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VARIATIONS IN TURBULENT KINETIC ENERGY AT A BUOYANT JET DISCHARGE INDUCED BY TIDES AND WAVE SET-UP

By

SABRINA MARIE PARRA

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

2013

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© 2013 Sabrina Marie Parra

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To my mami

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ACKNOWLEDGMENTS

I thank my mother and sister for all their support throughout my graduate career

and everything else. I thank my amazing advisor, Dr. Arnoldo Valle-Levinson, for

believing in me and pushing me to be better. I also thank Dr. Robert Thieke for all the

guidance and talks throughout my undergraduate and graduate careers.

I thank Edgar Escalante, Francisco Ruiz and Roberto Iglesias from the Puerto

Morelos station of the ICMyL of UNAM for providing bathymetric and meteorological

data and for the support received during fieldwork, and Emanuel Sanchez for the

support in fieldwork. I gratefully acknowledge support from the NSF Bridge to the

Doctorate program. This research was funded by NSF project OCE-0825876 and

CONACYT, Mexico project #84847.

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TABLE OF CONTENTS

page

ACKNOWLEDGMENTS .................................................................................................. 4

LIST OF FIGURES .......................................................................................................... 7

LIST OF ABBREVIATIONS ............................................................................................. 8

ABSTRACT ................................................................................................................... 11

CHAPTER

1 INTRODUCTION .................................................................................................... 13

Motivation ............................................................................................................... 13 Submarine Groundwater Discharges ...................................................................... 14

Significance ...................................................................................................... 15 Driving Forces .................................................................................................. 16 Momentum Balance ......................................................................................... 18

Turbulent Kinetic Energy .................................................................................. 18

2 METHOD ................................................................................................................ 26

Study Area .............................................................................................................. 26 Data Collection ....................................................................................................... 27

Two Inlets ......................................................................................................... 27 Pargos Spring ................................................................................................... 28 Winds ............................................................................................................... 28

Data Processing ..................................................................................................... 29 Incident Waves ................................................................................................. 29

Lagoon Circulation ........................................................................................... 29 Spring Discharge .............................................................................................. 30

3 RESULTS ............................................................................................................... 33

Wind-Waves ........................................................................................................... 33

Lagoon Circulation .................................................................................................. 33 Pargos Spring ......................................................................................................... 34

Wave Set-up ..................................................................................................... 34

Turbulent Kinetic Energy .................................................................................. 35 Salinity .............................................................................................................. 35 Temperature ..................................................................................................... 36 Turbulent Kinetic Energy Production and Dissipation ....................................... 36

4 DISCUSSION ......................................................................................................... 44

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5 CONCLUSION ........................................................................................................ 48

LIST OF REFERENCES ............................................................................................... 50

BIOGRAPHICAL SKETCH ............................................................................................ 53

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LIST OF FIGURES

Figure page 1-1 Karst topography global map .............................................................................. 22

1-2 Nearshore SGD driving forces ............................................................................ 23

1-3 Idealized reef lagoon schematic ......................................................................... 24

2-1 Bathymetric map of the Puerto Morelos fringing coral reef lagoon ..................... 32

3-1 Winds and waves ............................................................................................... 38

3-2 Inlet velocity contours ......................................................................................... 39

3-3 Channel momentum balance parameters ........................................................... 40

3-4 Inlet and Pargos spring parameters .................................................................... 41

3-5 TKE components ................................................................................................ 42

3-6 Pargos spring TKE dissipation............................................................................ 43

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LIST OF ABBREVIATIONS

Coefficient of thermal expansivity (1/°C)

Coefficient of saline expansivity (g/kg)

x

Calculated pressure gradient

x

Pressure gradient

Dissipation (m2/s3)

Water surface variations (m)

Angle of rotation for primary axis of flow (°)

Temperature deviations (°C)

Wave number (1/m)

Viscosity

Water density (kg/m3)

0 Background density (kg/m3)

Density variations (kg/m3)

σ Standard deviation

ADCP Acoustic Doppler current profiler

ADP Acoustic Doppler profiler

ADV Acoustic Doppler velocimeter

B Buoyancy flux (m2/s3)

iBF Body force per unit volume

DC Bottom drag coefficient

CTD Conductivity temperature and depth recorder

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t

k

Turbulent kinetic energy flux (m2/s3)

)(E Spectral energy

f Frequency (Hz)

FFT Fast Fourier transform

g Gravity (9.81 m/s2)

GMT Greenwich Mean Time

h Channel depth (m)

Hs Significant wave height (m)

k Turbulent kinetic energy (m2/s2)

p Water pressure (dbar)

S Salinity (g/kg)

s Salinity deviations (g/kg)

SGD Submarine groundwater discharge

T Temperature (°C)

TKE Turbulent kinetic energy

UNAM Universidad Nacional Autónoma de México

U Mean channel velocity (m/s)

iu Velocity vector (m/s)

jiuu Reynolds stress tensor (m2/s2)

u East-west velocity component (m/s)

u East-west velocity anomalies (m/s)

u East-west filtered velocity (m/s)

v North-south velocity component (m/s)

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v North-south velocity anomalies (m/s)

v North-south filtered velocity (m/s)

w Vertical velocity component (m/s)

w Vertical velocity anomalies (m/s)

w Vertical filtered velocity (m/s)

w Mean vertical velocity (m/s)

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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

