<%BANNER%>

Modeling of Wind-Driven Interaction at the Estuary/Ocean Transition

Permanent Link: http://ufdc.ufl.edu/UFE0042048/00001

Material Information

Title: Modeling of Wind-Driven Interaction at the Estuary/Ocean Transition
Physical Description: 1 online resource (164 p.)
Language: english
Creator: Lee, Jung
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: bathymetry, estuary, modeling, ocean, plume, roms, wind
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Coastal and Oceanographic Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Earlier studies on estuarine dynamics mostly have been focused on the impact of river discharge and tidal oscillation. Some studies have been done by accumulating field data from several estuaries, and others by using numerical simulation. Several prior studies suggest that the bathymetry could affect the estuarine dynamics, and its? effect could be characterized by the ratio between friction and the Earth?s rotation effect, and the width of the estuary and internal Rossby radius. However, it still remains unclear that the importance of shape of bathymetry in the estuary and shelf bathymetry on the estuarine circulations. In addition, most studies separately focused on the in-estuary and out-estuary hydrodynamics. However, the region between an estuary and open ocean (estuary mouth) could have different flow characteristics with in-estuary and out-estuary having both boundary effects. The estuary/ocean transition region often meets wide open ocean and a narrow estuary channel, and this specific geometry could have an affect on the flow characteristics differing in-estuary flow characters. For this reason, this study focuses on the reciprocal influence that an estuary and its adjacent shelf exert under the influence of wind forcing especially depending on the channel and shelf bathymetry. To perform this specific study, 21 types of channel are ideally designed under four directional winds effects, and the Regional Ocean Modeling System (ROMS) is used. Distinct simulations are performed to compare wind-driven patterns resulting over each bathymetry under weak wind stress. The effects of density gradients are added to the patterns that arise for wind-driven flow over bathymetry. Finally, the effects of tidal forcing are assessed. The model results show that (1) vertically sheared flow pattern changes into laterally sheared pattern as channel width increased and depth decreased, (2) the channel width does not effect much on salinity intrusion but the channel depth does, (3) the extended channel toward offshore strengthens stratification, (4) plume can be located more offshore with a flat shelf than a sloping shelf, and (5) plume expansion can be restricted by flow curtain effects near the edge of a channel. It is concluded that channel shape in the estuary and existence of the underneath channel at the offshore plays a crucial role in flow and plume dynamics at an estuary/ocean transition.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jung Lee.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Valle-Levinson, Arnoldo.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042048:00001

Permanent Link: http://ufdc.ufl.edu/UFE0042048/00001

Material Information

Title: Modeling of Wind-Driven Interaction at the Estuary/Ocean Transition
Physical Description: 1 online resource (164 p.)
Language: english
Creator: Lee, Jung
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: bathymetry, estuary, modeling, ocean, plume, roms, wind
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Coastal and Oceanographic Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Earlier studies on estuarine dynamics mostly have been focused on the impact of river discharge and tidal oscillation. Some studies have been done by accumulating field data from several estuaries, and others by using numerical simulation. Several prior studies suggest that the bathymetry could affect the estuarine dynamics, and its? effect could be characterized by the ratio between friction and the Earth?s rotation effect, and the width of the estuary and internal Rossby radius. However, it still remains unclear that the importance of shape of bathymetry in the estuary and shelf bathymetry on the estuarine circulations. In addition, most studies separately focused on the in-estuary and out-estuary hydrodynamics. However, the region between an estuary and open ocean (estuary mouth) could have different flow characteristics with in-estuary and out-estuary having both boundary effects. The estuary/ocean transition region often meets wide open ocean and a narrow estuary channel, and this specific geometry could have an affect on the flow characteristics differing in-estuary flow characters. For this reason, this study focuses on the reciprocal influence that an estuary and its adjacent shelf exert under the influence of wind forcing especially depending on the channel and shelf bathymetry. To perform this specific study, 21 types of channel are ideally designed under four directional winds effects, and the Regional Ocean Modeling System (ROMS) is used. Distinct simulations are performed to compare wind-driven patterns resulting over each bathymetry under weak wind stress. The effects of density gradients are added to the patterns that arise for wind-driven flow over bathymetry. Finally, the effects of tidal forcing are assessed. The model results show that (1) vertically sheared flow pattern changes into laterally sheared pattern as channel width increased and depth decreased, (2) the channel width does not effect much on salinity intrusion but the channel depth does, (3) the extended channel toward offshore strengthens stratification, (4) plume can be located more offshore with a flat shelf than a sloping shelf, and (5) plume expansion can be restricted by flow curtain effects near the edge of a channel. It is concluded that channel shape in the estuary and existence of the underneath channel at the offshore plays a crucial role in flow and plume dynamics at an estuary/ocean transition.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jung Lee.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Valle-Levinson, Arnoldo.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042048:00001


This item has the following downloads:


Full Text

PAGE 1

1 MODELING OF WIND DRIVEN INTERAACTION AT THE ESTUARY/OCEAN TRANSITION By JUNGWOO LEE 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 2010

PAGE 2

2 2010 Jungwoo Lee

PAGE 3

3 To my wife Jongsung Kim and parents

PAGE 4

4 ACKNOWLEDGMENTS I would like to appreciate to the academic advisor and supervisory committee chair, Dr. Arnoldo ValleLevinson, Pro fessor of Civil and Coastal Engineering at the University of Florida, for his unlimited guidance and financial assistance throughout my Ph.D. study I also would like to thank the other committee members, Dr. Alexandru Sheremet, Dr. Donald Slinn, and Dr. P eter N. Adams for their review of my dissertation In addition, I am greatly indebted to the Dr. Robert J. Thieke for his financial support for spring semester in 2007; without his support, I might not be able to pursue my goal for Ph.D. I am also thankful to Dr. Y. Peter Sheng for giving me an opportunity to study 3D hydrodynamic model. I am extremely grateful to my colleagues, Amy, Chloe, Berkay, Peng, Jun Lee, Kijin Park, Taeyun Kim, Sangdon So, Bilge, Ma, Andrew, Andy, Su, and all students in the coast al program for their help and friendship. A big gratitude is owed to Chulseung, Jeongsu, Junyoung, and some Korean students in our department for making life easier. Most importantly, none of this would have been possible without the love and patience of my family. My father and mother have been a constant source of love, concern, support and strength all these years. I am grateful to my sister, Jinju, and my brother, Taewoo, for their aide and support me throughout this endeavor. Finally, I would like to express my heart felt gratitude to my wife, Jongsung Kim, and parents in law.

