By KIMBERLY ARNOTTufdcimages.uflib.ufl.edu/UF/E0/04/13/45/00001/arnott_k.pdf3-1 Along Estuary Tidal Flow (cm/s) for February 24. A) Transect 1. B) Transect 2. C) Transect 3. D) Transect

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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

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© 2009 Kimberly Arnott

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To my father

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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.

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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 Circulation ............................................................................................................... 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

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LIST OF 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 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. .................................................................. 48

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. ........................................................................................ 49

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3-14 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. .................................................................. 50

3-15 Mean Temperature (Celsius), 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 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. ..................... 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) Richardson 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

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LIST OF ABBREVIATIONS

Density (kg/m3)

Velocity gradient

Vertical eddy viscosity

Kinematic viscosity

Shear stress

B Basin width

Bi Body force

cics An O(1) constant

cvc Constant related to spectrum in viscous subrange

cw An O(1) constant

DT Diffusivity of heat

f Coriolis

F Fourier transform of

F* Complex conjugate

H Water depth (m)

k Max wavenumber

K Kelvin number

k Rad m-1

k Wavenumber (rad m-1)

kB Batchelor wavenumber

kk Kolmogorov wavenumber

L Length in describing flow

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q Universal constant

rad Radians

Re Reynolds Stresses

Ri Internal Rossby Radius

T’ Temperature fluctuation

To Temperature center of region

u Sensor velocity relative to water

U Velocity of flow

w Internal waves

z’ Vertical ordinate

α Dimensionless wavenumber

γ & β Are constants

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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 2009

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, 2009, 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 < 30 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

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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.

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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., 2007) 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 (2008)’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-

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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,

2009a). The parameters u, v, and w represent the along, across, and vertical

components of velocity, while f, g, ρ, 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 assumptions, Equation 1-1 reduces to Equation 1-2.

(1-2)

Equation 1-2 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)

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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 1-4

demonstrates becomes a geostrophic balance between Coriolis and pressure gradient.

(1-4)

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,

2008). 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

(2008). Valle-Levinson (2008)’s model is a semi-analytical solution that solves density-

driven exchange flows in terms of Ekman, Ek, and Kelvin, K, numbers:

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(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 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. 48-51). 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.

94-97). 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

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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, ui,j, p, μ, 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 turbulent 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), 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, uj,

ui, θ, g, w represent the turbulent kinetic energy, velocity shear, subscale velocity fluxes,

potential temperature, gravity, and vertical velocity. Equation 1- 10 represents turbulent

dissipation.

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(1-10)

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, 2004). The

observed data are measured with a microstructure profiler that samples at 100 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, 2001). The higher wave number of the temperature gradient

spectrum is a function of ε and the dissipation of the temperature variance, χT. 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 To is the temperature at the center of the origin (Luketina &

Imberger, 2001). The temperature gradient can then be given by Equation 1-12.

(1-12)

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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 1-14 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 ρ. The wave number can then be calculated using

the maximum wavenumber, as shown in Equation 1-16.

(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.

(1-17)

Cics is a constant and χt is the dissipation of the temperature variance. Equation 1-18

represents the dissipation of temperature variance due to turbulence.

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(1-18)

(1-19)

DT is the diffusivity of heat, T’ is the temperature, cvc 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, 2004). The one-dimensional

Batchelor spectrum is represented by Equation 1-20 (Luketina & Imberger, 2001).

(1-20)

(1-21)

The variable kB represents the Batchelor wavenumber and α is a dimensionless

wavenumber. Equation 1-22 is representative of the normalized Batchelor spectrum.

(1-22)

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, 2001). 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, 1980). The last

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method uses an algorithm to fit the Batchelor spectrum to the measured spectrum

(Ruddick et al., 2000). 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., 2000). Using the following equation

in conjunction with the measured values of χT, kB becomes the only free variable.

(1-23)

The dissipation, ε is then solved from the Batchelor wavenumber, Equation 1-24.

(1-24)

The algorithm seeks the best kB within a range of 9 x 10-11 m2s-3 to 1.5 x 10-5 m2s-3

(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 Valle-Levinson (2008)’s analytical

solution. The methods used for collecting and processing the data will be discussed in

the next chapter.