VARIATIONS IN TURBULENT KINETIC ENERGY AT A BUOYANT JET DISCHARGE

INDUCED BY TIDES AND WAVE SET-UP

By

Sabrina Marie Parra

May 2013

Chair: Arnoldo Valle-Levinson Major: Coastal and Oceanographic Engineering

The influence of tides and waves on turbulent kinetic energy (TKE) variations at a

buoyant jet discharge in a fringing reef lagoon in the Yucatan Peninsula, Mexico, was

observed using acoustic velocimeters, profilers and hydrographic instruments through a

three-day period. Tidal variations within the lagoon modulated TKE, temperature and

salinity at the buoyant jet. An inverse relationship between TKE and tides was

observed, with low TKE values (<0.01 m2/s2) during high tide and high values (>0.2

m2/s2) during low tides. When the water surface over the spring remained >0.04 m

above the mean, TKE was largely suppressed (<0.01 m2/s2). This demonstrates the

high sensitivity of the jet discharge to tides, despite the small tidal range (<0.2 m) in the

study area during the study. Additionally, wind-waves generated by a passing storm

created a wave set-up within the lagoon, further suppressing the spring discharge. TKE

fluxes were highly variable (up to ±2x10-4 m2/s3) during periods of low tide, pointing to

high levels of production and dissipation. TKE fluxes were diminished (<0.01x10-4 m2/s3)

during high tides. Periods of high tide showed a buoyancy dominant flow (up to 2x10-4

m2/s3), while low tides could have been driven by shear production, although no

estimates of shear production were available. Buoyancy production was broken down

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into its salinity and temperature components, with salinity dominating over temperature

with a two to one ratio. TKE dissipation estimates, obtained with spectral analyses, were

only calculated during high tides, when the log-log spectra displayed a -5/3 slope within

the inertial subrange. TKE dissipation displayed an inverse relationship with respect to

tidal oscillations over the jet. During the approach of high tide, TKE dissipation reached

its minimum (<1x10-6 m2/s3). As high tide receded, TKE dissipation began to increase

(up to 2x10-6 m2/s3). It was evident that water level oscillations changed the turbulence

dynamics of the spring, with buoyancy fluxes dominating when the discharge was low,

and shear production dominating at peak discharge periods. Therefore, the combination

of wave set-up and high tides is expected to threaten delicate aquifer conditions and

vital water resources for coastal communities worldwide.

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CHAPTER 1 INTRODUCTION

Motivation

Contamination of precious freshwater resources through salt intrusion into

estuaries, rivers and aquifers is an imminent threat of the expected global sea level rise

during the next century. Saltwater intrusion into estuaries and rivers can be studied and

predicted with well-established theories (e.g. Heatland and Geyer 2004; MacCready

2007). However, intrusion into groundwater aquifers is not well understood, though it is

expected that the combination of rising ocean waters and over-pumping will limit

groundwater reserves. Many coastal communities worldwide are threatened by rising

sea levels and therefore the resulting saltwater intrusion into the local freshwater

aquifers. Because of this threat, it is imperative to understand the sensitivity of

submarine groundwater discharges (SGDs) to sea level changes. Such a topic is the

focus of the current study.

Aquifers are particularly vulnerable to sea level rise because they are

hydraulically connected to coastal oceans via permeable substrates (e.g. sand) or

subterranean conduits (springs or sinks). Such connections allow relatively slow (< 1

m/day) seepage discharges of groundwater (Taniguchi et al. 2002) or relatively fast (~1

m/s) spring discharges (Valle-Levinson et al. 2011), respectively. These types of

hydraulic connections are found in most co astal areas around the world (Corbett et al.

1999; Zektser 2000). Fast buoyant discharges (springs) are typically found in karst

topography that is largely composed of calcium carbonate found in limestone or

dolomite bedrock. This topography can easily erode or dissolve to form caves and

subterranean conduits. Karst topography exists in all continents except Antarctica, and

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is typically located within or near the coast in the Bahamas, Mediterranean Sea, Gulf of

Mexico and Caribbean Sea, among others (Figure 1-1).

Submarine Groundwater Discharges

The term submarine groundwater discharge (SGD) is “any and all flow of water

on continental margins from the seabed to the coastal ocean, regardless of fluid

composition or driving force” (Burnett et al. 2003). This definition includes both

submarine fresh groundwater discharges from land and recirculated saline groundwater

discharges from the sea.

SGDs are an important source of freshwater to coastal environments. Despite its

importance, they are not as well understood as rivers and estuaries. SGDs provide a

significant freshwater and nutrient source to coastal seas as both natural and

anthropogenic caused by activities on land. Natural sources include atmospheric

systems ranging from hours to decadal periods that impact freshwater reserves.

Nutrients that can naturally occur in the soil are transported by groundwater fluxes. The

anthropogenic effects include increased nutrient concentrations due to farming practices

and decreased water quantity due to groundwater over-pumping.

Coastal ecosystems can also be affected by SGDs. Until recently, SGDs have

often been overlooked as a significant component of water, salt and nutrient budgets of

coastal and estuarine ecosystems, because these discharges are out of view and

difficult to quantify in terms of flux and nutrient transport (Valiela et al. 1999). Studies

have estimated SGDs from seepage discharges (Uchiyama et al. 2000; Taniguchi 2002;

Stieglitz 2005; Ganju 2011), but few studies have focused on spring discharges

(Swarzenski et al. 2001; Peterson et al. 2009; Valle-Levinson et al. 2011).

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It is believed that slow seepage may provide greater volume flux than spring

discharges because of the larger area of discharge. Spring discharges provide a direct

and uninhibited connection between the sea and freshwater aquifers. Because of this

direct connection it is imperative to study these systems which can be affected by rapid

salt intrusion into coastal aquifers.

These studies on submarine springs have been “rare and sketchy” (Fleury et al.

2007) and are usually limited to flow rates but with low-resolution data. Recent

estimates by Peterson et al. (2009) of point-source SGDs using aerial thermal infra-red

imaging and natural geochemical tracers demonstrate that point-source discharges

dominate over diffuse SGDs along the western coast of the Big Island of Hawaii. The

study of point-source SGDs suggests that the common assumption of uniform SGD

fluxes over an area that is also influenced by point-source discharges can provide a

misleading approximation of bed fluxes.