PAGE 5

5 TABLE OF CONTENTS ACKNOWLEDGMENTS .................................................................................................. 4 page LIST OF TABLES ............................................................................................................ 7 LIST OF FIGURES .......................................................................................................... 8 ABSTRACT ................................................................................................................... 11 CHAPTER 1 INTRODUCTION AND OBJECTIVE ....................................................................... 13 1.1 Introduction ....................................................................................................... 13 1.2 Objectives and Organization ............................................................................. 17 2 LITERATURE REVIEW .......................................................................................... 19 2.1 Estuarine Dynamics .......................................................................................... 19 2.2 Fresh Water Plume Dynamics .......................................................................... 25 3 C ONSERVATION LAWS OF FLUID MOTION AND BOUNDARY CONDITIONS .. 38 3.1 Mass Conservation in Three Dimensions (3D) ................................................. 38 3.2 Momentum Equat ion in Three Dimensions (3D) ............................................... 40 3.3 Navier Stokes Equations for a Newtonian Fluid ................................................ 43 3.4 Reynolds Averaged Navier Stokes Equations (RANS) ..................................... 44 4 INTRODUCTION OF OCEAN CIRCULATION MODELS ....................................... 49 4.1 General Features of Several Coastal Ocean Models ........................................ 49 4.2 Governing Equations of Regional Ocean Model System (ROMS) .................... 53 4.3 Vertical Boundary Conditions of ROMS ............................................................ 55 4.4 Open Boundary Conditions ............................................................................... 56 4.4.1 Free Surface Open Boundary Conditions ................................................ 56 4.4.2 Vertically Integrated Velocity Boundary Conditions ................................. 58 5 MODEL VERIFICATION WITH ANALYTICAL SOLUTIONS .................................. 60 5.1 WindInduced Setup ......................................................................................... 60 5.2 Seiche Oscillation Test ..................................................................................... 61 5.3 Tidal Propagation .............................................................................................. 62 5.4 Baroclinic Fl ow .................................................................................................. 65 5.5 WindDriven Flow in an Elongated, Rotating Basin .......................................... 66 5.6 Residual Tidal Circulation ................................................................................. 67

PAGE 6

6 6 THE EFFECT OF BATHYMETRY ON ESTUARY/OCEAN EXCHANGE ............... 80 6.1 Model Grids and Description ............................................................................. 80 6.2 S alinity and Flow Patterns at the Estuary/Ocean Transition Depending on Bathymetries ........................................................................................................ 82 6.3 Salinity and F low P atterns D epending on E stuary W idths ................................ 86 6.4 Salinity and Flow Patterns Depending on Estuary Depths ................................ 89 6.5 NonDimensionalized Number and Momentum Analysis .................................. 91 6. 6 Plume D ynamics ............................................................................................... 93 6. 7 The Effect of Winds ........................................................................................... 96 7 SUMMARY AND CONCLUSIONS ........................................................................ 150 LIST OF REFERENCES ............................................................................................. 156 BIOGRAPHICAL SKETCH .......................................................................................... 164

PAGE 7

7 LIST OF TABLES Table page 2 1 Summary of studies in the estuarine dynamics .................................................. 29 2 2 Summary of studies in the fresh water plume dynamics ..................................... 35 5 1 Summary of the model verification tests ............................................................. 6 8 5 2 Comparison between analytical and numerical solutions (ROMS) ..................... 68 5 3 List of op en boundary conditions for numerical tests .......................................... 68 6 1 Description of JW0000000.h file ..................................................................... 100 6 2 Density gradients: along channel (d( )/km), cross channel (d( )/km), and vertical (d( )/m). ............................................................................................... 101 6 3 Ekman, internal Rossby radius, and Kelvin number depending on the cases. 101 6 4 Plume and salinity intrusion distance from the estuary mouth. ........................ 102 6 5 Plume distance and salinity intrusion from the estuary mouth for each case. 103

PAGE 8

8 LIST OF FIGURES Figure page 3 1 F luid element for conservation laws ................................................................... 47 3 2 Mass flows in and out of a flui d element ............................................................. 47 3 3 Surface forces in the x direction. ........................................................................ 48 5 1 Schematic diagram of windinduced setup problem ........................................... 69 5 2 ROMS results for wind induced setup at three different locations ...................... 69 5 3 ROMS results of Seiche test .............................................................................. 70 5 4 Schematic diagram of a rectangular basin for the tidal propagation test ............ 70 5 5 Case 1: Free surface Chapman and M2 Flather condition with ANA_FSOBC and ANA_M2OBC. Line: Analytical Solution Circle: Numerical Solution ........... 71 5 6 Case 2: Free surface Clamped and M2 Flather condition with ANA_FSOBC and ANA_M2OBC. Line: Analytical Solution Circle: Numerical So lution ........... 72 5 7 Case 3: Free surface Clamped and M2 Reduced with ANA_FSOBC. Line: Analytical Solution Circle: Numerical Solution ................................................... 73 5 8 Case 4: Free surface Clamped and M2 Reduced with ANA_FSOBC and FSOBC_REDUCED. Line: Analytical Solution Circle: Numerical Solution ........ 74 5 9 Case 5: Free surface Chapman and M2 Reduced wi th ANA_FSOBC and FSOBC_REDUCED. Line: Analytical Solution Circle: Numerical Solution ........ 75 5 10 Case 6: Free surface Chapman and M2 Reduced with ANA_FSOBC and FSOBC_REDUCED. Line: Analytical Sol ution, Circle: Numerical Solution ........ 76 5 11 Left panel: Lower grid has higher density and there is no horizontal density gradient. ............................................................................................................. 77 5 12 Left Panel: Initial salinity condition for baroclinic flow test. Right Panel: Salinity distribution and velocity vector after 9.96 day simulation. ...................... 77 5 13 3D view of the coordinate s ystem for model domain. Figure source: Winant (2004). ................................................................................................................ 78 5 14 Left panel shows Winants (2004) result at the middle of the basin, and right panel shows ROMS result ................................................................................ 78