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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., 2006). As Florida’s 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 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 100 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 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

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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., 2006).

Data Collection

Current velocity, temperature and conductivity measurements were collected over

one semidiurnal tidal period across Hillsborough Bay on February 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 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

1200 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 20°. Currents were measured in North- South and East- West

components. WinRiver software was used to collect the data obtained from the

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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 rate of 10 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.

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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 10% 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 (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

25

used (1e-04, 10e-04, and 20e-04 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, 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

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 mid-

depth) due to stratification. The mean density, ρm, was calculated for each column

(McDowell & O’Conner, 1977, pp. 48-51) and then the potential energy anomaly, Φ

(Simpson et al, 1990).

(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).

(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

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.

28

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

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

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 -30 to 50 cm/s (Figures 3-1 and 3-2). The across-estuary

tidal current velocities showed positive and negative values (Figures 3-4 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 -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 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 along-

estuary 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,

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 0 to 30 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 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 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 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 3-6). The

greatest values were over the left shoal and channel and the smallest values were mid-

distance 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

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 20 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 3-8). 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

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 (~0 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

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 3-10). 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 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

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/m3 (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

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 3-14).

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 0 to 2 Jm-3. The fifth and six

36

transects peaked in the channel and decreased linearly over the right shoal, ranging

from 0 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 0 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 10 -8 to 10 -4 m2s-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.

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 3-20). 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 were 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

ranged from 0 to 2.5 (Figure 3-22). 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 3-23). The results showed that friction dominates

the flow over Coriolis, with friction being one order of magnitude higher than Coriolis.

38

Distance Across (km)

Depth

(m

)

(a) Transect 1

1 2 3 4-14

-12

-10

-8

-6

-4

-2


Depth

(m

)

(b) Transect 2

1 2 3 4-14

-12

-10

-8

-6

-4

-2


Depth

(m

)

(c) Transect 3

1 2 3 4-14

-12

-10

-8

-6

-4

-2


Depth

(m

)

(d) Transect 4

1 2 3 4-14

-12

-10

-8

-6

-4

-2


Depth

(m

)

(e) Transect 5

1 2 3 4-14

-12

-10

-8

-6

-4

-2

-20

-10

0

10

20

30

40

50


Depth

(m

)

(f) Transect 6

1 2 3 4-14

-12

-10

-8

-6

-4

-2

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.

39


Dep

th (m

)

(a) Transect 7

1 2 3 4-14

-12

-10

-8

-6

-4

-2


Dep

th (m

)

(b) Transect 8

1 2 3 4-14

-12

-10

-8

-6

-4

-2


Dep

th (m

)

(c) Transect 9

1 2 3 4-14

-12

-10

-8

-6

-4

-2


Dep

th (m

)

(d) Transect 10

1 2 3 4-14

-12

-10

-8

-6

-4

-2


Dep

th (m

)

(e) Transect 11

1 2 3 4-14

-12

-10

-8

-6

-4

-2

-20

-10

0

10

20

30

40

50


Dep

th (m

)

(f) Transect 12

1 2 3 4-14

-12

-10

-8

-6

-4

-2

Figure 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.

40


Depth

(m

)

(a) Transect 7

1 2 3 4-14

-12

-10

-8

-6

-4

-2


Depth

(m

)

(b) Transect 8

1 2 3 4-14

-12

-10

-8

-6

-4

-2


Depth

(m

)

(c) Transect 9

1 2 3 4-14

-12

-10

-8

-6

-4

-2


Depth

(m

)

(d) Transect 10

1 2 3 4-14

-12

-10

-8

-6

-4

-2


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


Depth

(m

)

(f) Transect 12

1 2 3 4-14

-12

-10

-8

-6

-4

-2

Figure 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.