Significance

SGDs are an important pathway for nutrients and freshwater to coastal

ecosystems throughout the world. Even with a relatively small discharge flux of

submarine groundwater, a relatively large nutrient flux, including organics, inorganics

and microorganisms can be driven into coastal seas (Kroeger et al. 2007; Moore 2010).

Generally, groundwater has a higher concentration of inorganic nutrients than seawater

because of surface-applied fertilizers (Uchiyama 2000). These nutrient fluxes are known

to be an important source to salt marshes, estuaries, coral reefs, and other nearshore

communities (Moore 2010). Nevertheless, these nutrient fluxes can be detrimental to

the coastal oceans as harmful algal blooms have also been attributed or sustained by

SGDs (Hu et al. 2006).

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Anthropogenic pressures to coastal aquifers have also made SGDs more

vulnerable to salt intrusion, “the encroachment of saline water into fresh groundwater

regions in coastal aquifer settings” (Werner and Simmons 2009). Some of these

pressures include dredging of channels, increased groundwater usage, and expansion

of hard surfaces that reduce infiltration, among others (Moore 2010). These

extraordinary and ever-expanding demands on groundwater are adding pressure on an

ever-decreasing and valuable water commodity.

Furthermore, sea levels are expected to rise due to climate changes associated

with atmospheric pressure changes, thermal expansion of oceans and melting of ice

caps (Werner and Simmons 2009). The Intergovernmental Panel on Climate Change

(IPCC 2007) predicts that by the end of the 21st century (2090-2099), sea levels will

rise between 0.18 and 0.59 m relative to 1980-1999 levels. This sea level rise is

expected to result in saltwater intrusion into coastal aquifers worldwide. Therefore it is

essential to understand the driving forces between sea level changes and SGDs.

Driving Forces

The physical forces that drive and modulate SGDs include (Figure 1-2):

changes in hydrostatic pressure head within the aquifer,

oscillations in sea level,

current induced pressure gradients, and

anthropogenic alterations (Moore et al. 2010). Changes in hydrostatic pressure head within the aquifer can be caused by seasonal

atmospheric changes or unusual atmospheric events. Dry and wet seasons cause

cyclical changes in aquifer conditions. Additionally, infrequent atmospheric events like

hurricanes have been shown to dramatically increase the hydraulic head within aquifers

(Hu et al. 2006).

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Previous studies have shown that oscillations in sea level cause fluctuations in

SGDs. Oscillations in sea level can be caused by tidal pumping (Li et al. 1999;

Uchiyama et al. 2000; Kim and Hwang 2002; Taniguchi 2002; Ganju 2011; Valle-

Levinson et al. 2011), wave set-up (Li et al. 1999; Kim and Hwang 2002), and sea level

rise (Werner and Simmons 2009), among others. According to Santos et al. (2009), tidal

pumping is an exchange of groundwater and seawater driven by three main

components:

1. hydraulic gradient-driven fresh SGD, e.g. during low tide there are sharper hydraulic gradients triggering stronger fresh groundwater discharges than during high tides,

2. seawater recirculation, e.g. during high tide seawater infiltrates into the beach sand, which is later released at low tide, and

3. current driven recirculation, e.g. enhanced benthic exchange driven by stronger seawater current velocities.

Subtidal pumping is another type of mechanism driving groundwater and seawater

exchange. It is a wave-driven advective exchange near the coast caused by wave

breaking and swashing that causes flushing of permeable sediments (Riedl et al. 1972).

One possible example of subtidal pumping is wind-waves but this phenomenon has only

been documented in laboratory experiments and numerical models. Laboratory tracer

experiments have showed that “shallow water waves can increase fluid exchange

between sandy sediment and overlying water” (Precht et al. 2003). Numerical models

by Xin et al. (2010) found that waves generated an onshore wave set-up. The resulting

wave set-up produced pore water circulations in the nearshore zone of the coastal

aquifer, similar to pore water circulations observed during tidal pumping. However,

mixing of freshwater and seawater was less pronounced when induced by wave set-up

than by tides.

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Wave set-up caused by wind-waves has been observed forcing circulation in

coastal reef lagoons (Coronado et al. 2007; Taebi et al. 2011). Wind-waves that break

on the forereef and over the reef flats generate a cross-shore gradient that drives a

shoreward current through the surf zone (Figure 1-3A). This cross-shore current is

powered by a pressure gradient across the reef flat, with a maximum in water surface at

the top of the forereef (where wave breaking occurs) and decreasing towards the shore.

The pressure gradient drives a volume flux into the lagoon, which generates a wave set-

up. The wave set-up creates a pressure gradient that drives flow out through the

lagoon’s channels (Figure 1-3B and 1-4) (Taebi et al. 2011). It is postulated here that

such wave set-up can also affect the intensity and direction of buoyant jet discharges

within these lagoons.

Momentum Balance

Lagoon circulation through the inlets can be characterized by a momentum

balance between pressure gradient and bottom friction (Figure 1-4):

gh

UUC

x

D

(1-1)

where x

is the pressure gradient between the water surface within the lagoon and at

sea, DC is the bottom drag coefficient, U is the mean channel velocity, g is gravity, and

h is the channel depth. Field estimates of DC range between 10-2 and 10-3, depending

on bottom roughness scales (Friedrichs 2010).

Turbulent Kinetic Energy

In this study turbulence observations are used to quantify the effects of tides and

waves on spring discharges. Turbulent flow is unsteady and characterized by chaotic

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fluid motion. This chaotic motion is created by spatial and temporal variations in

pressure and velocity caused by a variety of forcing including bathymetric, wind, and

wave driven, among others. These variations create flow instabilities characterized by

the presence of vorticity and mixing in all three dimensions (Munson, et. al. 2006).

Turbulence is calculated using the nonlinear terms of the momentum equation.

The momentum equation originates from Newton’s second law and it relates

accelerations of the fluid particle to surface and body forces experienced by that fluid.

