvin, K, numbers: PAGE 15 15 (1 5) (1 6) The parameters in the previous two equations are vertical eddy viscosity, Az, Coriolis forcing, f water column height, H basin width, B, and internal Rossby Radius, Ri. The internal Rossby Radius is a scale where the rotational effects become as significant as buoyancy effects. The model solves for the along and across estuary component residual flows. These flows are produced by pressure gradients and are assumed to only be affected by fricti on and Coriolis, ignoring advective effects. The most appropriate way to represent friction in the momentum balance is through turbulence, which is explained next. Turbulence Turbulence is the unstable flow of a fluid and is characterized by random propert y changes (McDowell & OConner, 1977, pp. 4851) Turbulent fluid can be thought of as a collection of eddies which are created by flow instabilities, bed irregulari ties and wind and wave action. Turbulent eddies are distorted by velocity gradients, which can increase the length of the vortex tube while decreasing the area, subsequently causing the eddy to rotate faster. T hese distorted eddies are continuously reduced in size until viscous friction between layers of varying velocities damp out the eddy motion. In this process the kinetic energy of the eddy is converted to heat energy (Lewis, 1997, pp. 9497) Three main sources of velocity shears exist in estuaries: shears from wind, shears from bottom stresses, and internal shears from velocity gradient s in the water column. In shallow tidal areas, vertical shear commonly occurs from the frictional drag PAGE 16 16 of the bed, with the greatest magnitudes in the principal direction of flow. Strong shears can occur during the turn of the tide, when differences in phase result in distortion of the direction of the current over depth. Turbulence is representative of the non linear terms of the momentum equation (Hughes & Brighton, 1999, p. 248). The momentum equation used to derive turbulence, Equation 17, assumes the flow is incompressible and the viscosity is constant. (1 7 ) The parameters ui,j, p, and Bi represent the density, velocity components, pressure, viscosity, and body force per unit volume. The turbulent kinetic energy equation (Equation 1 8) is achieved by multiplying the flow by the t urbulent flow momentum equation (Pielke, 2002, p. 167). (1 8 ) (1 9 ) The total change turbulent kinetic energy (term on the l.h.s. of the equation) can be thought of as the balance of the transport of turbulent kinetic energy by advection (first two terms on the r.h.s of the equation) the shear production (third term on the r.h.s. side of the equation) vi scous dissipation (fourth term on the r.h.s. of the equation) and the buoyancy production (fifth term on the r.h.s. of the equation) The parameters e, uj, ui, g, w represent the turbulent kinetic energy, velocity shear, subscale velocity fluxes, potent ial temperature, gravity, and vertical velocity. Equation 110 represents turbulent dissipation. PAGE 17 17 (1 10) The following section will discuss the theory behind how the turbulent kinetic energy dissipation, used to invest igate the frictional influences in the water column, is measured with a microstructure profiler Turbulent Kinetic Energy Dissipation Theory Turbulent kinetic energy dissipation, is estimated by fitting a theoretical form of the temperature gradient spectrum to observed data (Soga & Rehmann, 2004). The observed data are measured with a microstru cture profiler that samples at 100 Hz. The temperature gradient is a physical quanti ty describing the direction and rate of the temperature change. A temperature gradient contains five portions : fine structure, internal waves, inertial convective subrange, Batchelor spectrum, and noise spectra ( Luketina & Imberger, 2001). The higher wave number of the temperature gradient spectrum is a function of and the dissipation of the temperature variance, T The fine structure is observed when the field instrument vertically travels through a stationary fluid stratified by density. The following vertical temperature profile equation represents the case where heat is causing stratification. (1 11) The variables and are constants, z is the vertical ordinate with the center at the origin of interest, and To is the temperature at the cent er of the origin (Luketina & Imberger, 2001). The temperature gradient c an then be given by Equation 112. (1 12) PAGE 18 18 Equation 113 then becomes the onesided finestructure power spect rum of t he temperature gradient (1 13) F is the Fourier transform of the temperature gradient, the asterisk signifies the complete conjugate, and k represents the wavenumber. Equation 1 14 is representative of the temperature gradient spectrum where the internal waves have a wavelength smaller than the internal Rossby radius (1 14) The variable cw denotes the wave speed of the internal waves. The internal waves are bounded by a max frequency of N which is shown in the following equation. (1 15) The fluid density is represented by The wave number can then be calculated using the maximum wavenumber, as shown in Equation 116. (1 16) The sensor velocity relative to the water is denoted by u The inertial convective subrange portion of the temperature gradient is present for scales that are big enough to be influenced by viscosity, yet smaller than the max imum wavenumber. The following equation represents the i nertial convective subrange portion of the temperature gradient. (1 17) Cics is a constant and t is the dissipation of the temperature variance. Equation 118 represents the dissipation of temperature variance due to turbulence. PAGE 19 19 (1 18) (1 19) DT is the diffusivity of heat, T is the temperature, cvc is a constant, and is the fluid viscosity. The Batchelor spectrum segment of the temperature gradient is a derived temperature gradient spectrum with the assumptions that for high Reynolds turbulence, the small scale comp onents of the temperature distribution are statistically homogenous, steady, and isotropic ( Soga & Rehmann, 2004). The onedimensional Batchelor spectrum is represented by Equation 120 ( Luketina & Imberger, 2001) (1 20) (1 21) The variable kB represents the Batchelor wavenumber and is a di mensionless wavenumber. Equation 1 22 is r epresentative of the normalized Batchelor spectrum. (1 22) The final part of the temperature gradient is the noise spectra. This section is created from noise associ ated with the sensors or the processing circuitry. Presently, there are three ways of fitting the observed temperature gradient to the Batchelor spectrum from which turbulent dissipation can be estimated. The first method involves making a graphical fit of the temperature gradient data to the nondimensionalized Batchelor spectrum (Luketina & Imberger, 2001) A second is to make a nonlinear least squares fit method of the Batchelor spec trum to the temperature gradient spectra using high signal to noise levels (Dillion & Caldwell, 1980). The last PAGE 20 20 method uses an algorithm to fit the Batchelor spectrum to the measured spectrum (Ruddick et al., 2000) The S elf C ontained A utonomous M icrostructure P rofiler (SCAMP, used in this experiment) processing software uses the last method to es timate the rate of dissipation which is used in this study The dissipation is estimated by fitting the Batchelor spectrum and noise