PAGE 9

9 5 15 Tidal residual velocities at different axial positions in the nonrotating (f=0) basin. .................................................................................................................. 79 6 1 Model domains and bathymetries. .................................................................... 104 6 2 Tidally averaged s alinity distribution pattern at the estuary mouth with different channel and shelf types. ..................................................................... 105 6 3 Tidally averaged along channel velocities (contour), across channel and vertical velocities (vectors) at the estuary mouth. ............................................ 106 6 4 (a) jw0110000.h. Along channel salinity distribution and velocity vectors (u and w ) for three sections: north, center, and south. .......................................... 107 6 5 Vertical salinity gradients in three cross sectional locations depending on the channel shape ................................................................................................. 113 6 6 Vertical along channel velocity gradients in three cross sectional locations depending on the channel shape. ..................................................................... 113 6 7 Width dependent tidally averaged salinity distribution pattern at the estuary mouth .............................................................................................................. 114 6 8 Width dependent residual along channel velocities (contour), across channel and vertical velocities (vectors) at the estuary mouth. ...................................... 115 6 9 (a) jw0110200.h (1 km). Width dependent along channel salinity distribution and velocity vectors (u and w) for three sections: north, center, and south. ..... 116 6 10 Vertical salinity gradients in three cross sectional locations depending on channel width. ................................................................................................... 120 6 11 Vertical along channel velocity gradients in three cross sect ional locations depending on channel width. ............................................................................ 120 6 12 Depth dependent tidally averaged salinity distribution pattern at the estuary mouth .............................................................................................................. 121 6 13 Depth dependent residual along channel velocities (contour), across channel and vertical velocities (vectors) at the estuary mouth. ...................................... 122 6 14 (a) jw0110700.h (25m). Depth dependent along channel salinity distribution and velocity vectors (u and w) for three sections: north, center, and south. ..... 123 6 15 Mean flow patterns at the lower Chesapeake Bay. ValleLevinson et al. (2007). .............................................................................................................. 127 6 16 (a) v ertically averaged vertical eddy viscosity (Av) (b) local Ekman number (Ek) at the estuary mouth (JW0110700.h). ....................................................... 128

PAGE 10

10 6 17 Spatial variability of Ekman number in the domain for JW0110200.h ............. 129 6 18 Cross sectional variability of Internal Rossby Radius at the estuary mouth for (a) JW0110 6 0 0.h and (b) JW0110 2 00.h. ...................................................... 130 6 19 Residual velocities depending on Kelvin and Ekman number at the estuary mouth: (a) moderate slope and (b) steep slop (ValleLevinson, 2008). ............ 131 6 20 Vertical profiles of the tidally averaged absolute value of along channel momentum terms at the center and shoals for a shallow (a, jw0110600.h) and deep (b, jw0111000.h) estuary. ................................................................ 132 6 21 Cross sectionally averaged momentum terms for different channel depth ....... 133 6 22 3D salinity distribution for different channel shapes .......................................... 134 6 23 Salinity iso surface of 20, 25, 30, 34 psu Right panels are the plain views. .... 135 6 24 3D depth dependent salinity dis tribution and iso surface ................................. 137 6 25 3D width dependent salinity distribution and isosurf ac e .................................. 139 6 26 Cross shelf salinity and velocity vectors (left panel) and along shelf velocity (right panel) at three different positions for jw0111600.h ................................ 141 6 27 Plume distance from the estuary mouth. 'dx' and 'dy' are the plume wi dths in x and y direction respectively. ........................................................................... 142 6 28 Given total wind stress of 0.01 Pa on the domain. In this case, south easterly wind blows over the domain, and it has magnitude of 0.00707 Pa i n both u and v components. ........................................................................................... 142 6 29 Salinity iso surface of 20, 25, 30, and 34 psu depending on wind direction: (a 1) upwelling, (a2) downwelling, (a3) off shore, and (a4) onshore winds. 143 6 30 Plume width in x direction depending on wind direction for jw0110600.h ...... 149 6 31 Plume width in y direction depending on wind direction for jw0110600.h ...... 149 6 32 Salinity intrusion from the estuary mouth depending on wind direction for jw0110600.h ................................................................................................... 149

PAGE 11

11 Abstract of Dissert ation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy MODE LING OF WIND DRIVEN INTERACTION AT THE ESTUARY/OCEAN TRANSITION By Jungwoo Lee Augus t 2010 Chair: Arnoldo ValleLevinson Major: Coastal and Oceanographic Engineering Earlier studies on estuarine dynamics mostly have been focused on the impact of river discharge and tidal oscillation. Some studies have been done by accumulating field dat a from several estuaries, and others by using numerical simulation. Several prior studies suggest that the bathymetry could affect the estuarine dynamics, and it s effect could be characterized by the ratio between friction and the Earth s rotation effect, and the width of the estuary and internal Rossby radius. However, it still remains unclear that the importance of shape of bathymetry in the estuary and shelf bathymetry on the estuarine circulations. In addition, most studies separately focused on the inestuary and out estuary hydrodynamics However, the region between an estuary and open ocean (estuary mouth) could have different flow characteristics with inestuary and out estuary having both boundary effects. The estuary/ocean transition region often meets wide open ocean and a narrow estuary channel, and this specific geometry could have an affect on the flow characteristics differing in estuary flow characters. For this reason, t his study focuses on the reciprocal influence that an estuary and its adjacent shelf exert under the influence of wind forcing especially depending on the channel and shelf bathymetry To perform this specific study, 21 types of channel are ideally designed