Surface forces are molecular while body forces are gravitational (Pope 2000). The

momentum equation assumes the viscosity of the fluid is constant, and flow is

incompressible as follows:

iji

j

i

jij

ij

i BFuux

u

xx

p

x

uu

t

u

(1-2)

where is the fluid density (assumed to be 1000 kg/m3), iu are the velocity

components, p is water pressure, is viscosity and iBF is the body force per unit

volume. From this equation, turbulent kinetic energy (TKE) is calculated by using the

normal stresses of the Reynolds stress tensor, jiuu :

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2222wvuu

ki

(1-3)

(Monismith, 2010) where u , vand w are velocity anomalies from the means u , v

and w . The anomalies are given by uuu , for the x component, for example. The

velocities u , v and w represent the instantaneous time series of the east, north and

vertical velocity components, respectively. TKE was calculated to seek relationships

between water surface variations, , at the spring and spring discharge variations.

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Furthermore, TKE flux can be calculated to compare causative agents. TKE

fluxes are assumed to be dominated by shear, buoyancy production, and dissipation:

BP

t

k (1-4)

where t

k

is TKE flux, P is production, B is buoyancy flux and is dissipation

(Monismith et. al. 2010). Contributions from buoyancy flux and dissipation were

estimated because the other TKE components required spatial measurements that were

not available.

Buoyancy flux was determined with:

wswgwg

B0

(1-5)

where 0 is the background density, are density variations, is the coefficient of

saline expansivity, s are salinity deviations from the mean, is the coefficient of

thermal expansivity, and are temperature deviations from the mean. Buoyancy

fluxes are produced by fluctuations in fluid densities caused by salinity or temperature

variations relative to the surrounding fluid, therefore B can be broken down into its

salinity and temperature components.

TKE dissipation is estimated by using Kolmogorov’s -5/3 law. According to the

Kolmogorov hypotheses, in any turbulent flow, the spectrum adopts a universal shape

within the inertial subrange of turbulence. When plotted on a log-log plot, the spectra of

flow velocities within the inertial subrange display a -5/3 slope. Using this section of the

spectra, can be inferred with the following:

3/53/234.0)( E (1-6)

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where is the wave number and )(E is the spectrum section with the -5/3 slope (Pope

2000).

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Figure 1-1. Karst topography global map (Map obtained from http://web.env.auckland.ac.nz/our_research/karst/#karst5).

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Figure 1-2. Nearshore SGD driving forces, both terrestrial and oceanic in origin, that affect the complex nearshore

dynamics of coastal environments (figure from Moore et al. 2010).

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Figure 1-3. Idealized reef lagoon schematic. A) Reef lagoon cross section including the momentum balance for the forereef and reef flats. B) Reef lagoon plan view showing the flow direction starting with wave induced current over the reef flats and ending with the wave set-up driving outflow through the channel (figure from Monismith 2007).

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Figure 1-4. Idealized scheme for the cross section of a lagoon channel, including the expected momentum balance.

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CHAPTER 2 METHOD

Study Area

The main objective of this study is to determine the influence of tides and wave

set-up on (a) the intensity and direction of water and salt fluxes, (b) the modulation of

TKE levels, and (c) buoyancy flux and TKE dissipation variations in a buoyant jet

discharge. Ideal natural settings to address these objectives are the reef lagoons of the

Caribbean, where ubiquitous buoyant jet discharges are influenced by tides, albeit of

small range (<0.5 m), and where waves are the main drivers of circulation.

The objective of this study was addressed in the Puerto Morelos coral reef

lagoon, located in the western Caribbean Sea, on the northeast coast of the Yucatan

Peninsula (Figure 2-1). The Puerto Morelos lagoon has a mean water depth between 3

and 4 m with a maximum depth of 8 m, and is delimited by fringing coral reefs that in

turn are interrupted by three major inlets. The northern inlet is around 1200 m wide and

6 m deep, while the central inlet is around 300 m wide and 6 m deep and the southern

inlet is a 400 m wide navigational channel with a dredged depth of 8 m. This lagoon is

influenced by dominant semidiurnal microtides and persistent trade winds that drive

onshore wind-waves. The reef area is comprised of submerged shallow coral banks that

experience substantial wave action and although it is a microtidal region, the reefs can

be exposed during low tides.

The lagoon is punctuated on its bottom by numerous (~10 to 15) buoyant jet

discharges, some of which can feature distinguishable surface expressions. The

buoyant jet discharge of interest in this study is the Pargos spring, named after the large

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number of snappers that used to congregate at this location. It has the largest discharge

rate of all the springs within the lagoon, at estimated values up to 1 m3/s.

Two distinct seasons are identified in the region: dry and wet. The dry season

extends from March through June and the wet season is generally from July through

November. Between December and February, brief cold fronts characterized by

northerly winds with light rains, locally known as nortes, are common. The average

rainfall is approximately 1000 mm per year. Puerto Morelos lagoon circulation is

predominantly influenced by tides and thermohaline circulations during periods of

minimal wave activity and wind-waves (wave set-up) during periods of substantial wave

activity (Coronado et al. 2007).

Data Collection

In order to study the effects of tides and wave set-up on a buoyant jet discharge,

data were collected between July 27th and 30th, 2010, with four instruments fixed on the

bed of the lagoon. Instruments were deployed at three locations: at two lagoon inlets

and at the jet associated with Pargos spring. A combination of two current velocity

profilers, a hydrographic recorder and a single-point acoustic velocimeter were

deployed. Additionally, wind speed and direction were also obtained.

Two Inlets

A 1500 kHz Sontek acoustic Doppler profiler (ADP) and a 2000 kHz Nortek

Aquadopp acoustic Doppler current profiler (ADCP) were moored at the lagoon’s central

and northern inlets, respectively, both at depths of ~6 m (Figure 2-1).

The ADP deployed at the northern inlet measured the current profiles with 3

beams, each tilted at a 25° angle, measuring upwards. The range of the beams was

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between 1 and 8 m from the bottom and it was broken down into 15 cells of 0.5 m each.