spectrum to the observed temperature gradient. The model noise spectrum filters out noise occurring from the thermistor and the process ing circuitry with a 6 pole low pass filter (Ruddick et al., 2000). Using the following equation T, kB becomes the only free variable. (1 23) Equation 124. (1 24) The algorithm seeks the best kB within a range of 9 x 1011 m2s3 to 1.5 x 105 m2s3 (Steinbuck et al., 2009) Using this background knowledge, field observations of hydrographic structure and tidal flows were investigated and compared to the results of Meyers (2007)s Estuarine Coastal Ocean Circulation Model and the results of ValleLevinson (2008)s analytical solution. The methods used for collecting and processing the data will be discussed in the next chapter. PAGE 21 21 CHAPTER 2 METHODS The chapter will be presented by a brief overview of the Hillsborough Bay study area. The techniques of collecting the desired data will be ex plained, followed by the description and methodology behind the instruments used in these field observations. This chapter will conclude with a description of how the data are separated, outlined and processed. Study Area Tampa Bay, located on the west cen tral coast of Florida, is a drowned riverbed estuary (Morrison et al., 2006). As Floridas largest open water estuary, Tampa Bay has an area of approximately 1030 km2, a shallow mean depth of 4 m, and a drainage area of 1,930 km2. The Bay is subdivided int o four sections: Old Tampa Bay, Hillsborough Bay, McKay Bay, and New Tampa Bay. Tampa Bays watershed reaches from the Hillsborough River and extends to the Gulf of Mexico. Over 100 small tributaries contribute to the Bays freshwater sources. Shipping channels have been dredged to 14 m and reach from the mouth of the bay through the lower and m iddle Tampa Bay. From there the channels are directed toward Old Tampa Bay and Hillsborough Bay. This investigation was conduct ed along a transect across Hillsborou gh Bay which has a surface area of 96 km2 (Morrison et al., 2006). Being the most industrialized of all four Bay segments, the cross sectional bathymetry is characterized by two shoals separated by a 14 m deep channel. The channel is located biased toward the left (North West) shoal, looking into the bay, which is markedly smaller than the right. The Bay is governed by a mixed (diurnal and semi diurnal ) tide which is often characterized PAGE 22 22 by unequal high and low tides and a maximum spring range of 1 m. The vertical water column is partial ly to wellmixed (Morrison et al., 2006) Data Collection Current velocity, temperature and conductiv ity measurements were collected over one semidiurnal tidal period across Hillsborough Bay on Fe bruary 24, 2009. The transect line was 4.5 km in length and contained five vertical hydrographic stations, four located over the shoals and one in the channel (Figure 2 1). Sampling lasted approximately 11.35 hours and yielded a tota l of 12 transect repetitions, 6 of which included hy drographic transects. Current velocity measurements are necessary to determine the exchange flow, while temperature and electrical conductivity measurements are needed to investigate the frictional effects. An Acoustic Doppler Current Profiler (ADCP ) and a Self Contained Autonomous Microstructure Profiler ( SCAMP) were the two instruments utilized in collecting the data. The RD I nstruments Workhorse ADCP used in this investigation measures profiles of current s by transmitting pings of sound at a constant fr equency into the water The sound waves returning to the instrument from particles moving away from the instrument have a lower frequency than those returning from particles moving toward it. The difference between frequencies is known as the Doppler Shift and is used to calculate the velocity of the particle and subsequently water surrounding it. The 1200 kHz A DCP was positioned on a small catamaran and towed off the starboard side of the boat. The boat traveled at a speed o f 1.5 to 2 m/s. The beam range was from 1.7 m to 14.7 m and each ping was recorded at .5 m bins. The ping rate was 2 Hz with a beam angle of 20. Currents were measured in NorthSouth and East West components. WinRiver software was used to collect the data obtained from the PAGE 23 23 instrument which incorporated navigational data collected from a Garmin Global positioning system (GPS) The Self Contained Autonomous Microstructure Profiler (SCAMP) is a small, lightweight device that measures small scale values and fluctuations of temperature and electrical conductivity. Developed by Precision Measurement Engineering (PME), the SCAMP samples at a rate of 100 Hz and can be deployed either ascending or descending, depending on the area of interest. For this particular investigation, the bottom of the water column was of interest and the descending mode was used. This instrument was utilized to investigate the turbulence occurring in the water column and to relate that to friction. The instrument was weighted and released directly downward at a rat e of 10 cm/s until it reached the bottom. Data from casts were recorded inter nally and uploaded onto a comput er. The software supplied allowed for calibration, data acquisition and shows a graphical display of the previous casts parameters such as velocit y, temperature and salinity profiles MATLAB is used for analysis in which salinity and density can be computed and turbulent kinetic energy dissipation can be derived. Data Processing To further explore tid al variability, the ADCP data were converted to ASCII files and loaded into MATLAB for analysis The raw data were arranged into a large matrix, where velocities were corrected by taking into account the ships velocity (Joyce, 1989) Finally, the or igin was defined to separate the large data set into transect repetitions and the data were interpolated onto a regular grid. T ime was either measured or converted to Greenwich Mean Time (GMT). The process for calculating the residual exchange flow pattern in order for it to be compared with the numerical mo del and theoretical results is discussed next. PAGE 24 24 Tidal Variability T he E W and N S current velocities were rotated into along and across estuary components. To find the principal axis of maximum variance, N S velocities were plotted along the y axis, and the E W velocities were plotted along the x axis. A trend line was determined, and the angle bet ween this line and the x axis was computed. This angle was needed to rotate the flows in order to achieve the appropriate along and across estuary components. A g rid of current measurements for the cross section looking into the estuary was created for each transect, resulting in 29 rows and 179 columns, with vertical spacing of .5 m and a horizontal spacing of 25 m. Using the current velocities, flow contours were created for depth versus distance across for each transect in the along and across components. A mean bathymetry was calculated and plotted onto each of these contours, masking the lower 10% to account for error from the ADCPs side lobe effects. The grid cells of th e five hydrographic stations were found usi ng the latitude and longitude coordinates. Contours of along and across estuary flow were also plotted with depth versus time for each of the five hydrographic stations. Using a least squares technique, the data were fitted to a periodic function with a