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«TEMPORAL VARIATIONS OF VERTICAL MIXING ACROSS A COASTAL PLAIN ESTUARY By KIMBERLY DAWN ARNOTT A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE ...»

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TEMPORAL VARIATIONS OF VERTICAL MIXING ACROSS A COASTAL PLAIN

ESTUARY

By

KIMBERLY DAWN ARNOTT

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL

OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

© 2013 Kimberly Dawn Arnott To my Mother and Father

ACKNOWLEDGMENTS

I would like to thank my advisor, Arnoldo Valle-Levinson, for all of his guidance and support while pursuing both my M.S. and Ph.D. He has the wonderful ability to intrigue and inspire students, as I have seen with my own personal experience and with others after me. He is the reason I love research and has a lot to do with why I came back to school. I also want to acknowledge his patience and availability, which are two things I am very grateful for. I would also like to thank Alex Souza for introducing me to the structure function and for providing helpful suggestions for my research at conferences. Additionally, I would like to thank Jim O’Donnell for his kind comments, for sharing another technique to calculate dissipation, and for taking the time to help me.

Input from these two greatly helped my progress in research. I would like to thank my committee, Dr. Donald Slinn, Dr. Lawrence Ukieley and Dr. Robert Thieke for their input during my qualifying exams and for taking the time to listen and give comments about my research. Thanks to Arnoldo, Bob Chant, Ming Li and everyone involved in collecting such a comprehensive data set. I could not have improved my oral presentations without Arnoldo’s research group, namely Lauren Ross and Sabrina Parra, who have given me constructive criticism and comments that have helped me improve along the way. Lastly, I would like to give thanks to Amy Waterhouse and Chloe Winant, who helped and supported me with my very first talk in Rome.

TABLE OF CONTENTS

page ACKNOWLEDGMENTS

LIST OF FIGURES

LIST OF ABBREVIATIONS

Abstract

CHAPTER 1 INTRODUCTION

2 TEMPORAL VARIABILITY OF TKE DISSIPATION FROM CHANNEL TO

CHANNEL SLOPE ACROSS A COASTAL PLAIN ESTUARY

Synopsis

Background

Methodology

Data Collection

Data Processing

Results

Hydrographic and Meteorological Variability

Neap/ Spring Snapshots of TKE Dissipation

Spectral Analysis

Empirical Orthogonal Function Analysis

Coherence Analysis

Discussion

Summary

3 VARIABILITY OF VERTICAL MIXING ACROSS A COASTAL PLAIN ESTUARY.. 48

Synopsis

Background

Methods

Data Collection

Mixing Theory

Data Processing

Results

Spring Tide: Late Flood

Spring Tide: Late Ebb

Spring Tide: Lateral Circulation

Spring Tide: Timescale Analysis

Neap Tide: Late Ebb

Neap Tide: Maximum Flood

Neap Tide: Lateral Circulation

Stratification Versus Shear Analysis

Discussion

Summary

4 INFLUENCE OF TIDAL MIXING ASYMMETRIES ON RESIDUAL EXCHANGE

FLOW IN THE JAMES RIVER ESTUARY

Synopsis

Background

Background on Mixing Asymmetries

Methods

Data Collection

Data Processing

Results

Tidal Variability of Vertical Mixing

Stratification

Residual Flows

Vertical Mixing

Mixing Asymmetry Induced Flow- Observations and Model Comparison......... 97 Advection and Mixing Asymmetry Comparison

Depth-averaged Subtidal Momentum Terms

Non-dimensional Analysis

Discussion

Summary

5 CONCLUSIONS

Summary

Near-surface TKE Dissipation

Near-surface Vertical Mixing

Tidal Asymmetries in Vertical Mixing and Subtidal Dynamics

Implications of Findings

LIST OF REFERENCES

BIOGRAPHICAL SKETCH

–  –  –

2-1 Map and cross-section of study site.

2-2 Hydrographic and meterologis observations.

