FRICTION-DOMINATED WATER EXCHANGE IN A FLORIDA ESTUARY

Transcription

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 29 1

2 29 Kimberly Arnott 2

3 To my father 3

4 ACKNOWLEDGMENTS I thank my advisor and chair, Dr. Arnoldo Valle-Levinson, 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-Levinson s group of research students, who gave me insightful comments and suggestions throughout this study. 4

5 TABLE OF CONTENTS page ACKNOWLEDGMENTS... 4 TABLE OF CONTENTS... 5 LIST OF FIGURES... 6 LIST OF ABBREVIATIONS... 8 ABSTRACT... 1 CHAPTER 1 INTRODUCTION Motivation Estuarine Background Circulation Turbulence Turbulent Kinetic Energy Dissipation Theory METHODS Study Area Data Collection Data Processing Tidal Variability Subtidal Structure RESULTS Tidal Variability... 3 Exchange Flow Ekman- Kelvin Solution Hydrographic Variables TKE Dissipation DISCUSSION CONCLUSION LIST OF REFERENCES BIOGRAPHICAL SKETCH

6 LIST OF FIGURES Figure page 2-1 Map of Hillsborough Bay Estuary, showing transect line and five hydrographic stations 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 Along Estuary Tidal Flow for February 24. A). Transect 7. B) Transect 8. C) Transect 9. D) Transect 1. E) Transect 11. F) Transect Across Estuary Tidal Flow for February 24. A) Transect 1. B) Transect 2. C) Transect 3. D) Transect 4. E) Transect 5. F) Transect Across Estuary Tidal Flow for February 24. A). Transect 7. B) Transect 8. C) Transect 9. D) Transect 1. E) Transect 11. F) Transect 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 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 Depth Averaged Along Estuary Tidal Flow (cm/s) for Time versus Distance Across for February 24, Residual Along and Across Channel Flow (cm/s) for February 24, as calculated using least squares fit to semi-diurnal tidal cycle Results from Ekman Kelvin Model for Along Estuary Residual Flow using low, middle, and high Ekman numbers Results from Ekman Kelvin Model for Across Estuary Residual Flow using low, middle, and high Ekman numbers 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 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

7 3 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 Mean Temperature (Celsius), Salinity (psu), and Density Anomaly (kg/m3) Contours for February 24. The x symbol represents the five hydrographic stations 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 Potential Energy (J/m3) Contours for Time versus Distance Across for February Mean Potential Energy Anomaly (J/m3) and Bathymetry for February 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 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. The x symbols represent the hydrographic stations Mean Turbulent Kinetic Energy Dissipation using 128 and 256 scans for February 24. The x symbol represents the five hydrographic stations Time series contours for Station 2. A) Richardson Number. B) TKE Dissipation using 128 Scans. C) TKE Dissipation using 256 Scans Comparison of Friction and Coriolis Momentum Balance Terms

8 LIST OF ABBREVIATIONS Density (kg/m 3 ) Velocity gradient Vertical eddy viscosity Kinematic viscosity Shear stress B B i c ics c vc c w D T f F Basin width Body force An O(1) constant Constant related to spectrum in viscous subrange An O(1) constant Diffusivity of heat Coriolis Fourier transform of F * H k K Complex conjugate Water depth (m) Max wavenumber Kelvin number k Rad m -1 k Wavenumber (rad m -1 ) k B k k L Batchelor wavenumber Kolmogorov wavenumber Length in describing flow 8

9 q rad R e R i Universal constant Radians Reynolds Stresses Internal Rossby Radius T Temperature fluctuation T o u U w Temperature center of region Sensor velocity relative to water Velocity of flow Internal waves z Vertical ordinate α Dimensionless wavenumber γ & β Are constants 9

10 Abstract of Thesis 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 29 Chair: Arnoldo Valle-Levinson Major: Coastal and Oceanographic Engineering The pattern of net exchange flow typically observed in estuaries consists of a vertically sheared distribution with 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 cross-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 with theoretical results for a flow dominated by friction. The main purpose of this investigation was then to obtain observational evidence that supported theoretical and numerical results. A 12-hour field survey was conducted on February 24, 29, where current velocity measurements and profiles of temperature and electrical conductivity were collected. Observations from Hillsborough Bay were compared to numerical model results and to an analytical solution. The along-estuary tidal currents had amplitudes < 3 cm/s, which were relatively weak when compared to other estuaries. Tidal current amplitudes were largest at the surface of the channel and weakest over the shoals. The isotachs mimicked the bathymetry, indicative of frictional 1