semidiurnal (12.42 hr) harmonic The amplitu de and phase (necessary to investigate frictional influences from the bottom) as well as the residual exchange flow were obtained from this fit T hese contour s were plotted over bathymetry for the along and across components. After determining the tidally averaged flow patterns, it was necessary to compute the theoretical exchange flow patterns to compare with the observed exchange flow. T he model described by Valle Levinson (2008 ) was used to obtain theoretical along and across estuary flows using the observed bathymetry and various values of vertical eddy viscosity, Az The Kelvin number used in the analysis was 49. Three values of Az were PAGE 25 25 used (1e04, 10e0 4, and 20e04 m3/s ). These three values were chosen to represent low, moderate, and high frictional influences. These calculations were plotted against bathymetry and used to compare with the observed residual flows to determine the influence of frictional effects. To investigate the frictional effects on the hydrographic variables, t he SCAMP processing software was used to extract profiles of tem perature, salinity, and density for each drop, which resulted in 6 casts per station. The data were interpolate d onto a uniform grid and temperature, sa linity, and density contours were created for depth versus distance across with the bathy metry plotted on top. This was completed for all transects. To study the friction term of the momentum balance, the turbulent kinetic energy must be examined. To calculate the turbulent kinetic energy dissipation, the profiles must first be separated into segments before the TKE dissipation can be estimated. Several methods are currently being used to divide the profile into seg ments of SCAMP data, which are each individually fitted to the Batchelor spectrum as discussed in Chapter 1. Supplied with the SCAMP processing software was the option to use either an adaptive method or a stationary segment method. For this investigation, t he rate of turbulent kinetic energy dissipation was processed using the stationary segmentation method. Dissipation rates were calculated using 128 and 256 scans per segment. The dissipation estimates for each drop along with the associated mean depths w ere extracted for every cast. The interpolated dissipation contours were plotted for depth versus distance across for all the tra nsect repetitions In addition, dissipation time series PAGE 26 26 contours were created for each of the five stations for the duration of the sampling period using 128 and 256 scans per segment. Given that stratification is known to suppress turbulence, the areas of high stratification are of interest. In order to investigate the variations in stratification, the potential energy anomaly E quation 21, was utilized. This is a measurement of the stratification of a whole water column and is representative of the potential energy deficit in the water column (departure of the waters column center of mass from middepth) due to stratification. The mean density m, was calculated for each column (McDowell & OConner, 1977, pp. 4851) and then the potential energy anomaly, (Simpson et al, 1990). (2 1) Values of were then plotted over the bathymetry for each of the hydrographic transect repetitions. P otential energy anomaly contours were also generated for time versus distance across the estuary to observe the temporal stratification variation. To look at the influences of velocity gradients and density gradients from an energy standpoint, the Richardson number was utilized (Equation 22). (2 2) The Richardson number is a dimensionless ratio that determines the importance of mechanical energy and buoyancy effects in the water column. It is the ratio of buoy ancy production and shear production. When Ri is small (< .25), velocity shears are considered significant enough to overcome the stratifying effects of density. This concept will be compared to temporal variations of TKE dissipation to see if there is any PAGE 27 27 correlation of buoyancy and she ar production with dissipation. The next section describes the time averaged distribution of the hydrographic variables, which was used to investigate the temporal influences of friction on these parameters. Subtidal Struct ure In order to study the temporal influences of friction on hydrography, the temperature, salinity, density, and TKE dissipation were averaged over time. From the previously calculated temperature, salinity, density and dis sipation data, tidally averaged distribution s were computed and plotted for the cross section sampled. PAGE 28 28 Figure 21. Map of Hillsborough Bay Estuary, showing the transect line and five hydrographic stations. PAGE 29 29 CHAPTER 3 RESULTS The results o f this investigation are presented i n terms of tidal flow variability, residual flow and its comparison to the Ekman Kelvin solution, hydrographic variables, and TKE dissipation sections. Within the tidal variability section, the tidal flow phase and amplitude and resi dual exchange flow ar e calculated. The tidal phase and amplitude are used to investigate the frictional influences on the flow from the bottom The observed exchange flow is used to compare to the numerical model and semi analytical solution results, which was subsequently cal culated. The results of the semi analytical solution are sh own in the EkmanKelvin parameter space These results are used to compare to the observed exchange flow, to make inferences on the whether the pattern is being influenced by low, moderate, or high frictional conditions. In order to examine the frictional influences on hydrography, t he temperature, salinity, density, and potential energy anomaly are shown as transect repetitions and time averaged contours in the hydrographic variables section. Given that the most appropriate way to represent friction is through tur bulence, the following section presents the results for the turbulent kinetic energy distributions. These results were calc ulated using 128 and 256 scans and are shown as transect repetitions and time averaged contours. In order to examine the influences of v elocity and density gradients on TKE dissipation, the Richardson number was used. The time series contours of TKE dissipation using 128 and 256 scans for Station 2 were compared to the R ichardson num ber contours to see if any correlations exist between them After examining the frictional influences from an energy perspective, the subsequent section expl ores the frictional effects on the momentum PAGE 30 30 balance. The friction and C oriolis terms f rom the momentum equatio n were plotted over bathymetry, in order to determine the dominating force in the momentum balance. Tidal Variability The along channel tidal velocities varied markedly each of the 12 transect repetitions and ranged from 30 to 50 cm/s (F igures 31 and 32). The across estuary tidal current velocities showed positive and negative values (Figures 34 and 35). The positive current s were representative of across estuary currents traveling to the left (looking into the estuary) of the crosssection (NorthWest), and the negative values indicated current traveling to the right (SouthEast) and these current velocities ranged from 30 to 20 cm/s. The initial conditions began with strongly positive along estuary flow, flood tide, in the bottom of the channel and weak (~0 cm/s) velocities