41


Dep

th (

m)

(a) Transect 7

1 2 3 4-14

-12

-10

-8

-6

-4

-2


Dep

th (

m)

(b) Transect 8

1 2 3 4-14

-12

-10

-8

-6

-4

-2


Dep

th (

m)

(c) Transect 9

1 2 3 4-14

-12

-10

-8

-6

-4

-2


Dep

th (

m)

(d) Transect 10

1 2 3 4-14

-12

-10

-8

-6

-4

-2


Dep

th (

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


Dep

th (

m)

(f) Transect 12

1 2 3 4-14

-12

-10

-8

-6

-4

-2

Figure 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.

42


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


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 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.

.

43


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


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 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.

44


Tim

e (h

ours

)

0.5 1 1.5 2 2.5 3 3.5 414

15

16

17

18

19

20

21

22

23

24

-5

0

5

10

15

20

25

30

Figure 3-8. Depth Averaged Along Estuary Tidal Flow (cm/s) for Time versus Distance Across for February 24, 2009.

45


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


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 3-9. Residual Along and Across Channel Flow (cm/s) for February 24, as calculated using least squares fit to semi-diurnal tidal cycle.

46


Dep

th (m

)Along Channel Flow in terms of Ekman and Kelvin numbers (K=.49 Az=1E-04)

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


Dep

th (m

)

Along Channel Flow in terms of Ekman and Kelvin numbers (K=.49 Az=10E-04)

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


Dep

th (m

)

Along Channel Flow in terms of Ekman and Kelvin numbers (K=.49 Az=25E-04)

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 3-10. Results from Ekman Kelvin Model for Along Estuary Residual Flow using low, middle, and high Ekman numbers.

47


Dep

th (m

)

Across Channel Flow in terms of Ekman and Kelvin numbers (K=.49 Az=1E-04)

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


Dep

th (m

)


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


Dep

th (m

)


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 3-11. Results from Ekman Kelvin Model for Across Estuary Residual Flow using low, middle, and high Ekman numbers.

48


Depth

(m

)

(a) Transect 1

0.5 1 1.5 2 2.5 3

0

2

4

6

8

10

12

14


Depth

(m

)

(b) Transect 2

0.5 1 1.5 2 2.5 3

0

2

4

6

8

10

12

14


Depth

(m

)

(c) Transect 3

0.5 1 1.5 2 2.5 3

0

2

4

6

8

10

12

14


Depth

(m

)

(d) Transect 4

0.5 1 1.5 2 2.5 3

0

2

4

6

8

10

12

14


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


Depth

(m

)

(f) Transect 6

0.5 1 1.5 2 2.5 3

0

2

4

6

8

10

12

14

Figure 3-12. 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.

49


Depth

(m

)

(a) Transect 1

0.5 1 1.5 2 2.5 3

0

2

4

6

8

10

12

14


Depth

(m

)

(b) Transect 2

0.5 1 1.5 2 2.5 3

0

2

4

6

8

10

12

14


Depth

(m

)

(c) Transect 3

0.5 1 1.5 2 2.5 3

0

2

4

6

8

10

12

14


Depth

(m

)

(d) Transect 4

0.5 1 1.5 2 2.5 3

0

2

4

6

8

10

12

14


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


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.

50


Depth

(m

)

(a) Transect 1

0.5 1 1.5 2 2.5 3

0

2

4

6

8

10

12

14


Depth

(m

)

(b) Transect 2

0.5 1 1.5 2 2.5 3

0

2

4

6

8

10

12

14


Depth

(m

)

(c) Transect 3

0.5 1 1.5 2 2.5 3

0

2

4

6

8

10

12

14


Depth

(m

)

(d) Transect 4

0.5 1 1.5 2 2.5 3

0

2

4

6

8

10

12

14


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


Depth

(m

)

(f) Transect 6

0.5 1 1.5 2 2.5 3

0

2

4

6

8

10

12

14

Figure 3-14. 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.

51


Depth

(m

)(a) Temperature (Celsius)

0.5 1 1.5 2 2.5 3

0

5

10

16

16.5

17

17.5

18


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

y g p y


Depth

(m

)

(a) Density Anomaly (kg/m3)

0.5 1 1.5 2 2.5 3

0

5

10

Figure 3-15. Mean Temperature (Celsius), Salinity (psu), and Density Anomaly (kg/m3) Contours for February 24. The “x” symbol represents the five hydrographic stations.