11 influences from 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 horizontally sheared pattern, with net volume inflow in the channel 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, the friction term of the momentum equation was compared against Coriolis acceleration 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 stratification 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 currents and greatest stratification took place in the channel. Even though this estuary has weak tidal currents, observational evidence showed that there can still be considerable frictional effects, resulting in a frictionally dominated exchange flow. 11

12 CHAPTER 1 INTRODUCTION Motivation Pritchard (1956) proposed that the hydrodynamics of a coastal 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 inflow in the middle and outflow over the shallow sides. The exchange flow typically observed in estuaries is 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., 27) showed that the exchange flow pattern was horizontally sheared: inflow in the entire water column of the channel and outflow over the shoals. This laterally sheared exchange flow pattern 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 purpose of this analysis is to compare field observations from Hillsborough Bay with the results of the numerical model as well as with Valle Levinson (28) s analytical solution. Estuarine Background The region encompassing the meeting point between the ocean and river is loosely defined as an estuary. Typically composed of brackish water, estuaries can be classified by their circulation and can be categorized into four groups: highly stratified, fjords, partially mixed, and homogeneous. Estuaries are typically described in along- 12

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 1-1 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 left-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 gradients (second term on the r.h.s.), and horizontal and vertical mixing (third, fourth, and fifth terms on the r.h.s.) (Valle-Levinson, 29a). The parameters u, v, and w represent the along, across, and vertical components of velocity, while f, g, ρ, and A x, 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 A Z (Valle-Levinson, 29a). With these assumptions, Equation 1-1 reduces to Equation 1. (1) Equation 1 demonstrates a balance between pressure gradient and friction. Equation 1-3 represents the mean dynamical balance for the across-estuary component of momentum. (1-3) 13

14 This equation consists of local acceleration (first term on the l.h.s), advection (second, third and fourth terms on the l.h.s.), Coriolis 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 terms on the r.h.s.). Equation 1 demonstrates becomes a geostrophic balance between Coriolis and pressure gradient. (1) This is the reduction of Equation 1-3, utilizing the following assumptions: steady state, frictionless, 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 water, after the tidal effects have been removed. Typical estuarine circulation is a density-driven flow, characterized 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 Coriolis (Valle-Levinson, 28). Estuarine circulation can be characterized as vertically or horizontally sheared. Vertical shearing is defined as outflow 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 Valle-Levinson (28). Valle-Levinson (28) s model is a semi-analytical solution that solves densitydriven exchange flows in terms of Ekman, E k, and Kelvin, K, numbers: 14

15 (1-5) (1) The parameters in the previous two equations are vertical eddy viscosity, A z, Coriolis forcing, f, water column height, H, basin width, B, and internal Rossby Radius, R i. 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 friction 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 property changes (McDowell & O Conner, 1977, pp ). Turbulent fluid can be thought of as a collection of eddies which are created by flow instabilities, bed irregularities 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. These 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 ). Three main sources of velocity shears exist in estuaries: shears from wind, shears from bottom stresses, and internal shears from velocity gradients in the water column. In shallow tidal areas, vertical shear commonly occurs from the frictional drag 15

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 1-7, assumes the flow is incompressible and the viscosity is constant. (1-7) The parameters ρ, u i,j, p, μ, and B i represent the density, velocity components, pressure, viscosity, and body force per unit volume. The turbulent kinetic energy equation (Equation 1) is achieved by multiplying the flow by the turbulent flow momentum equation (Pielke, 22, p. 167). (1) (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), viscous 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, u j, u i, θ, g, w represent the turbulent kinetic energy, velocity shear, subscale velocity fluxes, potential temperature, gravity, and vertical velocity. Equation 1-1 represents turbulent dissipation. 16