PAGE 12

12 under four directional winds effects, and the Regional Ocean Modeling System (ROMS) is used. Distinct simulations are performed to compare winddriven patterns resulting over each bathymetry under weak wind stress The effects of density gradients are added to the patterns that arise for winddriven flow over bathymetry. Fi nally, the effects of tidal forcing are assessed. The model results show that (1) vertically sheared flow pattern changes into laterally sheared pattern as channel width increased and depth decreased, (2) the channel width does not effect much on salinity intrusion but the channel depth does, (3) the extended channel toward offshore strengthens stratification, (4) plume can be located more offshore with a flat shelf than a sloping shelf, and (5) plume expansion can be restricted by flow curtain effects near the edge of a channel It is concluded that channel shape in the estuary and existence of the underneath channel at the offshore plays a crucial role in flow and plume dynamics at an estuary/ocean transition.

PAGE 13

13 CHAPTER 1 INTRODUCTION AND OBJECTIVE 1.1 Introduction Oceans are connected to the atmosphere at the air sea interface and to the land through rivers and estuaries ( Mellor, 1996) which are joined to continental shelves O ne of the relevant areas that link s fresh water and salt water is an estuary. Historica lly, a lower tidal reach of a river was defined as an estuary. Simply, an estuary is any area where salt water and fresh water interact (Dyer, 1973). However, the most rigid definition was given by Pritchard (1952), and it has been the most common definiti on, which states that an estuary is a semi enclosed body of water having a free connection with the open ocean and within which sea water is measurable diluted with fresh water derived from land drainage. Based on this definition, estuaries can be sub cl assified according to their origin and their stratification. From their origin, there are four major types of estuaries (Pritchard, 1967; Pinet, 2003; Discovery of Estuarine Environments, 2001): (1) drowned river valleys (e.g., Chesapeake Bay, USA; Narragansett Bay, USA; Delaware Bay, USA; Thames River, England; Ems River, Germany; Seine River, France; Si Kiang River, Hong Kong), (2) fjord (e.g., Norway; Alaska; Labrador), (3) bar built estuary (e.g., Mississippi; Amazon; Nile) and (4) tectonic estuary (e.g ., San Francisco Bay). In addition, we can classify estuaries into three types according to their stratification (Pinet, 2003): (1) salt wedge estuary (e.g., Mississippi River; Columbia river, Hudson River), (2) partially mixed estuary (e.g., Puget Sound; San Francisco Bay) and (3) well mixed estuary (e.g., Delaware Bay). Understanding estuarine dynamics is important because estuaries are valuable to the environment and to society. E stuaries provide major natural resources and

PAGE 14

14 economic benefits: (1) each es tuary can make up an individual ecosystem, (2) estuaries provide a safe shelter for young fish and shellfish avoiding predators, (3) estuaries can filter small amount of pollutant s and runoff, (4) marshes and mangroves in estuaries provide home for birds, and (5) estuaries support commercial and recreational fisheries as well as attract many tourists often being the center of coastal community (Hum phreys et al., 1993). By studying estuarine dynamics, we can better understand general or specific characteris tics of estuaries and protect the most valuable ecosystem in the coastal area. With special boundary conditions such as freshwater input to the system through river and the oceanic boundary providing saline and oscillatory hydrodynamic forcing to the syst em, understanding dynamics in an estuary is complex and difficult to understand ( O Donnell, 2010 ). Even more difficulty arises with the complicated shape of the coastal boundary and the irregular bathymetry of estuaries. There are three major sources, whic h produce motion and mixing in an estuary: freshwater inflow, tidal oscillation and winds (Pritchard, 1967). The primary role of freshwater inflows to an estuary is diluting sea water to a brackish condition. Tidal energy generates mixing in an estuary and serves as a force for resuspending and transporting sediments. When wind blows over water, it exerts a shear stress on the water surface. Although the wind shear stress is usually small, its effect, when integrated over a large body of water, can be catas trophic (Dean and Dalrymple, 1991). Several studies have investigated the estuarine outflow plume dynamics with the majority of studies focus ing on Earth s rotation effects (e.g., Kasai et al. 2000; Winant 2004; ValleLevinson et al. 2003). Some studies hav e focused on estuar ies where

PAGE 15

15 Earth s rotation effects are important. To assess Earth s rotation effect s on different estuar ies Kasai et al. (2000) focused on its competition with viscous effects, which can be described in terms of the Ekman number Ek ( 2/[]vEkAfH where vA is the vertical eddy viscosity, and H is water depth) T hey found that Earth s rotation effects can be negligible in an estuary with high Ek (>1) where net inflow in the midchannel reach es the waters surface and outflow develops on both shoals. However, in their study, only channel depth was considered to explain flow patterns in an estuary, and the study does not explain the asymmetric nature of exchange flows Th is lack of asymmetry in their results was attributed to the shape of the initial sea level slop e, even though they included the Earth s rotation effects. ValleLevinson et al. (2003, 2007) and ValleLevinson (2008) focused on the basin s width effects int roducing Kelvin number Ke ( 1/ KeBR where B is channel width, and 1R is the internal Rossby Radius, which is given by ( '/ ghf ) ), which compares the basin s width t o internal Rossby radius. They successfully described asymmetric flow pattern due to the Coriolis effect, and summarized flow characteristics depending on an estuary s geometric ratio, i.e. basin s width versus depth. However, all of these studies used constant vertical eddy viscosity and reduced gravity to get the specific value of Ekman number and Kelvin number respectively. It is inadequate to see the sole estuary geometric ratio effects when a specific estuary has identical open boundary conditions suc h as tidal and river discharge effects. Thus, it is essential to explore this problem with a model that calculates frictional terms by itself and explore the channel s aspect ratio effect on flow patterns.