2-3 Neap tide snapshot: along- and across-channel velocity and velocity shears.... 41 2-4 Neap tide snapshot: potential energy anomaly, near-bottom density anomaly, and TKE dissipation

2-5 Spring tide snapshot: along- and across-channel velocity and velocity shears.. 43 2-6 Spring tide snapshot: potential energy anomaly, near-bottom density anomaly, and TKE dissipation

2-7 Spectra of velocity,velocity shears and TKE dissipation

2-8 EOF results: spatial structure, weighted amplitude, and spectrum of weighted amplitude.

2-9 Coherency results between weighted amplitude Mode 1 and hydrography and velocity shear in channel and channel slope

3-1 James River plan view of study site and cross-section

3-2 Neap conditions Station 1

3-3 Neap conditions Station 2

3-4 Neap conditions Station 3

3-5 Neap conditions Station 4





3-6 Differential advection forcing and Coriolis forcing.

3-7 Spring conditions Station 1

3-8 Spring conditions Station 2

3-9 Spring conditions Station 3

3-10 Spring conditions Station 4

3-11 Differential advection forcing and Coriolis forcing

3-12 Four timescales characteristic of lateral circulation processes.

3-13 Richardson numbers, Ri for Station 2 and 3 during neap and spring tide conditions.

4-1 James River plan view of study site and cross-section

4-2 Neap and spring stress divergences at Stations 1-4

4-3 Tidally averaged density anomaly and buoyancy frequency.

4-4 Along- and across-channel residual exchange flow

4-5 Tidally averaged vertical eddy viscosity and vertical shear.

4-6 Tidally averaged stress divergence, mean and fluctuating component of tidally averaged stress divergence

4-7 Residual along-channel exchange flow induced by mixing asymmetries......... 112 4-8 Neap and spring fluctuating component of tidally averaged stress divergence and tidally averaged along-channel advective acceleration

4-9 Subtidal momentum balance for neap and spring..

–  –  –

N Buoyancy frequency Cv2 Constant taken to be 2.1 in meteorology f Coriolis parameter h Depth of the water column ρm Depth-mean water density ε Dissipation of TKE r Distance, analogous to turbulent eddy length scale s’ Fluctuating salinity Rf Flux Richardson number

–  –  –

ρo Reference density ρo Reference water density Reynolds averaged across-channel velocity Reynolds averaged along-channel velocity Reynolds averaged vertical velocity u’w’ Reynolds stress

–  –  –

v’ Turbulent fluctuating velocities ui ’ Turbulent fluctuating velocity TKE Turbulent Kinetic Energy Prt Turbulent Prandtl number

–  –  –

Chair: Arnoldo Valle-Levinson Major: Coastal and Oceanographic Engineering An experiment in the James River was carried out to investigate the temporal variability of TKE dissipation and vertical mixing across an estuary. Time series of dissipation exposed large values during greater floods, with larger values during spring than neap tide. In the channel, the largest values were near-bottom and surface, but were focused near-surface over the channel slope. While the bottom-generated dissipation in the channel was an anticipated finding, a novel discovery was displayed at the surface. Statistical analyses suggested that the surface dissipation was generated by vertical gradients in lateral velocities near-surface, which developed from lateral circulation. On a smaller time scale, a 12 hr spring tide survey displayed large vertical mixing results near-bottom during flood. Ebb revealed large mixing near-bottom and surface at two locations across the estuary. The near-surface mixing developed from the combined influences of a subsurface velocity jet within the pycnocline and lateral flows moving in opposing directions, similar to the near-surface TKE findings. These results suggested that not only does vertical mixing develop from bottom-generated turbulence, but it can also arise from vertical gradients in velocity near-surface. This result poses the need to reexamine well-accepted theory behind estuarine circulation modeling. The relative influence of mixing asymmetries on the subtidal momentum balance was compared to that from lateral advection. During neap conditions, the flow induced by mixing asymmetry augmented the gravitational circulation at depth in the channel, similar to one-dimensional theory. During spring conditions, the residual flow was laterally sheared with landward flow over the south shoal and seaward flow throughout most of the channel and provided a distribution that compared favorably with cross-estuary section analytical model results. An examination of depth-averaged subtidal momentum balance terms contrasted the relative size between laterally advection and Coriolis during weakly stratified conditions over the channel slope. In the channel, asymmetric mixing competed with lateral advection. During stratified conditions, discrepancies amongst lateral advection and other terms suggested the other advection terms likely influenced the balance. Lastly, a non-dimensional number analysis provided evidence that lateral advection, Coriolis acceleration, and mixing asymmetries are, indeed, influential in the subtidal dynamics.