17 (1) The following section will discuss the theory behind how the turbulent kinetic energy dissipation, used to investigate the frictional influences in the water column, is measured with a microstructure profiler Turbulent Kinetic Energy Dissipation Theory Turbulent kinetic energy dissipation, ε, is estimated by fitting a theoretical form of the temperature gradient spectrum to observed data (Soga & Rehmann, 24). The observed data are measured with a microstructure profiler that samples at 1 Hz. The temperature gradient is a physical quantity 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, 21). The higher wave number of the temperature gradient spectrum is a function of ε and the dissipation of the temperature variance, χ 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 γ and β are constants, z is the vertical ordinate with the center at the origin of interest, and T o is the temperature at the center of the origin (Luketina & Imberger, 21). The temperature gradient can then be given by Equation 1. (1) 17

18 Equation 1-13 then becomes the one-sided finestructure power spectrum of the 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 is representative of the temperature gradient spectrum where the internal waves have a wavelength smaller than the internal Rossby radius. (1) The variable c w 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 ρ. The wave number can then be calculated using the maximum wavenumber, as shown in Equation (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 maximum wavenumber. The following equation represents the inertial convective subrange portion of the temperature gradient. C ics is a constant and χ t is the dissipation of the temperature variance. Equation 1-18 represents the dissipation of temperature variance due to turbulence. (1-17) 18

19 (1-18) (1-19) D T is the diffusivity of heat, T is the temperature, c vc is a constant, and ν 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 components of the temperature distribution are statistically homogenous, steady, and isotropic (Soga & Rehmann, 24). The one-dimensional Batchelor spectrum is represented by Equation 1 (Luketina & Imberger, 21). (1) The variable k B represents the Batchelor wavenumber and α is a dimensionless wavenumber. Equation 12 is representative of the normalized Batchelor spectrum. (11) (12) The final part of the temperature gradient is the noise spectra. This section is created from noise associated 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, 21). A second is to make a nonlinear least squares fit method of the Batchelor spectrum to the temperature gradient spectra using high signal to noise levels (Dillion & Caldwell, 198). The last 19

20 method uses an algorithm to fit the Batchelor spectrum to the measured spectrum (Ruddick et al., 2). The Self Contained Autonomous Microstructure Profiler (SCAMP, used in this experiment) processing software uses the last method to estimate 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 processing circuitry with a 6-pole low-pass filter (Ruddick et al., 2). Using the following equation in conjunction with the measured values of χ T, k B becomes the only free variable. (13) The dissipation, ε is then solved from the Batchelor wavenumber, Equation 14. (14) The algorithm seeks the best k B within a range of 9 x 1-11 m 2 s -3 to 1.5 x 1-5 m 2 s -3 (Steinbuck et al., 29). Using this background knowledge, field observations of hydrographic structure and tidal flows were investigated and compared to the results of Meyers (27) s Estuarine Coastal Ocean Circulation Model and the results of Valle-Levinson (28) s analytical solution. The methods used for collecting and processing the data will be discussed in the next chapter. 2

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 explained, 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-central coast of Florida, is a drowned riverbed estuary (Morrison et al., 26). As Florida s largest open water estuary, Tampa Bay has an area of approximately 13 km 2, a shallow mean depth of 4 m, and a drainage area of 1,93 km 2. The Bay is subdivided into four sections: Old Tampa Bay, Hillsborough Bay, McKay Bay, and New Tampa Bay. Tampa Bay s watershed reaches from the Hillsborough River and extends to the Gulf of Mexico. Over 1 small tributaries contribute to the Bay s freshwater sources. Shipping channels have been dredged to 14 m and reach from the mouth of the bay through the lower and middle Tampa Bay. From there the channels are directed toward Old Tampa Bay and Hillsborough Bay. This investigation was conducted along a transect across Hillsborough Bay which has a surface area of 96 km 2 (Morrison et al., 26). 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 21

22 by unequal high and low tides and a maximum spring range of 1 m. The vertical water column is partially to well-mixed (Morrison et al., 26). Data Collection Current velocity, temperature and conductivity measurements were collected over one semidiurnal tidal period across Hillsborough Bay on February 24, 29. 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 hours and yielded a total of 12 transect repetitions, 6 of which included hydrographic 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 Instruments Workhorse ADCP used in this investigation measures profiles of currents by transmitting pings of sound at a constant frequency 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 12 khz ADCP was positioned on a small catamaran and towed off the starboard side of the boat. The boat traveled at a speed of 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 2. Currents were measured in North- South and East- West components. WinRiver software was used to collect the data obtained from the 22