52

0.5 1 1.5 2 2.5 3 3.50

2

4

6


(PH

I J/m

3)

(a) Transect 1

0.5 1 1.5 2 2.5 3 3.50

2

4


(PH

I J/m

3)

(b) Transect 2

0.5 1 1.5 2 2.5 3 3.50

1

2


(PH

I J/m

3)

(c) Transect 3

0.5 1 1.5 2 2.5 3 3.50

1

2


(PH

I J/m

3)

(d) Transect 4

0.5 1 1.5 2 2.5 3 3.50

2

4


(PH

I J/m

3)

(e) Transect 5

0.5 1 1.5 2 2.5 3 3.50

2

4


(PH

I J/m

3)

(f) Transect 6

0.5 1 1.5 2 2.5 3 3.5-15

-10

-5

0


Depth

(m

)

(g) Bathymetry

0.5 1 1.5 2 2.5 3 3.5-15

-10

-5

0


Depth

(m

)(h) Bathymetry

0.5 1 1.5 2 2.5 3 3.5-15

-10

-5

0


Depth

(m

)

(i) Bathymetry

Figure 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.

53


Tim

e(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 3-17. Potential Energy (J/m3) Contours for Time versus Distance Across for February 24.

54

0.5 1 1.5 2 2.5 3 3.50

1

2

3

4


PH

I (J/

m3)

gy y

0.5 1 1.5 2 2.5 3 3.5-15

-10

-5

0Bathymetry


Dep

th (m

)

Figure 3-18. Mean Potential Energy Anomaly (J/m3) and Bathymetry for February 24.

55


Dep

th (m

)

(a) Transect 1

0.5 1 1.5 2 2.5 3

-12

-10

-8

-6

-4

-2


Dep

th (m

)

(b) Transect 2

0.5 1 1.5 2 2.5 3

-12

-10

-8

-6

-4

-2


Dep

th (m

)

(c) Transect 3

0.5 1 1.5 2 2.5 3

-12

-10

-8

-6

-4

-2


Dep

th (m

)

(d) Transect 4

0.5 1 1.5 2 2.5 3

-12

-10

-8

-6

-4

-2


Dep

th (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


Dep

th (m

)

(f) Transect 6

0.5 1 1.5 2 2.5 3

-12

-10

-8

-6

-4

-2

Figure 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.

56


Dep

th (m

)

(a) Transect 1

0.5 1 1.5 2 2.5 3

-12

-10

-8

-6

-4

-2


Dep

th (m

)

(b) Transect 2

0.5 1 1.5 2 2.5 3

-12

-10

-8

-6

-4

-2


Dep

th (m

)

(c) Transect 3

0.5 1 1.5 2 2.5 3

-12

-10

-8

-6

-4

-2


Dep

th (m

)

(d) Transect 4

0.5 1 1.5 2 2.5 3

-12

-10

-8

-6

-4

-2


Dep

th (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


Dep

th (m

)

(f) Transect 6

0.5 1 1.5 2 2.5 3

-12

-10

-8

-6

-4

-2

Figure 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. The “x” symbols represent the hydrographic stations.

57


Dep

th (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


Dep

th (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 3-21. Mean Turbulent Kinetic Energy Dissipation using 128 and 256 scans for February 24. The “x” symbol represents the five hydrographic stations.

58

Time (hr)

Dep

th (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)

Dep

th (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)

Dep

th (m

)

(c) TKE Dissipation using 256 scans

14 16 18 20 22-14-12-10-8-6-4-2

Figure 3-22. Time series contours for Station 2. A) Richardson Number. B) TKE Dissipation using 128 Scans. C) TKE Dissipation using 256 Scans.

59

0 20 40 60 80 100 120 140 160 1800

1

2x 10

-5

(cd

u2)/

H

Friction Term

0 20 40 60 80 100 120 140 160 180-5

0

5x 10

-6

fv

Coriolis Term

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5-15

-10

-5

0


Dep

th (

m)

Bathymetry

Figure 3-23. Comparison of Friction and Coriolis Momentum Balance Terms.