The ADP recorded velocity throughout the water column at 1 min intervals.

The ADCP deployed at the central inlet measured current profiles, water

pressure and bottom temperature. It had 3 beams, each tilted at a 25° angle, measuring

upwards. The range of the beams was between 0.7 and 8.2 m from the bottom and it

was broken down into 16 cells of 0.5 m each. The current profiles throughout the water

column were recorded at 10 min intervals. In addition, the ADCP logged 2048 2-Hz

measurements of water pressure per burst at the beginning of each hour; this was used

to estimate incident wave height, Hs, and spectral energy.

Pargos Spring

A 6000 kHz Nortek Vector acoustic Doppler velocimeter (ADV) and a

Schlumberger conductivity, temperature and depth Diver recorder (CTD) were moored

in the Pargos spring jet (Figure 2-1) and gathered data simultaneously.

The Nortek Vector ADV had 3 beams and a pressure sensor used to record

three-dimensional velocity point measurements and water pressure continuously at 8

Hz. The three-dimensional velocity measurements were used to calculate TKE at the jet

via anomalies. The CTD logged point measurements of the conductivity, temperature

and depth continuously every 10 s. Salinity, density and buoyancy flux were estimated

using the CTD data.

Winds

Wind speeds and direction were obtained from a meteorological station located

within the lagoon at the Universidad Nacional Autónoma de México (UNAM) facility.

Wind measurements were provided for the three-day observation period, measuring

every hour.

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Data Processing

The data obtained from these instruments were used to analyze how lagoon

circulation and incident wave activity affected spring discharge. The raw data were

uploaded into MATLAB and arranged into large matrices for ease of analysis. All time

measurements were converted to Greenwich Mean Time (GMT).

Incident Waves

Incident waves were derived from water pressure measurements (frequency of 2

Hz) obtained at the central inlet with the ADCP. Water pressure was converted to water

elevation by assuming 1 dbar in pressure is equivalent to 1m in depth. A spectral

analysis was performed from each burst using a fast Fourier transform (FFT). In order to

obtain smooth FFT results, the data were broken down into 10 Hamming windows. The

FFT for each window was calculated and averaged, and the hourly spectra are

averaged every 3 hours.

The significant wave height, Hs, was obtained by multiplying by 4 the standard

deviation, σ, of the surface elevation recorded during each burst (Neumann and Pierson

1966).

Lagoon Circulation

The lagoon circulation was characterized by the current profiles obtained from

the northern and central inlets. Both profiles were smoothed with a 30-min low-pass

Lanczos filter. Additionally, the profiles were rotated to the primary axis of flow. In order

to find the primary axis of flow, the east velocity was plotted on the x-axis and the north

velocity was plotted on the y-axis of a scatter plot. These scatter plots showed a trend,

which was quantified with a trend line. The angle between the line and the x axis

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became the angle of rotation. The along channel flows are the ones of importance,

showing currents in and out of the lagoon.

Lagoon circulation through the channels can be represented by the momentum

balance between pressure gradient and bottom friction (equation 1-1). Using equation

1-1 and the data for the central inlet, only DC is unknown, thus this momentum balance

can be resolved for the channel. The pressure gradient between the jet and central inlet

was calculated by taking the difference between at the inlet and the jet and dividing

over the distance between the two (1,200 m). The DC was estimated throughout the

measurement period.

Spring Discharge

The effects of incident waves and lagoon circulation were observed with three-

dimensional instantaneous velocities, conductivity and temperature observations of the

spring discharge.

Spring velocities were used to calculate TKE (equation 1-2). The brackets of

equation 1-2 represent a 10-min low-pass filtered time series obtained with a Lanczos

filter. TKE calculated with equation 1-2 is further filtered, to obtain a smooth

representation, using a 30-min low-pass Lanczos filter.

The CTD measured temperature, conductivity and depth. From these

measurements we estimated salinity and density. Practical salinity was calculated from

temperature, conductivity and depth (Perkin and Lewis 1980). Density was then

estimated using salinity, temperature and depth. The spring salinity calculations and

temperature observations were smoothed using a 30-min low-pass Lanczos filter.

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Additionally, the instantaneous salinity and temperature data were used to

calculate buoyancy fluxes (equation 1-4). Buoyancy fluxes called for coefficients of

saline expansivity, , and thermal expansivity, . These are calculated using the

following equations:

S

1 (2-1)

T

1 (2-2)

where is water density, S is salinity and T is temperature. Buoyancy fluxes were

calculated using these coefficients, as `well as the salinity and temperature changes. A

30-min low-pass Lanczos filter was also applied to B .

Spectral energy of jet vertical velocities was used to estimate TKE dissipation.

The vertical velocities are used to estimate dissipation because they are the least noisy

(Voulgaris and Trowbridge 1998). In similar fashion as for determining wave energy, the

spectra of vertical velocities were windowed and broken down into hourly spectra. The

spectra are averaged every 3 hours to further smooth the results. The wave number, ,

is obtained from the frequency, f , and mean vertical velocity, w , for each spectrum, as

follows:

fw

2 (2-3)

with the wave number and spectra within the inertial subrange, dissipation is estimated

using Kolmogorov’s -5/3 law (equation 1-5).

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Figure 2-1. Bathymetric map of the Puerto Morelos fringing coral reef lagoon on the eastern Yucatan Peninsula of Mexico (depth in meters).

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CHAPTER 3 RESULTS

Wind-Waves

During the measurement period, the lagoon experienced predominantly westerly

and west-southwesterly winds at ~9 m/s near the start of the record, whereas towards

the end winds were southwesterly and decreased to ~4 m/s (Figure 3-1A). The

important wind component for wind-wave formation in this lagoon was the east wind.

The shoreward wind started at ~8 m/s and decreased to around 3 m/s towards the end.