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 1 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 rate of 1 cm/s until it reached the bottom. Data from casts were recorded internally and uploaded onto a computer. The software supplied allowed for calibration, data acquisition and shows a graphical display of the previous cast s parameters such as velocity, 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 tidal 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 ship s velocity (Joyce, 1989). Finally, the origin was defined to separate the large data set into transect repetitions and the data were interpolated onto a regular grid. Time 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 model and theoretical results is discussed next. 23

24 Tidal Variability The 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 between 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 grid 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 1% to account for error from the ADCP s side lobe effects. The grid cells of the five hydrographic stations were found using 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 amplitude and phase (necessary to investigate frictional influences from the bottom) as well as the residual exchange flow were obtained from this fit. These contours 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. The model described by Valle-Levinson (28) was used to obtain theoretical along and across estuary flows using the observed bathymetry and various values of vertical eddy viscosity, A z. The Kelvin number used in the analysis was.49. Three values of A z were 24

25 used (1e -4, 1e -4, and 2e -4 m 3 /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, the SCAMP processing software was used to extract profiles of temperature, salinity, and density for each drop, which resulted in 6 casts per station. The data were interpolated onto a uniform grid and temperature, salinity, and density contours were created for depth versus distance across with the bathymetry 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 segments 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, the 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 were extracted for every cast. The interpolated dissipation contours were plotted for depth versus distance across for all the transect repetitions. In addition, dissipation time series 25

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, Equation 2-1, 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 water s column center of mass from middepth) due to stratification. The mean density, ρ m, was calculated for each column (McDowell & O Conner, 1977, pp ) and then the potential energy anomaly, Φ (Simpson et al, 199). (2-1) Values of Φ were then plotted over the bathymetry for each of the hydrographic transect repetitions. Potential 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 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 buoyancy 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 26

27 correlation of buoyancy and shear 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 Structure 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 dissipation data, tidally averaged distributions were computed and plotted for the cross-section sampled. 27

28 Figure 2-1. Map of Hillsborough Bay Estuary, showing the transect line and five hydrographic stations. 28

29 CHAPTER 3 RESULTS The results of this investigation are presented in terms of tidal flow variability, residual flow and it s comparison to the Ekman- Kelvin solution, hydrographic variables, and TKE dissipation sections. Within the tidal variability section, the tidal flow phase and amplitude and residual exchange flow are 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 calculated. The results of the semi-analytical solution are shown in the Ekman-Kelvin 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, the 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 turbulence, the following section presents the results for the turbulent kinetic energy distributions. These results were calculated using 128 and 256 scans and are shown as transect repetitions and time averaged contours. In order to examine the influences of velocity 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 Richardson number contours to see if any correlations exist between them. After examining the frictional influences from an energy perspective, the subsequent section explores the frictional effects on the momentum 29

30 balance. The friction and Coriolis terms from the momentum equation 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 -3 to 5 cm/s (Figures 3-1 and 3). The across-estuary tidal current velocities showed positive and negative values (Figures 3 and 3-5). The positive currents were representative of across-estuary currents traveling to the left (looking into the estuary) of the cross-section (North-West), and the negative values indicated current traveling to the right (South-East) and these current velocities ranged from -3 to 2 cm/s. The initial conditions began with strongly positive along estuary flow, flood tide, in the bottom of the channel and weak (~ 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 the 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 bottom friction effects. The alongestuary current velocities eventually decreased and the flow became weak in the channel and close to zero 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 positive in the channel, before eventually becoming negative, indicating ebb tide. Ebb tide developed everywhere except in the lower half of channel, 3

31 where the current was nearly zero. Across-estuary velocities eventually became positive over the right shoal, during ebb. The sampling concluded with strongly ebbing (negative) along estuary currents near the surface, weakening with depth until they reached positive values near the bottom. The greatest positive across-estuary current was in the upper surface waters of the channel and the left shoal, where the velocity decreased with depth. The along-estuary tidal current amplitude ranged from to 3 cm/s, and depicted the greatest amplitude near the surface over the channel and left shoal (looking into the estuary), 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.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 3-5). 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 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 rad (Figure 3). The greatest values were over the left shoal and channel and the smallest values were middistance across the cross-section as well as along the bottom of the channel. 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 31