over the shoals and at surface waters of the channel. Negative across estuary currents were in the channel and positive values in the right shoal. The along estuary flow progressively strengthened across th e entire cross section, where it was strongest throughout the entire water column of the channel and was weaker over the shoals. Negative across estuary flow increased as the flood waters increased, with peak values near the surface and decreasing positive flow along the right shoal. The isotachs of constant flow velocity followed the bathymetry over the shoals indicating bot tom friction effects. The along estuary current velocities eventually decreased and the flow became weak in the channel and close to z ero over the shoals. Negative across estuary velocities decreased as the flood waters decreased, with most velocities nearly zero except over the surface waters of the channel. The current velocities became negative first over the shoals and remained posit ive in the channel, before eventually becoming negative, indicating ebb tide. Ebb tide developed everywhere except in the lower half of channel, PAGE 31 31 where the current was nearly zero. Acrossestuary velocities eventually became positive over the right shoal, d uring ebb. The sampling concluded with strongly ebbing (negative) along estuary currents near the surface, weakening with depth until they reached positive values near the botto m. The greatest positive across estuary current was in the upper surface water s of the channel and the left shoal, where the velocity decreased with depth. The along estuary tidal current amplitude ranged from 0 to 30 cm/s, and depicted the greatest amplitude near the surface over the channel and left shoal (looking into the estuar y), where it weakened with depth. The lowest amplitude was located along the right shoal, which also decreased with depth. The isopleths of the amplitude contours followed the bathymetry. The phase for along channel flow was measured in radians and ranged from 1.4 to 0.4. The smallest phase for the along channel component was present in the far right shoal, located along the bottom as well as the right wall of the channel. The largest phase is in the surface waters above of the channel (Figure 35). This indicated that semidiurnal tidal currents changed earlier over shoals, relative to the channel, and near the bottom, relative to the surface. The across estuary tidal current amplitude ranged from 0 to 16 cm/s and was greatest at the surface waters over the channel and left shoal where it decreased with depth. Weaker amplitudes were over the right shoal. The tidal current phase ranged from 3.14 to 3.14 rad (Figure 36). The greatest values were over the left shoal and channel and the smallest values were mi d distance across the cross section as well as along the bottom of the ch annel. The depth averaged along estuary tidal flow (cm/s) for time versus distance across was calculated to show the transition between flood and ebb tide across the transect (Figure 3 7). This PAGE 32 32 showed the strongest flows in the channel for both flood and ebb tides. The transi tion between flood and ebb took place between the hours of 20 and 21, with the shoals leading the channel. The next section describes the observed exchange flow results, w hich was needed to compare with the numerical model results. Exchange Flow The observed along channel residual exchange flow ranged from 5 to 25 cm/s and was strongly positive in the channel and left shoal, where it i ncreased with depth (Figure 3 8 ). Negative flow existed on the far right shoal, the surface waters of the channel and adjacent portion of the right shoal. The isotachs followed the bathymetry o ver the right shoal indicating frictional influences from the bottom The across channel res idual flow, which ranged from 5 to 6 cm/s showed positive values near the surface over the left shoal and far right shoal. Negative and weak (~0 cm/s) flow values were mid depth of the channel and shoals. Given that the observed exchange flow has been ca lculated, the theoretical exchange was used to find indications of frictional influences that are causing the pattern. Ekman Kelvin Solution The results of the model for the al ong estuary component mean flow showed that under low friction, the isotachs were horizontal and a vertical ly sheared pattern developed This p attern featured inflow at depth of the channel, and outflow at the surface (Figure 3 9 ). Under moderate friction, a combined horizontal and vertical sheared exchange flow was observed. This pattern showed i nflow at depth in the channel, and outfl ow at the surface as well as over the shoals. Under high friction, horizontally sheared exchange flow was observed. The frictional influences allows for outflow to occur over the shoals while net volum e inflow intrudes in the channel The PAGE 33 33 acrossestuary component of residual flow for the low frictional condition showed negative flow (SouthEast) along the surface and positive (NorthWe st) flow beneath it (Figure 3 10). For the moderate frictional condit ions, the solution showed positive (North West) flow throughout the water column of the channel and negative (SouthEast) flow over the shoals. For the high frictional conditions, the flow was negative (SouthEast) in the channel and positive (NorthWest) over the shoals. Provided that the theoretical solution indicated a highly frictional condition causing this exchange, patterns from frictional influences on hydrography were used to verify this condition. Hydrographic Variables The hydrographic variables were examined to investigate the frictional influences from the bottom. Temperature over the sampling period ra n ged from 16 to 18C (Figure 3 11). The survey began with the lowest temperatures located on the left shoal and generally increased from left to right. Temperature was characterized by sharp gradients along the shoals and upper waters of the channel. Progressively, the temperature over the right shoal developed a trend where the highest values were located near the surface, decreasing with depth and marked by horizontal isotherms. The channel was distinguished by sharp temperature gradients. This trend grew with an expanding thermocline that eventually reached across the entire cross section. As the sampling concluded, the thermocline was marked by crowded isotherms in the first few meters of water. Below the thermocline, the isotherms transitioned vertically, indicating a uniform temperature water column. The temperature was much cooler with the minimum temperature values located along the bottom of the left shoal and channel. Salinity over the sampling period rang e d from 30 to 32 psu (Figure 3 12). Salinity was low in the surface waters of the left shoal, and increased from left to right across PAGE 34 34 the estuary, marked by sharp salinity gradients. The s alinity increased with depth, separated by layers of horizontal isohalines, indicating a stratified water column, with the highest values in the shipping channel. As time progressed, the cross section showed low values of salinity located everywhere except in the shipping channel, where the salinity increased with depth. Eventually, this high salinity area in the channel began to increase encompassing the surface waters over the channel and the initial portion of the adjacent shoals. The salinity increases