The stronger winds at the beginning of the record were associated with the remnants of

a storm.

At the start of the observation period, Hs were ~0.4 m and decreased to 0.25 m

toward the end (Figure 3-1B). Significant wave heights oscillated with an 8 h period.

Power spectra of the hourly bursts showed dominant frequencies between 0.08 and

0.25 Hz (13 and 4 s periods, respectively) at the beginning of the record (Figure 3-1C).

These were associated with swells and seas from the storm. Dominant frequencies

narrowed to a range between 0.1 Hz and 0.25 Hz (10 and 4 s periods, respectively) by

the end. Wave spectral energy was also higher at the beginning, >5 m2/Hz, and

decreased to a local maximum of ~1 m2/Hz near the end.

Lagoon Circulation

The highest wave action during the observation period caused the strongest inlet

flows. The northern and central inlet velocities produced outflows during most of the

three-day period (Figure 3-2). On the first day, high outflow velocities (~0.5 m/s) at both

inlets showed weak semidiurnal oscillations, with greater velocities during and after low

tide. Outflow velocities, ~0.4 m/s during and after low tides, were persistent in the

34

central inlet through the first 40 h of measurement, while outflows of ~0.4 m/s for the

northern inlet were only persistent during the first 20 h. Inflow through the inlets was

only observed at the end (~60 h), around high tides and when wave action was at its

lowest (Hs = 0.23 m).

Lagoon circulation was characterized by a momentum balance between pressure

gradient and bottom friction (Figure 3-3). Mean velocity, U , of the channel are highly

correlated to the pressure gradient between Pargos spring and the central inlet (Figure

3-3A). Channel depth varied on a semidiurnal tidal period with a range of 0.15 m (Figure

3-3B). Using pressure gradient, mean velocity and channel depth, bottom drag values

were estimated and ranged mostly between 10-2 and 3x10-3 and are within commonly-

observed field observations (Figure 3-3C). A DC spike at hour 60 was observed and

corresponded with a drop in inlet velocities.

Pargos Spring

Wave Set-up

Persistent outflows at the lagoon’s northern and central inlets indicated a wave

set-up within the lagoon caused by wave action prior to and during the first day of

instrument deployment. Indeed, a wave set-up was observed in the difference between

the demeaned at the jet and at the central inlet (Figure 3-4A). This difference showed

an initial value of ~0.025 m over a distance of 1200 m ( 5102

x

x

) and also exhibited

a clear semidiurnal pattern. Furthermore, a direct relationship between wave set-up and

Hs was observed throughout the record, as Hs decreased so did wave set-up. The

second half of the record showed water level differences (spring - inlet) between the two

locations that were hovering around zero, indicating a relaxation of the wave set-up.

35

Turbulent Kinetic Energy

At the spring discharge, TKE varied in a distinctive semidiurnal pattern and with

an inverse relationship to the tides, as maxima occurred at low tides and minima

developed at high tides (Figure 3-4B). Greatest TKE values per unit mass were

between 0.2 and 0.4 m2/s2, around low tide. Among these high TKE values, the largest

peaks were observed during the lowest low tides and smallest wave set-up (hour 40

and 65). On the other hand, when the water surface over the spring remained 0.04 m

above the mean and beyond (grey shaded areas of Figure 3-4B), TKE was largely

suppressed (<0.01 m2/s2).

Salinity

Tidal variations in jet discharge were also apparent in the salinity and

temperature data. In similar fashion to TKE, salinity at the spring varied in a semidiurnal

pattern (Figure 3-4C). High and fluctuating values (up to 34 g/kg, which was the

lagoon’s background salinity) appeared immediately preceding high tide, while low and

smooth values (29-30 g/kg) occurred approximately 2 h after high tide. Salinity maxima

occurred at periods of lowest TKE and salinity minima occurred between high and low

tide, when TKE was intensifying. Salinity gradually and smoothly increased around low

tides, when TKE was at its highest, causing the most vigorous mixing between aquifer

and ocean waters. Between low and high tide, the smooth salinity increases changed to

abrupt oscillations, as TKE diminished. This general pattern was observed repeatedly

throughout the entire three-day period. The highest salinity spike of 34 g/kg at hour 7

was observed just before high tide and also coincided with a pulse of high Hs combined

with the strongest outflows from the inlets and the greatest wave set-up.

36

Temperature

Water temperatures at the jet showed distinct temporal variations from those at

the central inlet throughout the period (Figure 3-4D). Aquifer temperatures were lower

than lagoon and surface ocean temperatures at that time of year, therefore jet

temperatures were able to be traced and showed similar variations to those of salinity.

Water temperature maxima (~ 28 °C) occurred during high tides, while minima (< 27 °C)

occurred during low tides. Periods of smooth low temperatures coincided with highest

TKE values and indicated mixing in the spring discharge. An atypical spike in

temperature (~29 °C) observed during hour 7 coincided with a corresponding salinity

spike, suggesting a pulse of salty and warm ocean water into the spring.

In contrast to the spring, the temperature at the inlet varied in a diurnal pattern

associated with atmospheric heat fluxes. During the first 20 h, the temperature

maximum at the inlet was not as high (<29.5 °C) as in subsequent days due to cloud

cover related to the storm.

Turbulent Kinetic Energy Production and Dissipation

TKE fluxes were calculated to determine the TKE budget of the jet. TKE flux,t

k

,

varied in a semidiurnal pattern, as did TKE, with periods of greatest oscillations

occurring throughout low tides (Figure 3-5B). Positive values represent TKE increases,

while negative values represent TKE decreases. TKE increases in general can be

attributed to shear production, negative buoyancy fluxes or transport. Only buoyancy

fluxes and dissipation could be calculated because of lack of measurements with spatial

resolution. Positive buoyancy fluxes represent buoyancy driven TKE production, e.g.

overturning of the water column caused by lower density water below higher density

37

water. Negative buoyancy production represents as a sink, meaning TKE mixing that

transports higher density fluid up and lower density fluid down (Monismith, 2010).