32 showed the strongest flows in the channel for both flood and ebb tides. The transition between flood and ebb took place between the hours of 2 and 21, with the shoals leading the channel. The next section describes the observed exchange flow results, which 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 increased with depth (Figure 3). 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 over the right shoal, indicating frictional influences from the bottom. The across-channel residual 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 (~ cm/s) flow values were mid-depth of the channel and shoals. Given that the observed exchange flow has been calculated, 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 along-estuary component mean flow showed that under low friction, the isotachs were horizontal and a vertically sheared pattern developed. This pattern 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 inflow at depth in the channel, and outflow 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 volume inflow intrudes in the channel. The 32

33 across-estuary component of residual flow for the low frictional condition showed negative flow (South-East) along the surface and positive (North-West) flow beneath it (Figure 3). For the moderate frictional conditions, the solution showed positive (North-West) flow throughout the water column of the channel and negative (South- East) flow over the shoals. For the high frictional conditions, the flow was negative (South-East) in the channel and positive (North-West) 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 ranged from 16 to 18 C (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 ranged from 3 to 32 psu (Figure 3). Salinity was low in the surface waters of the left shoal, and increased from left to right across 33

34 the estuary, marked by sharp salinity gradients. The salinity 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 with 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 cross-section, where the salinity distribution was increasing with depth. The density anomaly over the sampling period ranged from 22 to 32 kg/m 3 (Figure 3-13). This density structure initially showed the lowest values over the upper left shoal, where it gradually 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 sampling concluded with the entire cross section showing a density distribution that 34

35 increased with depth, separated by horizontal isopycnals which indicated stratified conditions. As seen, the water density structure followed the salinity structure closely. Time-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. Time-averaged 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 isopycnals were present (Figure 3). 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 transect 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 Jm -3. The second transect had a range from 2 to 4 Jm -3, and also decreased linearly over the right shoal before reaching a minimum on the right side of the mid-shoal spike in the bathymetry. 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 to 2 Jm -3. The fifth and six 35

36 transects peaked in the channel and decreased linearly over the right shoal, ranging from to 4 Jm -3. The potential energy anomaly time series contours for time versus distance across (Figure 3-16), showed highest values in the channel, between 14 to 17 hrs and 21 to 22 hrs. The mean potential energy anomaly ranged from to 3.5 Jm -3 and showed the highest values in the channel (Figure 3-17). 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 kinetic energy dissipation distribution ranged from 1 to 1 m 2 s -3 over the sampling period (Figure 3-18). 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 mid-distance across the transect line. The second transect repetition showed the highest dissipation in the left shoal and shipping channel. Generally, the 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 fourth 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 mid-depth of the channel. 36

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 channel or near the bathymetry (Figure 3-19). The only exception 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 segment (Figure 3). 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 were in the waters above the high dissipation values along the right shoal (Figure 31). To examine the role of velocity and density gradients on dissipation, the Richardson number was calculated. The Richardson number time series contours ranged from to 2.5 (Figure 32). This concept was utilized to see if a correlation existed between time series contours of Richardson number and TKE dissipation. Along the bottom, the Richardson number was consistently low, while the TKE dissipation was high. Other than this trend, there was no distinct correlation between these contours. To investigate friction from the momentum balance, the friction and Coriolis terms were plotted over bathymetry (Figure 33). The results showed that friction dominates the flow over Coriolis, with friction being one order of magnitude higher than Coriolis. 37

38 (a) Transect 1 (b) Transect 2 (c) Transect (d) Transect 4 (e) Transect 5 (f) Transect Figure 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

39 (a) Transect 7 (b) Transect 8 (c) Transect (d) Transect 1 (e) Transect 11 (f) Transect Figure 3. Along Estuary Tidal Flow for February 24. A). Transect 7. B) Transect 8. C) Transect 9. D) Transect 1. E) Transect 11. F) Transect

40 (a) Transect 7 (b) Transect 8 (c) Transect (d) Transect 1 (e) Transect 11 (f) Transect Figure 3. 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. 4