with depth in the channel and sharp salinity gradients appeared on the left and right side of the channel. Eventually the right side of the cross section showed a halocline with the lowest values of salinity located along the surface, where it increased w ith depth and were separated by crowded horizontal isohalines, indicating stratified conditions. The left side of the cross section had vertical isohalines and decreased from left to right. The survey concluded with a salinity gradient along the entire crosssection, where the salinity distribution was increasing with depth. The density anomaly over the sampling period ranged from 22 to 32 kg/m3 (Figure 3 13). This density structure initially showed the lowest values over the upper left shoal, where it gr adually increased from left to right, marked by sharp density gradients. The highest values were found in the channel, increasing with depth. As the tide progressed, density across the transect transitioned to low values of density everywhere except in the channel. Eventually, the low density water shifted to the right shoal, and higher values were found along the channel and left shoal, which increased with depth. This area of high density broadened to encompass part of the adjacent right shoal. The sampli ng concluded with t he entire cross section showing a density distribution that PAGE 35 35 increased with depth, separated by horizontal isopycnals which indicated stratified conditions. As seen, the water density structure followed the salinity structure closely. Tim e averaged temperature showed maximum temperatures along the surface that decreased with depth to minimum values located in the channel and along the bottom of the shoals. Horizontal isotherms were present across the entire sampling transect distance. Timeaveraged salinity contours showed the lowest values along the surface and in the far right shoal. The salinity distribution increased with depth to the maximum values located in the channel. Horizontally aligned isohaline were everywhere with the exception of the far right shoal, where the isohaline transitioned vertically indicating a mixed water column. The time averaged density distribution showed the lowest values along the surface and far right shoal. The density increased with depth, reaching maximum values in the channel. The density distribution was characterized by horizontal isopycnals everywhere except the far right shoal, where vertically oriented isop ycnal s were present (Figure 314). To find out where the stratification was the greatest across the transect, the potential energy anomaly was used. Peak values of potential energy anomaly were in the channel for all six hydrographic t ransect repetitions (Figure 3 15). This makes sense because this is the area of highest stratification. The first transect decreased linearly over the right shoal and ranged from 1 to 5.5 Jm3. The second transect had a range from 2 to 4 Jm3, and also decreased linearly over the right shoal before reaching a minimum on the right side of the midshoal spike in the bat hymetry. From there the potential energy anomaly slightly increased. The same trend was observed for the third and fourth transects with a notably smaller range of 0 to 2 Jm3. The fifth and six PAGE 36 36 transects peaked in the channel and decreased linearly over t he right shoal, ranging from 0 to 4 Jm3. The potential energy anomaly time series contours for time ver sus distance across (Figure 316), show ed highest values in the channel, between 14 to 17 hrs and 21 to 22 hrs. The mean potential energy anomaly ranged from 0 to 3.5 Jm3 and showed the highest values in the channel (Figure 317 ). Turbulent kinetic energy dissipation is one of the most appropriate ways to look at friction directly and these results were investigated next. TKE Dissipation Turbulent kinet ic energy dissipation distribution ranged from 10 8 to 10 4 m2s3 over the sampling period (Figure 318). The first transect repetition (using the 128 scans per segment processing method) displayed the highest dissipation values along the left shoal, near the bottom of the bathymetry of the far right shoal, and the bottom of the channel. Lower values are middistance across the transect line. The second transect repetition showed the highest dissipation in the left shoal and shipping channel. Generally, t he left side of the transect showed higher values than those of the right. The third transect showed maximum values located over the left shoal and bottom of the channel. The left side of the cross section showed higher dissipation than the right. The fou rth transect showed the highest values along the bathymetry of the right shoal and in the channel. The surface waters had the lowest dissipation. The fifth transect showed the highest dissipation in the channel and left shoal, again decreasing from left to right. The final repetition, showed the highest dissipation on the left shoal and middepth of the channel. PAGE 37 37 Generally being very similar to the 128 scans per segment method, the 256 scans per segment showed the highest values of dissipation in the channe l or near the bathymetry (Figure 319). The only except ion is the fourth transect, which showed high dissipation near the surface of the left shoal and channel. The mean turbulent dissipation shows very little variation between the 128 and 256 scans per se gment (Figure 3 20). The highest values were along the bottom of the left shoal, mid depth of the channel and along the bottom of the right shoal. The lowest values w ere in the waters above the high dissipation values along the right shoal (Figure 3 21). To examine the role of velocity and density gradients on dissipation, the Richardson number was calculated. The Richardson number time series contours r anged from 0 to 2.5 (Figure 322). This concept was utilized to see if a correlation existed between tim e series contours of Richardson number and TKE dissipation. Along the bottom, the Richardson number was consistently low, while the TKE dissipat ion was high Other than this trend, there was no distinct corr elation between these contours. To investigate fr iction from the momentum balance, t he friction and Coriolis terms were plotted over bathymetry (Figure 323). The results showed that friction dominates the flow over Coriolis, with friction being one order of magnitude higher than Coriolis. PAGE 38 38 Distance Across (km)Depth (m)(a) Transect 1 1 2 3 4 14 12 10 8 6 4 2 Distance Across (km)Depth (m)(b) Transect 2 1 2 3 4 14 12 10 8 6 4 2 Distance Across (km)Depth (m)(c) Transect 3 1 2 3 4 14 12 10 8 6 4 2 Distance Across (km)Depth (m)(d) Transect 4 1 2 3 4 14 12 10 8 6 4 2 Distance Across (km)Depth (m)(e) Transect 5 1 2 3 4 14 12 10 8 6 4 2 20 10 0 10 20 30 40 50 Distance Across (km)Depth (m)(f) Transect 6 1 2 3 4 14 12 10 8 6 4 2 Figure 31. Along Estuary Tidal Flow (cm/s) for February 24. A) Transect 1. B) Transect 2. C) Transect 3. D) Transect 4. E) Transect 5. F) Transect 6. PAGE 39 39 Distance Across (km)Depth (m)(a) Transect 7 1 2 3 4 14 12 10 8 6 4 2 Distance Across (km)Depth (m)(b) Transect 8 1 2 3 4 14 12 10 8 6 4 2 Distance Across (km)Depth (m)(c) Transect 9 1 2 3 4 14 12 10 8 6 4 2 Distance Across (km)Depth (m)(d) Transect 10 1 2 3 4 14 12 10 8 6 4 2 Distance Across (km)Depth (m)(e) Transect 11 1 2 3 4 14 12 10 8 6 4 2 20 10 0 10 20 30 40 50 Distance Across (km)Depth (m)(f) Transect 12 1 2 3 4 14 12 10 8 6 4 2 Figure 32. Along Estuary Tidal Flow for February 24. A). Transect 7. B) Transect 8. C) Transect 9. D) Transect 10. E) Transect 11. F) Transect 12. PAGE 40 40 Distance Across (km)Depth (m)(a) Transect 7 1 2 3 4 14 12 10 8 6 4 2 Distance Across (km)Depth (m)(b) Transect 8 1 2 3 4 14 12 10 8 6 4 2 Distance Across (km)Depth (m)(c) Transect 9 1 2 3 4 14 12 10 8 6 4 2 Distance Across (km)Depth (m)(d) Transect 10 1 2 3 4 14 12 10 8 6 4 2 Distance Across (km)Depth (m)(e) Transect 11 1 2 3 4 14 12 10 8 6 4 2 25 20 15 10 5 0 5 10 15 20 Distance Across (km)Depth (m)(f) Transect 12 1 2 3 4 14 12 10 8 6 4 2 Figure 34. Across Estuary Tidal Flow for February 24. A) Transect 1. B) Transect 2. C) Transect 3. D) Transect 4. E) Transect 5. F) Transect 6. PAGE 41 41 Distance Across (km)Depth (m)(a) Transect 7 1 2 3 4 14 12 10 8 6 4 2 Distance Across (km)Depth (m)(b) Transect 8 1 2 3 4 14 12 10 8 6 4 2 Distance Across (km)Depth (m)(c) Transect 9 1 2 3 4 14 12 10 8 6 4 2 Distance Across (km)Depth (m)(d) Transect 10 1 2 3 4 14 12 10 8 6 4 2 Distance Across (km)Depth (m)(e) Transect 11 1 2 3 4 14 12 10 8 6 4 2 25 20 15 10 5 0 5 10 15 20 Distance Across (km)Depth (m)(f) Transect 12 1 2 3 4 14 12 10 8 6 4 2 Figure 35. Across Estuary Tidal Flow for February 24. A). Transect 7. B) Transect 8. C) Transect 9. D) Transect 10. E) Transect 11. F) Transect 12. PAGE 42 42 Distance Across (km)Depth (m)Tidal Current Amplitude (cm/s) for Along Channel Flow 0.5 1 1.5 2 2.5 3 3.5 4 14 12 10 8 6 4 2 5 10 15 20 25 1.2 1 0.8 0.6 0.4 0.2 0 0.2 0.4 Distance Across (km)Depth (m)Tidal Current Phase (radians) for Along Channel Flow 0.5 1 1.5 2 2.5 3 3.5 4 14 12 10 8 6 4 2 Figure 36. Tidal Current Amplitude (cm/s) and Phase (radians) for Along Channel Flow in February 24, as calculated from the least squares fit to the semi diurnal tide. PAGE 43 43 Distance Across (km)Depth (m)Tidal Current Amplitude (cm/s) for Across Channel Flow 0.5 1 1.5 2 2.5 3 3.5 4 14 12 10 8 6 4 2 2 4 6 8 10 12 14 3 2 1 0 1 2 3 Distance Across (km)Depth (m)Tidal Current Phase (radians) for Across Channel Flow 0.5 1 1.5 2 2.5 3 3.5 4 14 12 10 8 6 4 2 Figure 37. Tidal Current Amplitude (cm/s) and Phase (radians) for Across Channel Flow in February 24, as calculated from the least squares fit to the semi diurnal tide. PAGE 44 44 Distance Across (km)Time (hours) 0.5 1 1.5 2 2.5 3 3.5 4 14 15 16 17 18 19 20 21 22 23 24 5 0 5 10 15 20 25 30 Figure 38. Depth Averaged Along Estuary Tidal Flow (cm/s) for Time versus Di stance Across for February 24, 2009. PAGE 45 45 Distance Across (km)Depth (m)Mean Along Channel Flow (cm/s) 0.5 1 1.5 2 2.5 3 3.5 4 14 12 10 8 6 4 2 5 0 5 10 15 20 4 3 2 1 0 1 2 3 4 5 Distance Across (km)Depth (m)Mean Across Channel Flow (cm/s) 0.5 1 1.5 2 2.5 3 3.5 4 14 12 10 8 6 4 2 Figure 39 Residual Along and Across Channel Flow (cm/s) for February 24, as calculated using least squares fit to semi diurnal tidal cycle. PAGE 46 46 Distance Across (km)Depth (m)Along Channel Flow in terms of Ekman and Kelvin numbers (K=.49 Az=1E04) 0.5 1 1.5 2 2.5 3 3.5 4 14 12 10 8 6 4 2 0.2 0 0.2 0.4 0.6 0.8 Distance Across (km)Depth (m)Along Channel Flow in terms of Ekman and Kelvin numbers (K=.49 Az=10E04) 0.5 1 1.5 2 2.5 3 3.5 4 14 12 10 8 6 4 2 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Distance Across (km)Depth (m)Along Channel Flow in terms of Ekman and Kelvin numbers (K=.49 Az=25E04) 0.5 1 1.5 2 2.5 3 3.5 4 14 12 10 8 6 4 2 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Figure 310. Results from Ekman Kelvin Model for Along Estuary Residual Flow using low, middle, and high Ekman numbers. PAGE 47 47 Distance Across (km)Depth (m)Across Channel Flow in terms of Ekman and Kelvin numbers (K=.49 Az=1E04) 0.5 1 1.5 2 2.5 3 3.5 4 14 12 10 8 6 4 2 1 0.8 0.6 0.4 0.2 0 Distance Across (km)Depth (m)Across Channel Flow in terms of Ekman and Kelvin numbers (K=.49 Az=10E04) 0.5 1 1.5 2 2.5 3 3.5 4 14 12 10 8 6 4 2 1 0.8 0.6 0.4 0.2 0 0.2 Distance Across (km)Depth (m)Across Channel Flow in terms of Ekman and Kelvin numbers (K=.49 Az=20E04) 0.5 1 1.5 2 2.5 3 3.5 4 14 12 10 8 6 4 2 1 0.5 0 0.5 Figure 311. Results from Ekman Kelvin Model for Across Estuary Residual Flow using low, middle, and high Ekman numbers. PAGE 48 48 Distance Across (km)Depth (m)(a) Transect 1 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 Distance Across (km)Depth (m)(b) Transect 2 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 Distance Across (km)Depth (m)(c) Transect 3 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 Distance Across (km)Depth (m)(d) Transect 4 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 Distance Across (km)Depth (m)(e) Transect 5 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 16 16.2 16.4 16.6 16.8 17 17.2 17.4 17.6 17.8 18 Distance Across (km)Depth (m)(f) Transect 6 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 Figure 312. Temperature (Celsius) for February 24. A) Transect 1. B) Transect 2. C) Transect 3. D) Transect 4. E) Transect 5. F) Transect 6. The x symbols represent the hydrographic stations. PAGE 49 49 Distance Across (km)Depth (m)(a) Transect 1 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 Distance Across (km)Depth (m)(b) Transect 2 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 Distance Across (km)Depth (m)(c) Transect 3 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 Distance Across (km)Depth (m)(d) Transect 4 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 Distance Across (km)Depth (m)(e) Transect 5 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 30 30.2 30.4 30.6 30.8 31 31.2 31.4 31.6 31.8 32 Distance Across (km)Depth (m)(f) Transect 6 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 Figure 3 13. Salinity (psu) for February 24. A) Transect 1. B) Transect 2. C) Transect 3. D) Transect 4. E) Transect 5. F) Transect 6. The x symbols represent the hydrographic stations. PAGE 50 50 Distance Across (km)Depth (m)(a) Transect 1 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 Distance Across (km)Depth (m)(b) Transect 2 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 Distance Across (km)Depth (m)(c) Transect 3 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 Distance Across (km)Depth (m)(d) Transect 4 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 Distance Across (km)Depth (m)(e) Transect 5 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 22 23 24 25 26 27 28 29 30 31 32 Distance Across (km)Depth (m)(f) Transect 6 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 Figure 314. Density Anomaly (kg/m3) for February 24. A) Transect 1. B) Transect 2. C) Transect 3. D) Transect 4. E) Transect 5. F) Transect 6. The x symbols represent the hydrographic stations. PAGE 51 51 Distance Across (km)Depth (m)(a) Temperature (Celsius) 0.5 1 1.5 2 2.5 3 0 5 10 16 16.5 17 17.5 18 Distance Across (km)Depth (m)(a) Salinity (psu) 0.5 1 1.5 2 2.5 3 0 5 10 30 30.5 31 31.5 32 22 24 26 28 30 32 ygp y Distance Across (km)Depth (m)(a) Density Anomaly (kg/m3) 0.5 1 1.5 2 2.5 3 0 5 10 Figure 315. Mean Temperature (Celsius), Salinity (psu), and Density Anomaly (kg/m3) Contours for February 24. The x symbol represents the five hydrographic stations. PAGE 52 52 0.5 1 1.5 2 2.5 3 3.5 0 2 4 6 Distance Across (km)(PHI J/m3)(a) Transect 1 0.5 1 1.5 2 2.5 3 3.5 0 2 4 Distance Across (km)(PHI J/m3)(b) Transect 2 0.5 1 1.5 2 2.5 3 3.5 0 1 2 Distance Across (km)(PHI J/m3)(c) Transect 3 0.5 1 1.5 2 2.5 3 3.5 0 1 2 Distance Across (km)(PHI J/m3)(d) Transect 4 0.5 1 1.5 2 2.5 3 3.5 0 2 4 Distance Across (km)(PHI J/m3)(e) Transect 5 0.5 1 1.5 2 2.5 3 3.5 0 2 4 Distance Across (km)(PHI J/m3)(f) Transect 6 0.5 1 1.5 2 2.5 3 3.5 15 10 5 0 Distance Across (km)Depth (m)(g) Bathymetry 0.5 1 1.5 2 2.5 3 3.5 15 10 5 0 Distance Across (km)Depth (m)(h) Bathymetry 0.5 1 1.5 2 2.5 3 3.5 15 10 5 0 Distance Across (km)Depth (m)(i) Bathymetry Figure 316. Potential Energy Anomaly (J/m3). A) Transect 1. B) Transect 2. C) Transect 3. D) Transect 4. E) Transect 5. F) Transect 6. G I) Bathymetry. PAGE 53 53 Distance Across (km)Time(hr) 0.5 1 1.5 2 2.5 3 3.5 14 15 16 17 18 19 20 21 22 23 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Figure 317. Potential Energy (J/m3) Contours for Time versus Distance Across for February 24. PAGE 54 54 0.5 1 1.5 2 2.5 3 3.5 0 1 2 3 4 Distance Across (km)PHI (J/m3) gy y 0.5 1 1.5 2 2.5 3 3.5 15 10 5 0 Bathymetry Distance Across (km)Depth (m) Figure 318. Mean Potential Energy Anomaly (J/m3) and Bathymetry for February 24. PAGE 55 55 Distance Across (km)Depth (m)(a) Transect 1 0.5 1 1.5 2 2.5 3 12 10 8 6 4 2 Distance Across (km)Depth (m)(b) Transect 2 0.5 1 1.5 2 2.5 3 12 10 8 6 4 2 Distance Across (km)Depth (m)(c) Transect 3 0.5 1 1.5 2 2.5 3 12 10 8 6 4 2 Distance Across (km)Depth (m)(d) Transect 4 0.5 1 1.5 2 2.5 3 12 10 8 6 4 2 Distance Across (km)Depth (m)(e) Transect 5 0.5 1 1.5 2 2.5 3 12 10 8 6 4 2 8 7.5 7 6.5 6 5.5 5 4.5 4 Distance Across (km)Depth (m)(f) Transect 6 0.5 1 1.5 2 2.5 3 12 10 8 6 4 2 Figure 319. Turbulent Kinetic Energy Dissipation (m2/s3) using 128 scans for February 24. A) Transect 1. B) Transect 2. C) Transect 3. D) Transect 4. E) Transect 5. F) Transect 6. The x symbols represent the stations. PAGE 56 56 Distance Across (km)Depth (m)(a) Transect 1 0.5 1 1.5 2 2.5 3 12 10 8 6 4 2 Distance Across (km)Depth (m)(b) Transect 2 0.5 1 1.5 2 2.5 3 12 10 8 6 4 2 Distance Across (km)Depth (m)(c) Transect 3 0.5 1 1.5 2 2.5 3 12 10 8 6 4 2 Distance Across (km)Depth (m)(d) Transect 4 0.5 1 1.5 2 2.5 3 12 10 8 6 4 2 Distance Across (km)Depth (m)(e) Transect 5 0.5 1 1.5 2 2.5 3 12 10 8 6 4 2 8 7.5 7 6.5 6 5.5 5 4.5 4 Distance Across (km)Depth (m)(f) Transect 6 0.5 1 1.5 2 2.5 3 12 10 8 6 4 2 Figu re 3 20. Turbulent Kinetic Energy Dissipation using 256 scans for February 24. A) Transect 1. B) Transect 2. C) Transect 3. D) Transect 4. E) Transect 5. F) Transect 6. Th e x symbols represent the hydrographic stations. PAGE 57 57 Distance Across (km)Depth (m)Mean TKE Dissipation 128 Scans (m2/s3) 0.5 1 1.5 2 2.5 3 12 10 8 6 4 2 8 7.5 7 6.5 6 5.5 5 4.5 4 Distance Across (km)Depth (m)Mean TKE Dissipation 256 Scans (m2/s3) 0.5 1 1.5 2 2.5 3 12 10 8 6 4 2 8 7.5 7 6.5 6 5.5 5 4.5 4 Figure 321. Mean Turbulent Kinetic Energy Dissipation using 128 and 256 scans for February 24. The x symbol represents the five hydrographic stations. PAGE 58 58 Time (hr)Depth (m)(a)Richardson Number 14 16 18 20 22 14 12 10 8 6 4 2 0 0.5 1 1.5 2 2.5 Time (hr)Depth (m)(b) TKE Dissipation using 128 scans 14 16 18 20 22 14 12 10 8 6 4 2 8 7 6 5 4 Time (hr)Depth (m)(c) TKE Dissipation using 256 scans 14 16 18 20 22 14 12 10 8 6 4 2 Figure 322. Time series contours for Station 2. A) Richardson Number. B) TKE Dissi pation using 128 Scans. C) TKE Dissipation using 256 Scans. PAGE 59 59 0 20 40 60 80 100 120 140 160 180 0 1 2 x 105 (cd u2)/HFriction Term 0 20 40 60 80 100 120 140 160 180 5 0 5 x 106 fvCoriolis Term 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 15 10 5 0 Distance Across (km)Depth (m)Bathymetry Figure 323. Comparison of Friction and Coriolis Momentum Balance Terms. PAGE 60 60 CHAPTER 4 DISCUSSION The purpose of this analysis was to compare the observed exchange flow pattern from Hillsborough Bay with the results Meyers (2007) numerical circulation model and Valle Levinsons (2008) semi analytical solution. It was also necessary to find observational evidence to support the high frictional theoretical condition that is causing this exchange p attern that is not often observed. To get an understanding of the water entering and exiting the estuary, the tidal flows were investigated. The observed along estuary current velocities began in flood tide, with the st rongest flows in the channel. Slack water, where the tide transitions from flood to ebb, occurred between the hours of 20 and 21. The ebb tide also showed the strongest velocit ies in the channel. The across estuary component showed negative (SouthEast) currents during ebb waters and positi ve currents during flood T he strongest currents were at the surfac e of the left shoal. The exchange flow pattern, computed using a least squares fit technique, was found to compare with the results of the numerical model and the theoretical solution. Th e along estuary residual exchange flow showed horizontally sheared distribution, with full net volume inflow in the channel and weak outflow over the shoals. This horizontally sheared distribution is among few observations of this exchange flow pattern. Th is pattern is consistent with Meyer s (2007) model results for Hillsborough Bay and is most consistent with the results of ValleLevinsons (2008) semi analytical solution using a high Ekman number. The high Ekman number indicated high frictional influence s. The tidal current phase and amplitude were examined to get an understanding of the frictional influences on the flow. The along estuary amplitude was strongest in the PAGE 61 61 surface waters of the channel and weakest over the shoals and at depth in the channel. These weaker flows are due to frictional influences from bottom drag affecting the entire water column over the shoals. Due to depth of the channel, frictional influences do not affect the entire water column, allowing for larger currents to take place. The isotachs mimicked the bathymetry, which also indicated the frictional effect of the bottom The phase distribution showed the lowest values were at the surface and in the channel T he highest phase values were near the bottom and at depth of the channel The currents at depth and near the bathymetry of the shoals lead the currents at the surface. Given that friction is causing weaker flows in these areas, the reversing tide is more capable of overcoming momentum. These results suggest ed high frictional influences occurring over the shoals. Now, to verify that there were high frictional influences taking place, t he hydrographic variables were examined. The temperature increased throughout the day and consistently decreased with depth. This is a result of diurnal effects from the sun heating the surface layers of the cross section. The salinity and density findings were very similar, suggesting that salinity governs when calculating the density for this particular survey. Both salinity and density distri bution increased with depth, with the highest values in the channel. This observation is consistent with the concept that denser water follows the path of least resistance. The contour lines were horizontal ly oriented in the channel, signifying stratified conditions. Over the shoals, the contour lines were more vertically oriented, which indic ated a more mixed condition than in the channel. This pattern is due to frictional influences from the bottom which af fected the entire water column Velocity shears from bottom drag created