60

CHAPTER 4 DISCUSSION

The purpose of this analysis was to compare the observed exchange flow pattern

from Hillsborough Bay with the results Meyer’s (2007) numerical circulation model and

Valle Levinson’s (2008) semi-analytical solution. It was also necessary to find

observational evidence to support the high frictional theoretical condition that is causing

this exchange pattern 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 strongest 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 velocities in the channel. The across-estuary component showed

negative (South-East) currents during ebb waters and positive currents during flood.

The strongest currents were at the surface 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.

The 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. This

pattern is consistent with Meyer’s (2007) model results for Hillsborough Bay and is most

consistent with the results of Valle-Levinson’s (2008) semi-analytical solution using a

high Ekman number. The high Ekman number indicated high frictional influences.

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

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.

The 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 suggested high frictional influences

occurring over the shoals.

Now, to verify that there were high frictional influences taking place, the

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 distribution 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 horizontally

oriented in the channel, signifying stratified conditions. Over the shoals, the contour

lines were more vertically oriented, which indicated a more mixed condition than in the

channel. This pattern is due to frictional influences from the bottom which affected the

entire water column. Velocity shears from bottom drag created turbulence, which

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 (>10-5 m2s-3) when

compared to other estuaries (Luketina & Imberger, 2001). These high values 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, turbulent kinetic energy is a balance of shear production, buoyancy

production, and dissipation, the 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

63

dissipation, not just shear and buoyancy production. The highest Richardson number

values occurred mid-duration of sampling.

Provided that the frictional influences have been investigated using the concept of

energy, friction was then analyzed using the momentum balance. The 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.

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 horizontally 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 in 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

water column in the channel allowed for stratification to develop, while stratification was

rather weak over the shoals. This is a sign of frictional effects from the bottom affecting

the entire water column over the shoals (creating turbulence that causes mixing). High

frictional influences yield high turbulent kinetic energy dissipation near the bottom when

compared to other estuaries. In conclusion, despite 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

friction and is among few observed examples of this type of exchange flows.

65

LIST OF REFERENCES

Batchelor, G.K. (1959) Small-scale Variation of Convected Quantities like Temperature in Turbulent Fluid, J. Fluid Mechanics, 5, 113-133. Dillion, T.M., & Caldwell, D.R. (1980) The Batchelor Spectrum and Dissipation in the Upper Ocean. J. Geophys. Res., 85, 1910-1916. Hughes, W.F., & Brighton, A.J. (1999) Schaum’s Outline of Theory and Problems of Fluid 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 Ship-Board ADCPs. J. Atmos. Oceanic Tech. 6, 169- 172. McDowell, D.M., & O’Conner, 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., Sherwood, E.T., Boler, R., & Barron, J. (2006), Variations in Water Clarity and Chlorophyll a in Tampa Bay, Florida, in Response to Annual Rainfall, 1985- 2004. Estuaries and Coasts, 29, 6A, 926-931. Pielke, R.A. (2002) Mesoscale Meteorological Modeling. San 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. Atmos. Ocean. Tech., 17, 1541-1555. 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), Dissipation of Turbulent Kinetic Energy near a Bubble Plumn. Journal of Hydraulic Engineering, 130, 441-119.

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Steinbuck, J.V., Stacey, M.T., & Monismith, S.G. (2009) An Evaluation of Xt Estimation Techniques: Implications for Batchelor Fitting and ε. 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.

67

BIOGRAPHICAL SKETCH

Kim began her educational career at the University of Central Florida, enrolled in

the Industrial Engineering Program. After several years, she decided to change her

major to civil engineering and move to Jacksonville. Finishing the final two years of

school at the University of North Florida, she received her bachelor’s degree in May

2008. After graduating, Kim moved to Gainesville to begin graduate school at the

University of Florida in the Coastal and Oceanographic Engineering Program.

Documents

By KIMBERLY ARNOTTufdcimages.uflib.ufl.edu/UF/E0/04/13/45/00001/arnott_k.pdf3-1 Along Estuary Tidal Flow (cm/s) for February 24. A) Transect 1. B) Transect 2. C) Transect 3. D) Transect