PAGE 16

16 Freshwater plume dynamics near the estuary mouth have been well documented in numerous studies (e.g., Chao and Boicourt 1986; Chao 1988 a; Chapman and Lentz 1994; Csanady 1984; Yankovsky and Chapman 1997); mostly focused on plume patterns depending on the s h elf slope. Chao (1988 a) studied sloping bottom (at the shelf) effects on the fresh water plume dynamics, and classified estuarine plumes in four types depending on plume shapes: supercritical subcritical, diffusive supercritical, and diffusivesubcritical. Chapman and Lentz (1994) and Yankovsky and C hapman (1997) also used sloping shelf to determine the plume characteristics. All of these studies have a rectangular channel or use evenly distributed fresh water inflow as the river source H owever, there is a lack of knowledge on estuarine and freshwat er plume dynamics when considering spatial variability in the freshwater source at the estuary mouth, also when we explor e how this variability could affect the entire plume system on the shelf. To fill this gap, the freshwater inflow should be located wel l upstream from the estuary/ocean transition, and it should be explor ed for di fferent channel shapes. Wind effects on estuarine dynamics have been studied in an estuary (e.g., Scully et al. 2005) and a shelf (e.g., Chao 1988 b). Scully et al. (2005) found that the along channel wind plays a larger role in straining the along channel density gradient in York River Estuary; downestuary winds enhance the along channel density gradient, and increase vertical stratification, in contrast to previous studies (Si mpson et al. 1990, 1991; Sharples et al. 1994). These studies have been conducted in and out of an estuary separately. H owever, they should be studied as a linked system where t he shape of the transition zone is influential.

PAGE 17

17 Even though a number of studies have successfully proposed dominant dynamics in an estuary, there is clearly a lack of research that allows understanding of the effect of bathymetry and offshore channel influence under windy condition s. Naturally a channel in an estuary extends toward a shelf and could influence the dynamics inside and out side the estuary system. In addition, all previous studies have excluded, for the most part, tidal effects and assum e steady state H owever, tidal forcing should be included because it c an generate n onlinear effects on t h e dynamics. In numerical stud ies practically all studies have used relatively coarse grids, > 1 km per side, which might make it diff icult to resolve internal waves thus establishing the need for finer grids. The hydrodynamics of estu arine systems cannot stand alone without concern for offshore tidal and bathymetry effects, which should also be included in the study of estuarine and plume dynamics. For this reason, bathymetry effects on winddriven exchange hydrodynamics at an estuary/ ocean transition are studied here with three bathymetry types and four wind directions. Results show that wind directional effects on an estuarine dynamics and freshwater plume depend on channel and a shelf bathymetry. However, the effects of the magnitude of wind stress, river discharge, and along channel slope are still open to study. 1.2 Objectives and Organization The goal of this study is to understand spatial distributions of flow patterns at estuar y/ocean transitions The major objective of this rese arch is to understand the effects of bathymetry and wind directions on the dynamics of estuaries and freshwater plumes. A h ydrodynamic Model, the Regional Ocean Modeling System (ROMS), was applied to different configurations in order to better understand t he flow and freshwater plume patterns associated with estuary/ocean exchange.

PAGE 18

18 The primary tasks performed to achieve this objective are to: compare ROMS results to analytical solutions, and understand advantages and disadvantages of the model, apply ROMS to idealized estuaries, which have three different types of bathymetry: (1) channel shape dependence (2) channel width dependence (3) channel depth dependence; elucidate tidally averaged along channel salinity and flow patterns depending on the three bat hymetry types mentioned above; describe tidally averaged across channel salinity and flow patterns at the estuary mouth depending on the three bathymetry types; establish the effect s of bathymetry on plume dynamics at the estuary/ocean transition; apply wi nds, freshwater inflows and tides, and determine the effect of each term on the exchange hydrodynamics ; and determine the estuary circulation response to wind direction and stress. This dissertation is organized in seven chapters to achieve the goals above. The following chapter (Chapter 2) reviews previous investigations related to estuarine and freshwater plume dynamics. In Chapter 3, the continuity, momentum, Navier Stokes, and Reynolds averaged Navier Stokes equations are derived for threedimensional C artesian coordinates. In Chapter 4, general features, advantages and disadvantages of several coastal ocean models such as POM, ROMS, CH3D, ELCIRC, UnTRIM, and FVCOM are presented. In Chapter 5, verification of the ROMS model comparing to analytical soluti ons, which include wind induced setup Seiche oscillation tidal propagation baroclinic flow wind driven flow in an elongated basin and residual tidal circulation tests, are conducted. Chapter 6 presents several numerical test results includ ing winds and bathymetry effects i n idealized estuaries. Conclusions are presented in Chapter 7.