The variations showed high variability (>0.5x10-4 m2/s3) during periods of TKE

inactivity and less variability (<0.5x10-4 m2/s3) during periods of high TKE activity (Figure

3-5C). Buoyancy flux can be broken down into the salinity and temperature components

to see their relative magnitudes. Salinity was the dominant component of buoyancy flux

(Figure 3-5D) when compared to temperature with a 2:1 ratio (Figure 3-5E). Clearly,

salinity is the driving force of buoyancy flux, while temperature plays a supportive role.

During periods of low TKE values, was estimated using the vertical velocity

anomalies (Figure 3-6A) power spectra within the inertial subrange that displayed a -5/3

slope (Figure 3-6B). Unfortunately for periods of high TKE values, the spectra produced

a horizontal or nearly horizontal spectra throughout the frequency ranges (Figure 3-6C),

therefore a -5/3 slope was not observed and dissipation could not be estimated.

Dissipation estimates range from 10-7 to 10-6 m2/s3. Dissipation appears to have an

inverse relationship with the tides, with low (<1x10-6 m2/s3) values during the middle of

minimal w’ variations and increasing (>1x10-6 m2/s3) as variations increase.

38

Figure 3-1. Winds and waves. A) Hourly wind velocity vectors (blue), and east (black) and north (red) components measured at a meteorological station within the Puerto Morelos lagoon, showing the direction toward which the wind blows. B) Hs (green) and η (blue) measured at the central inlet. C) Contours of wave energy power spectra at the central inlet.

39

Figure 3-2. Inlet velocity contours. A) Northern inlet velocity profiles. B) Central inlet velocity profiles. Both have been

rotated to the primary flow axis, the angle being counterclockwise from east. The black contour line represents the zero velocity contour line. Positive velocities represent outflow, negative represent inflow into the lagoon.

40

Figure 3-3. Channel momentum balance parameters. A) Pressure gradient between the jet and central inlet (blue) and

mean central inlet channel velocities (green). B) Water depth at the central inlet. C) bottom drag coefficient

estimates at the central inlet, green dashed line represents the common value of DC =0.025.

41

Figure 3-4. Inlet and Pargos spring parameters. A) Central inlet (black), spring (blue) and the difference between two

(red). B) Spring TKE. C) Spring salinity. D) Temperature at both the spring (blue) and central inlet (black). Gray shaded areas represent periods of suppressed TKE activity, when the water level over the spring was > 0.04 m above the mean (green dashed line).

42

Figure 3-5. TKE components. A) Water surface at the central inlet (black), at the spring

(blue) and the difference between the spring and the central inlet (red). B) dk/dt at the spring. C) Buoyancy flux. D) Salinity component of buoyancy flux. E) temperature component of buoyancy flux. F) Estimate of dissipation of turbulent kinetic energy at the spring.

43

Figure 3-6. Pargos spring TKE dissipation. A) Vertical velocity anomalies from the mean (black). B) TKE dissipation

estimates at the spring discharge. C) Power spectra contours of jet vertical velocity anomalies.

44

CHAPTER 4 DISCUSSION

Results indicated that relatively high incident waves originating from a passing

storm with onshore winds produced the following effects: wave set-up in the lagoon,

enhanced outflows at the northern and central inlets, increased salinity pumped into the

lagoon, and suppressed spring discharge.

A passing storm produced higher Hs and greater wave energy, in addition to

broader frequency bands during the first 1.5 days of the record, compared to the

remainder. Increased wave action prior to and during the first day created a wave set-up

in the lagoon. An interesting 8-hr Hs modulation, which typically arises from non-linear

interactions between diurnal (e.g. sea breeze) and semidiurnal (e.g. tidal) forcing,

seems to influence wave heights. Taebi et al. (2011) showed that wave heights on the

reef flats were strongly modulated by tides because as tides change the water depth at

the reef crest, wave energy at the surf zone also changes. This does not explain the 8-h

modulation seen at the central inlet. A longer time series is required to assess the

persistence of the 8-h modulation and its origin.

Strong outflows (up to 0.5 m/s) were observed through the northern and central

inlets at the start and decreasing with time. Both inlets showed weak semidiurnal

oscillations, with greater velocities during and after low tide. These increases in velocity

were generated by a steeper pressure gradient between the lagoon and sea. Outflow

velocities, ~0.4 m/s, were persistent in the central inlet through the first 40 h, while

outflows of ~0.4 m/s for the northern inlet were only persistent during the first 20 h. A

possible cause for this difference in discharge was the variation in inlet widths. The

northern inlet is approximately four times wider than the central inlet thus similar

45

transports with lower velocities. It is clear that inlet velocities were greatly correlated

with the pressure gradient between the jet and central inlet (Figure 3-3A). Drag

coefficient estimates proved to be within accepted value, with the exception of a large

peak (up to 0.1) at hour 60. This peak is attributed to a drop in mean channel velocity

occurring simultaneously. As U approached zero, solving the momentum balance for

DC confirmed that estimates for DC would spike since U is in the denominator. This

would cause DC to approach infinity as U approaches zero.

At the time of greatest wave action (hour 7), a spike in salinity and temperature

was observed. This spike was observed in conjunction with the second highest tide of

the observation period as well as a peak in wave height. The highest water levels within

the lagoon resulted in damping of TKE activity at the jet by the additional hydrostatic

pressure, which reduced the pressure head gradient that drives spring outflow.

Additionally, increased wave action and wave set-up within the lagoon likely resulted in

a pulse of warm salty lagoon water into the spring and aquifer. The second half of the

record showed water level differences (spring - inlet) between the two locations that

were around zero, indicating a relaxation of the wave set-up.