–  –  –

Understanding the spatiotemporal variability of turbulent mixing in coastal environments is the focus of several studies because of its direct influence on the transport of nutrients, sediments, and pollutants. The transport of these scalars can be described in numerical models, however vertical mixing is often parameterized with turbulence closures that need improvement in estuarine environments because of their complexity. A better understanding of turbulent mixing will indeed lead to better implementations of closures in models. Turbulent kinetic energy (TKE) dissipation, ε, is a value often used to estimate vertical mixing and can be measured readily. Given that stratification can suppress turbulent energy, the density structure of a water column is an important factor in the TKE balance. The degree of stratification can vary widely among estuaries, but for this investigation, the focus will be on a partially mixed water column. Estuaries with this stratification scheme are characterized by moderate to strong tidal forcing, weak to moderate river discharge and feature a weak pycnocline (Valle-Levinson, 2010). Simpson (1990) has found that stratification can be periodic in nature, resulting in a stratified water column during ebb and the destruction of stratification during flood. This tidal straining phenomenon arises from interactions between baroclinic (residual) and tidal flows with the water column structure. During flood, when dense ocean water is inundating an estuary, residual flow enhances the tidal flow, resulting in large current velocities and the breakdown of stratification.

Alternatively during ebb, currents flow out of the estuary and residual flow enhances stratification, weakens flows and suppresses turbulence. Less dense water is layered atop denser ocean water and differential advection in salinity creates stratification characterized by horizontal isopycnals (Nepf and Geyer, 1996).

Rippeth et al. (2001), Stacey et al. (1999), and Peters (1997) have proposed that the vertical structure of turbulence in a coastal plain estuary is dominated by bottomgenerated turbulence. Rippeth et al. (2001) investigated the fortnightly variability of the vertical structure of ε and found that during neap tide conditions, maximum values were confined to the near bottom region by stratification and peaked during the largest tidal velocities. During spring tide conditions, large values of ε were observed to extend the water column during the well mixed flood phases and were again confined to the lower half of the water column during the more stratified ebb phases. Stacey et al. (1999) and Peters (1997) investigated the vertical structure of vertical eddy viscosity, Az, and found that it was confined to near-bottom during stratified conditions. The measurements of Rippeth et al. (2001), Stacey et al. (1999), and Peters (1997) were all obtained at one point in the channel of a coastal plain estuary. Presently, no studies examine the structure of ε and Az across an estuary. Geyer et al. (2000) investigated the dynamics of a partially mixed estuary and found that estuarine circulation was found to only depend on the magnitude of bottom turbulence. This finding lead to the proposition that estuarine circulation could be modeled without knowledge of the vertical eddy viscosity.

The research in this manuscript aims to address any variability from accepted theory in context of the findings of Geyer et al. (2000) and examine the implication of it.

The subtidal momentum balance was determined by Pritchard (1956) to include baroclinic pressure gradient and friction, resulting in a vertically sheared two layer flow.

Dense ocean water intrudes into the estuary in the lower layer, while less dense water exits the estuary in the upper layer. Recent studies have proposed that other terms in the subtidal momentum balance are significant and should be included. Lerczak and Geyer (2004) showed the influence of laterally induced along-channel advection was actually larger than the along-channel pressure gradient with a numerical model experiment. Likewise, Scully et al. (2009) showed that advective terms worked in concert with baroclinic pressure gradient to enhance the residual exchange flow. It has also been shown by Jay (1991) that tidal asymmetries in vertical mixing developing from ebb/flood inequalities can enhance the gravitational exchange flow and also need to be considered when modeling the residual estuarine exchange flow.

The objectives of this dissertation are to determine the vertical structure of ε and Az and discuss the forcing mechanisms behind the observed variability. It also addresses the implications of these results on popular theory for estuarine circulation.



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