PAGE 19

19 CHAPTER 2 LITERATURE REVIEW An estuary has two major geographical features: fresh water discharge and tidal forcing. It makes understanding physical phenomena in and near an estuary difficult. This complex system has been studied dividing mainly into two parts in estuary and out estuary using observations, scaling analysis, analytical models, and complex numerical models. The studies of inestuary may include defining estuary types; spatial (along and across channel), temporal, and subtidal variation of momentum and salinity; finding main source of circulation inducing force. The studies of out estuary, on the other hand, may include fresh water plume dynamics. The first part of this chapter is focused on previous studies on the estuarine dynamics which is driven by tides (e.g., Guo and ValleLevinson 2007; Chao 1990; Manoj et al. 2009; Jay and Musiak 1994; Scully and Friedrichs 2007; Blanton et al. 2002; Brown an d Davies 2010) river discharges (e.g., Horrevoets et al. 2004; Miranda et al. 2005; Liu et al. 2001) and winds (e.g., Csanady 1973; Scully et al. 2005; Winant 2004; Wong 1994) The studies of fresh water plume dynamics at the estuary/ocean transition area are summarized at the second part of this chapter. 2.1 Estuarine Dynamics There are three major methods in studying estuarine dynamics : observation, analytical model, numerical model. First, t he observation method gives direct uncontaminated results incl uding every nonlinear effect and local characteristics, while other methods such as analytical and numerical model s give contaminated results by simplifying equations, characterizing of nonlinear terms, and numerical errors. Second, the advantage of an analytical model is that it takes less time than numerical models or

PAGE 20

20 observations, and it also gives accurate results. It has been used in many studies helping to understand a physical structure of an estuarine dynamics. Third, numerical solutions have several advantages over analytical solutions and observations; observations have temporal and spatial limitations, and analytical solutions have difficulties in solving complex geometry and equations. The Chesapeake Bay is the largest estuary in the United Stat es, and many studies have been conducted in this area. About a half century ago, Pritchard (1952) found that the salinity on the right side, when looking into the estuary, was higher than on the left side due to the Coriolis effect in the Chesapeake Bay. I n addition, he found that the flow characteristics in the Chesapeake Bay had a traditional simple two way circulation: inflow from the bottom and outflow from the surface. Valle Levinson and Lwiza (1995) focused on the lateral flow pattern in the lower Chesapeake Bay under low river flow condition (October 67, 1993). The observation results show that (1) the semidiurnal tide is dominant, (2) the flow has a maximum over the channel, (3) the lateral gradients of the flow have maximum values in the sharp bathymetry change regions, (4) the net inflow occurs in the channel and the net outflow over the shoals, (5) and a lateral baroclinic counter rotating circulation converging near surface over the channel exists. The buoyant outflow plume in the Chesapeake Bay could be refereed as a wide plume, which has a large Kevin number, and the bathymetry could control the outflow plume, surface salinity field, mean flows and the volume fluxes (ValleLevinson et al., 2007). Pritchard (1956) studied the relative importance term of each in the estuarine momentum balance in the James River which is located in the Chesapeake Bay The James River estuary has a pattern of the two layer circulation likely the Chesapeake

PAGE 21

21 Bay. The results show that the longitudinal momentum budget in the James River is mainly balanced between the pressure and the eddy frictional term, and the Coriolis term is primarily balanced with the lateral pressure gradient term in the lateral direction. Scully et al. (2005) carried out field experiments in the York River Estuary, Virginia, which can be classified in a partially mixed estuary, and found that the along channel wind plays a larger role in straining the along channel density gradient; the downestuary wind enhances the along channel density gradient, and it increases the vertical stratification. It is opposite to previous studies (Simpson et al. 1990, 1991; Sharples et al. 1 994), which explain the wind open provides energy to mix away estuarine stratification. T he residual along channel circulation in the York River Estuary was seaward over the channel and landward over the shoal opposi ng to the traditional concept, inflow through the channel and outflow through shoals ( Scully a nd Friedrichs, 2007). They explained that this untraditional pattern was caus ed by lateral tidal asymmetries; t he relatively strong stratification remains in the deep channel than in the shoal, in which relatively well mixed condition exists, during end of ebb, and this retards flood in the deep channel than in the shoal. Csa nady (1973) studied the wind effect on a lake (or closed basin) using a 2D vertically integrated analytical model. He found that windforced transport was in the same direction with winds at both shoals and opposite at the deeper part of the basin; the Cor iolis effect was ignored since he concerned a narrow basin only. This result is well agreed with Winant s (2004) results, which is focused on the flow pattern in an e longated barotropic wind basin, which has a triangular, parabolic and Gaussian bathymetry with the Coriolis effec t Velocities at the midpoint of the basin in the steady

PAGE 22

22 state show that (1) the axial velocities are in the same direction with the wind direction at both shoals and opposite direction at the midchannel, (2) the lateral circulation is to the right of the wind at the surface and compensating return flow near the bottom, (3) the axial velocity distribution is similar to the results of Wong (1994) for the case without rotation if rotation is set to be small, (4) the largest lateral and vertic al velocities are located in both shoals. Wong (1994) focused on the residual lateral variability of the flow and the salinity in the lower Delaware Bay. Observation results show that the highsalinity inflow is concentrated in the deeper channel and the low sa linity outflow is located in both shoals contradicting the conventional twolayer gravitational circulation: the low salinity at the surface and the high salinity at the bottom. His analytical model, which has a balance between the pressure g radient and the vertical shear stress, results show that the outflow locates at both shoals and the inflow locates at the channel in a triangular channel. If the wind effect was applied on the triangular channel, the current flows in the direction of the wind on both shoals and opposite on the channel; this result is well agreed with Csanady s (1973) result. Kasai et al. (2000) expanded Wong s study including the Earth s rotation effect. They found that (1) tidally averaged along channel flow depended on E kman number, (2) under a large Ekman number (E k > 1) condition, in flow locates in the midchannel reaching to the surface, and outflow at both shoals, (3) under an intermediate Ekman number (Ek ~ 0.1) and low Ekman number (Ek < 0.01) inflow concentrates i n the lower layer and outflow at the surface. However, his study did not explain the asymmetric nature of exchange flows which should be existed by the Earth s rotation effect. Valle Levinson et al. (2003) found that the initial sea level slop