It was evident that both tides and wind-waves affected the surface elevation in

the lagoon, which in turn modulated the jet discharge. TKE at the spring was inhibited

during periods of increased wave activity. TKE maxima occurred in conjunction with

periods of damped variations of salinity and temperature because of increased mixing at

the spring jet. Waves caused pumping of ocean water into the lagoon, augmenting the

water level within, and creating a corresponding set-up (Figure 3-5A). As wave action

diminished, outflows at the inlets and wave set-up in the lagoon decreased.

46

On the other hand, when the water surface over the spring remained 0.04 m

above the mean (grey shaded areas of Figure 3-3B), TKE was largely suppressed (<

0.01 m2/s2). This was a remarkable result that demonstrated the high sensitivity of the

jet discharge to tides, despite the small tidal range (< 0.2 m during the observation

period) in the study area.

Furthermore, highest salinities appeared to have been caused by increased

wave activity. Consequently, the aquifer is most susceptible to salt contamination at the

highest tides combined with intense wave action that pumps more salt into the lagoon

than under no wave conditions. This combination of processes, wave set-up, wave

pumping of salt and high tides, should favor salt intrusion into the aquifer as actually

observed by divers involved in equipment deployment. They witnessed neutrally

buoyant sea grass flowing into the spring opening and disappearing from sight into the

aquifer.

TKE fluxes showed that high variability (>0.5E-4 m2/s3) occurred during low tides,

when the water level over the spring was below the 0.04 m threshold. When the water

level was above the threshold, TKE fluxes were negligible (<0.1E-4 m2/s3). The

buoyancy flux component showed high variability (>0.5E-4 m2/s3) when the water level

hovered around the 0.04 m threshold or above. Meaning that buoyancy flux dominates

when spring discharge is at its lowest levels (during high tides), while during low tides

buoyancy fluxes are not as important. During low tides, spring discharge seems to be

primarily driven by advection and shear production. Spatial measurements of jet velocity

are required to properly assess this notion.

47

The driving force of buoyancy production was the salinity component, as it was

almost twice as much as the temperature component throughout the measurement

period (Figure 3-5D, F). Considering that changes in salinity cause four times more

changes in density than an equal change in temperature, in addition to the salinity and

temperature ranges of the data, it is clear that salinity should be the dominant factor in

density-driven buoyancy fluxes. Buoyancy production was greater (up to 2x10-4 m2/s3)

at the beginning, when wave action was at its highest, and decreased (<1x10-4 m2/s3) as

wave action decreased. This shows a direct connection between wave action and

buoyancy driven spring discharge.

TKE dissipation could only be estimated during high tides, when the spring water

level was near or beyond 0.04m above the mean. Although, these results were

scattered and minimal, they showed a pattern. There was an inverse relationship

between TKE dissipation and tides. As the water level over the spring increases, a

decrease in dissipation occurs, arriving at a minimum just before high tides. Then as

high tide recedes, TKE dissipation increases. A direct relationship between TKE and

dissipation is observed, with low TKE dissipation when low values of TKE, and vice

versa.

48

CHAPTER 5 CONCLUSION

Incident wave activity occurring before and during the first day of measurements

created a wave set-up within the lagoon, increased inlet discharge velocities and

suppressed jet discharge. Increase wave action appears to have also pumped saltier

and warmer Caribbean seawater into the lagoon and subsequently into the aquifer

(waves at hour 7). Wave set-up was also directly correlated with buoyancy flux at the

spring, with greater buoyancy fluxes during the greatest wave set-up. As wave action

decreased, so did inlet discharge, wave set-up within the lagoon and buoyancy flux at

the jet. An inverse relation between wave activity and spring discharge was observed,

as wave activity diminished spring discharge increased.

These results clearly show the effects of incident waves on the lagoon

circulation, but to a greater extent, on spring discharge. Increases in sea level caused

by tides, waves, thermal expansion or glacier melt, the latter two related to climate

change, thus represent a severe threat to coastal freshwater aquifers. The finding that

the spring at this site stops discharging when the water level goes beyond 0.04 m above

the mean, seems to have very serious implications. The Intergovernmental Panel on

Climate Change (IPCC 2007) predicts that by the end of the 21st century (2090-2099),

sea level will rise between 0.18 and 0.59 m relative to 1980-1999 levels. The local

aquifer system would then stop discharging completely into the ocean within 7 and 22

years, when the water level at the spring is at least 0.04 m higher than what it was in

2010.

Unfortunately, coastal aquifers are not just threatened by changes in sea level.

Widespread over-pumping of groundwater in coastal areas will further decrease the

49

freshwater supply and favor further salt intrusion through these submarine springs (Xin

et al. 2010; Vera et al. 2012). This scenario is occurring in many areas around the world

where coastal groundwater aquifers provide the essential resource. Therefore, it is

critical to expand our knowledge to other world areas where karst topography aquifers

are a major source of fresh water.

50

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53

BIOGRAPHICAL SKETCH

Sabrina began her higher education journey in June 2004 at the University of

Florida as a civil engineering undergraduate student. Once she discovered a love for all

things water thanks to Dr. Thieke’s Hydrodynamics and Hydraulics courses, she

decided to focus her civil engineering degree on Hydrology and Water Resources. In

the fall of 2009 she graduated Summa Cum Laude with a B.S. degree in civil

engineering. Following graduation, she worked at a groundwater laboratory at the

University of Florida under the leadership of Dr. Newman, as well as an office assistant

to Dr. Thieke and Nell Hinkle in the Undergraduate Advising office of civil engineering.

Although she loved water, she didn’t feel a great passion for Hydrology and Water

Resources, so after great advice from Dr. Thieke and many other great listeners, she

decided to pursue graduate studies in coastal and oceanographic engineering. After

much deliberation, in August 2010 she began her graduate studies at the University of

Florida in Coastal and Oceanographic Engineering under the guidance of Dr. Valle-

Levinson. She will continue her graduate education with the ultimate goal of a doctorate

degree with Dr. Valle-Levinson at the University of Florida.