turbulence which PAGE 62 62 resulted in mixing. Throughout the sampling, the potential energy anomaly was consistently highest in the channel, showing that the greatest stratification existed here. The potential energy anomaly contours showed that with time, the greatest stratification occurred in the beginning and end of the sampling duration. Given that the tidal phase and amplitude and hydrography indicated highly frictional conditions, the friction was investigated using the results for the turbulent kinetic energy dissipation. The 128 and 256 scans per segment turbulent dissipation distribution regularly showed the highest values and variation existed in the channel. This is where velocities were the strongest and stratification was the greatest. Peak dissipation values were also near the bathymetry of the shoals due to velocity gradients caused by bottom drag. These peak values were considered high (>105 m2s3) when compared to other estuaries (Luketina & Imberger, 2001). These high v alues indicated that there are high frictional influences taking place compared to other estuaries. Next, friction was investigated using the concept of energy. Given that, neglecting transported TKE, t urbulent kinetic energy is a balance of shear produc tion, buoyancy production, and dissipation, t he Richardson number was studied. The Richardson number contours were compared to TKE dissipation time series for Station 2 to see if there is any correlation between TKE dissipation created by velocity shears or density gradients. The Richardson number time series contours showed low (< .25) values near the bottom, where TKE dissipation was the highest which was expected because of the high frictional influences previously observed. Other than this trend, there was no distinct correlation between these three figures. This observation is valid because the turbulent kinetic energy is a balance of shear production, buoyancy production and PAGE 63 63 dissipation, not just shear and buoyancy production. The highest Richardson n umber values occurred midduration of sampling. Provided that the frictional influences have been investigated using the concept of energy friction was then analyzed using the momentum balance. T he friction and Coriolis terms were plotted over bathymetry The frictional term was one order of magnitude higher than the Coriolis term, indicating that friction is dominating the flow over Coriolis. The observed exchange flow pattern compares favorably with the results of the numerical model and the theoretical solution. Not only does the observed exchange flow pattern indicate highly frictional conditions, but the tidal phase and amplitude, hydrography, TKE dissipation and momentum balance suggest high frictional influences, which supports this claim. PAGE 64 64 CHAPTER 5 CONCLUSION The main findings of this study showed that the observed residual exchange flow in Hillsborough Bay compared favorably with both numerical and theoretical results. Showing a horizontal ly sheared pattern, it was characterized by net volume inflow in the channel, and outflow over the left shoal. The other observational evidence showed that highly frictional influences are evident in this estuary and further reinforced that high frictional conditions were present Stronger amplitudes were i n the channel and weaker values were over the shoals, due to frictional influences weakening the flows over the shoals. The phase distribution showed that the currents over the shoals and at depth in the channel lead the currents at the surface in the channel. The momentum of the weaker flow is overcome before the momentum of the water in the channel, attributable to frictional influences that slow down these flows over the shoals. The depth of the wa ter column in the channel allowed for stratification to develop, w hile stratification was rather weak over the shoals. This is a sign of frictional effects from the bottom affecting the enti re water column over the shoals ( creating turbulence that causes mixing ). High frictional in fluences yield high turbulent k inetic energy dissipation near the bottom when compared to other estuaries In conclusion, d espite sustaining weak tidal currents the Hillsborough Bay Estuary still exhibited significant frictional influences. This highly frictional condition resulted in a laterally sheared exchange flow that was dominated by fric tion and is among few observed examples of this type of exchange flows. PAGE 65 65 LIST OF REFERENCES Batchelor, G.K. (1959) Small scale Variation of Convected Quantities like Temperature in Turbulent Flui d, J. Fluid Mechanics, 5, 113133. Dillion, T.M., & Caldwell, D.R. (1980) The Batchelor Spectrum and Dissipation in the Upper Ocean. J. Geophys. Res., 85 19101916. Hughes, W.F., & Brighton, A.J. (1999) Schaums Outline of Theory and Problems of Flu id Dynamics New York: McGraw Hill Companies, Inc. Lewis, R. (1997) Dispersion in Estuaries and Coastal Waters. New York: John Wiley & Sons Ltd. Luketina, D.A., & Imberger, J. (2001), Determining Turbulent Kinetic Energy Dissipation from Batchelor Curve Fitting. J. Atmos. Ocean Tech., 18 100 113. Joyce, T. M., (1989) In situ Calibration of ShipBoard ADCPs. J. Atmos. Oceanic Tech. 6, 169172. McDowell, D.M., & OConner, B.A. (1977) Hydraulic Behavior of Estuaries New York: John Wiley & Sons, Inc. Meyers S D Luther M E Wilson M Havens H Linville A et al. (2007) A Numerical Simulation of Residual Circulation in Tampa Bay. Part I: Low frequency Temporal Variations. Estuaries and Coasts : Vol. 30, No. 4 pp. 679 697 Morisson, G., Sherw ood, E.T., Boler, R., & Barron, J. (2006), Variations in Water Clarity and Chlorophyll a in Tampa Bay, Florida, in Response to Annual Rainfall, 19852004. Estuaries and Coasts, 29, 6A 926 931. Pielke, R.A. (2002) Mesoscale Meteorological Modeling Sa n Diego: Academic Press. Pritchard, D.W. (1956) The Dynamic Structure of a Coastal Plain Estuary. Journal of Marine Research 13, 133 144. Ruddick,B., Anis, A., & Thompson, K. (2000) Maximum Likelihood Spectral Fitting: The Batchelor Spectrum. J. Atmo s. Ocean. Tech., 17, 15411555. Simpson, J.H., Brown, J., Matthews, J. & Allen, G. (1990) Tidal straining, density currents, and stirring in the control of estuarine stratification. Estuaries, 13 125 132. Soga, C.L.M., & Rehma, C.R. (2004), Dissipatio n of Turbulent Kinetic Energy near a Bubble Plumn. Journal of Hydraulic Engineering, 130, 441 119. PAGE 66 66 Steinbuck, J.V., Stacey, M.T., & Monismith, S.G. (2009) An Evaluation of Xt Estimation Techniques: Implications for Batchelor Fitting and American Meteorological Society. Valle Levinson, A. (2008), Density driven Exchange Flow in Terms of the Kelvin and Ekman Numbers, J. Geophys. Res., 113. Wong, K.C. (1994), On the Nature of Transverse Variability in a Coastal Plain Estuary. Journal of Gepphysical Research. 14, 209 222. PAGE 67 67 BIOGRAPHICAL SKETCH Kim began her educational career at the University of Central Florida, enrolled in the Industrial Engineering P rogram. After several years, she decided to change her majo r to civil engineering and move to Jac ksonville. Finishing the final two years of school at the University of North Florida, she received her b achelor s degree in May 2008. After graduating, Kim moved to Gainesville to begin graduate school at the Un iversity of Florida in the C oastal and O ceanographic E ngineering P rogram. 