PAGE 23

23 should be prescribed to get the asymmetric flow; Kasai et al. ignored the initial sea level slop They found that (1) the Earth s rotation effects could not be ignored under a low friction al condition (low Ekman number) even in the relatively narrow estuary, (2) lateral flows switched to the surface flow to the right and the bottom flow to the left when the frictional effects were large (high Ekman number). Lerczak and Geyer (2004) also studied the importance of the lateral circulation in a straight channel using ROMS They found that lateral advection terms could play an important role in the tidally averaged momentum budget under a weakly stratified condition within an estuary; if we concern ed flood and ebb, lateral advection is stronger during the flood than the ebb. Valle Levinson (2008) expanded the previous study (ValleLevinson et al. 2003) using a 3D numerical model (ROMS), and studied the pattern of density induced flow accounting for a basins width, friction, and the Coriolis acceleration. The study aims to p redict whether the density induced flow would be vertically sheared or horizontally sheared as a function of the Ekman (Ek) and the Kelvin (Ke) numbers. The results show that (1) the exchange flow has a horizontally sheared pattern, which means that the in flow and the out flow is located in the channel and over shoals respectively, under high frictional conditions (Ek > 1) independently of the width of the basin (Ke), (2) under the weak friction (Ek > 0) and in the wide (Ke > 2) basin, the flow pattern is changed to horizontally sheared. Simply, a wide estuary is likely to have the horizontally sheared flow pattern, and a narrow estuary is likely to have the vertically sheared flow pattern. Li and O Donnell (2005) studied the sub tidal circulation in a semi enclosed tidal basin using depth averaged 2D shallow water equations and they found that a short channel ( 0.7 4 L where L is a channel length, and is a wave length) had inflows at

PAGE 24

24 the midchannel and outflow s at both shoals; on the other hand, a long channel ( 0.7 4 L ) had inflows at both shoals and outflow s at the midchannel. They explained this sub tidal cir culation pattern was caused by the change in tidal wa ve characteristics from a progressive wave to a standing wave. Winant (2008) also, calculated three dimensional tidal flows in a semi enclosed tidal basin using an analytical model. The results show that (1) flow patterns are different depending on the bottom frictional strength and the Coriolis effect, (2) tidally averaged inflow and outflow regions at a cross section are changed depending on the axial position of the cross section in a basin, which revive Li and O Donnell s (2005) results One of the important mechanisms for the suspended sediment and the salt transport is the internal tidal asymmetry (e.g., Speer and Aubrey 1985; Blanton and Andrade 2001; Friedrichs and Aubrey 1988; Jay and Musiak 1994). Jay and Musiak (1994) found that the distortion of the M2 tide such as M4 and M6 generated by friction and channel morphology, internal tidal asymmetry, in narrow, stratified estuaries plays an important role in sediment and salt balances. The Columbia River estuary observations shows that M4 tide is the most prominent internal over tide, currents associated with which are three to 10 times larger than currents associated with the barotropic M4 tide. The internal (baroclinic) Rossby radius of deformation (Rossby 1938) is the ratio between the phase speeds of the long internal waves to the Coriolis parameter, and it gives the concept whether the Coriolis effects separate the inflow from the outflow or not in an estuary. The internal Rossby radius has been calculated in the ocean (e.g., Emery et al.1984; Fel iks 1985) and in many estuaries; 5 ~ 6 km in the Chesapeake Bay

PAGE 25

25 (Marmorino et al. 1999; Yankoysky and Chapman 1997); 8 ~ 10 km in the St. Lawrence Estuary (Mertz et al. 1990; Tang 1980); ~ 7 km in the Connecticut River/Estuary (Garvine 1974); ~ 5 km in the Great Whale River/Estuary (Ingram 1981); ~ 6 km in the Columbia River/Estuary (Jay and Smith 1990); ~ 5 km in the Hudson River/Estuary (Bowman and Iverson 1978). Alenius et al. (2003) studied the spatial and temporal variability of the internal Rossby radius, R1, over the Gulf of Finland using hydrographic data during the years 19931999. The results show that the average of R1 is about 2 (in shallow area) ~ 4 (in deep area) km, and the largest R1 (~7 km) occurs in summer, when the stratification is at its strongest. Table 2 1 provides an overview of previous studies in estuarine dynamics. 2.2 Fresh Water Plume Dynamics One of the interesting study topics in the coastal and an estuary area is associated with fresh water discharge plumes, which have a sharp density front separating the freshwater from the shelf water. The structure of these buoyant plumes may be affected by several sources such as characteristics of river inflow, bottom topography, and local wind forcing (Yankovsky and Chapman, 1997). There are two major types of plumes (1) a surfacetrapped plume, which has a strong vertical stratification (e.g., Garvine 1974; Boicourt 1973), and (2) a surfaceto bottom plume, which has a horizontally stratified pattern at a shelf (e .g., Blanton 1981; Munchow and Garvine 1993 a, b); Yankovsky and Chapman (1997) referred to these plumes as a surface advected plume and a bottom advected plume respectively. Many studies have been focused on the dynamics of surface trapped plumes usi ng numerical models (e.g., Chao and Boicourt 1986; Garvine 1987; Weaver and Hsieh 1987; O Donnell 1990; Chao 1988; Oey and Mellor 1993; Kourafalou et al. 1996),

PAGE 26

26 and on the surfaceto bottom plumes (e.g., Csanady 1984; Wright 1989; Chapman and Lentz 1994). Chao and Boicourt (1986) tried to figure out the onset of estuarine plume on the flat bottom shelf using a 3D numerical model (Bryan Cox threedimensional primitive equation model) They found that anti cyclonic turning zone with upwelling was existed wit hin the bulge, and cyclonic surface current with downwelling occurred at the fresh water plume front. Chao (1988 a) added sloping bottom to the previous study in 1986, and classified estuarine plumes in 4 types: supercritical, subcritical, diffusivesuperc ritical, and diffusivesubcritical. Adding wind effect s on the previous study (Chao, 1988 a ) Chao (1988 b) found that (1) downwelling favorable wind could elongate the plume along the shore, (2) the Ekman drift could be considerabl y retarded by the sea le vel setup or setdown by cross shelf winds, and (3) cross shelf winds are less effective in driving the local circulation. Garvine (1987) focused on the plume response to the Earth s rotation effect. H is results with a layer model showed that plumes with sm all rotation effect s had strong boundary fronts, while plumes with strong rotation effect s had a weak boundary fronts setting up coas tal currents. Garvine (1995) also used scaling analysis to classify buoyant plume dynamics in terms of the Kelvin number ( K e) which is the ratio of the primary physical length scale to the baroclinic Rossby radius. He divided the plume characteristic s into two groups: small K e and large K e The s mall Kelvin number refers to the s mallscale discharge, which has relatively fas t flows with narrow river mouths, and the large Kelvin number refers to the l arge scale discharge, which has relatively slow flow s.

PAGE 27

27 Observations reveal that fronts are most often located either near shore or near the shelf break since the continental slope tends to act as a barrier to the crossshelf exchange (Wright, 1989) Yankovsky and Chapman (1997) suggested the way of predict ion of the plume type, a bottom advective or a surfaceadvective, looking the relation between front locations and depths. They predict that (1) a surface advected plume (or surface trapped plume as in a convention) would occur when an equilibrium depth of a plume is less than the depth of an estuary mouth, (2) an intermediate plume would occur when an equilibrium depth of a pl ume is greater than the depth of an estuary mouth, and a bottom boundary layer distance is less than a surface boundary layer distance, (3) a bottom advected plume (or surface to bottom plume as in a convention) would occur when both an equilibrium depth and a bottom boundary layer distance are greater than the depth of an estuary mouth and a surface boundary layer distance respectively. Kourafalou et al. (1996) proposed a plume classification scheme based on the bulk Richardson number. They defined coast al plume as a supercritical, which had a wide bulge of plume and a coastal current meandering, and a subcritical, which had a small bulge, when the Richardson number ( R i) is greater than 1 and less than 1 respectively. The off shore canyon effects on plume s have been studied by Weaver and Hsieh (1987) using a 3D numerical model. The results show that t he shelf circulation becomes more energetic and barotropic than without a submarine canyon when a channel extends offshore. Both two cases, however, with and without a channel at the offshore, have same two layer residual flow patterns at the mouth, the inflow from the bottom and the outflow from the surface. They also found that t he reverse estuary such as the Bass

PAGE 28

28 Strait in the south of the Australia has more potential energy, which can be converted to kinetic energy and produce a stronger continental shelf circulation, than normal estuaries. Not only channel shapes, extension of canyon, and the Coriolis effect but also the magnit ude and the direction of alo ng shelf currents are the determining factor to form a plume shape (O Donnell, 1990) Plumes spread out more offshore under low ambient currents than under high ambient currents, which have a direction of left to right to the fresh water discharge in northern hemisphere.

PAGE 29

29 Table 2 1 Summary of studies in the estuarine dynamics Source (year) Subject Method Location Instruments/Parameters/Governing equations Summary Alenius et al. (2003) Spatial and temporal v ariability of the internal Rossby radius Observation Gulf of Finland, Europe Observation period: 1993-1999 NBIS MK B SeaBird 911 Plus CTD The average of R1 is about 2 (in shallow area) ~ 4 (in deep area) km. The largest R1 (~7 km) occurs in summer, when the stratification is at its strongest. Csanady (1973) Wind effect on the lake 2D vertically integrated analyt ical model N/A Assumption: narrow basin (no Coriolis effect), barotropic motion Governing equations: U ghF x tx V ghF y ty UV xyt The w ind forced transport is in the same direction with winds at both shoals and opposite at the deeper part of the basin. Ja y & Musiak (1994) Observation of the internal tidal asymmetry Observation Columbia River estuary, USA Observation period: fall 1990, summer 1991 and spring 1992 Moored ADCP Ocean Sensors 100 CTD Towed RDI -ADCP (1.2 mHz (narrow -band profiler), bin size: 1 m, 10 pings ensemble) The distortion of the M2 tide such as M4 and M6 generated by friction and channel morphology, internal tidal asymmetry, in narrow, stratified estuaries plays an important role in sediment and salt balances. The M4 tide is the most prominent internal over tide, and currents associated with which are three to 10 times larger than currents associated with the barotropic M4 tide. Kasai et al. (2000) Along channel flow pattern depending on Ek Analytical model & O bservation Assumption: s emi -geostrophic balance (Coriolis vs. pressure gradient vs. viscous effects), Tidally averaged along channel flow s depend on Ek. Under a large Ekman number condition (Ek > 1), the inflow locates in the midchannel reaching to the surface and outflow at b oth shoals

PAGE 30

30 Table 2 1 Continued Kasai et al. (2000) Ise bay, Japan Governing equations: 2 2 2 21 1 ,v o v opu fv A xz pv fu A yz p g z Under an intermediate Ekman number (Ek ~ 0.1) and a low Ekman number (Ek < 0.01), the inflow concentrates in the lower layer and outflow at the surface. Lerczak & Geyer (2004) Importance of lateral advection in an estuary Numerical model (ROMS) N/A An elongated estuary: 500 km 1 km Parabolic bottom (maximum h = 15 m) M2 tide (a = 0.75 m) River inflow (0.25 ~ 7.0 cm/ s) f = 0 & 1*104/s Ah = ignored Av = 3.3 ~ 21.9 m2/s Quadratic bottom stress Lateral advection terms play an important role in the tidally averaged momentum budget under weakly stratified condition within an estuary; if we concerned flood and ebb, the la teral advection is stronger during the flood than the ebb. Li & O Donnell (2005) Sub -tidal circulation pattern depending on the channel length Analytical model (depth averaged 2D shallow water equation s ) N/A A s emi -enclosed narrow basin (width = 2 km, length = 30 ~ 150 km) S2 tide f = 0 Quadratic bottom law (Cd = 0.0025) Governing equations: 22 22 ()() 0d d uuuCuuv uvg txyxh vvvCvuv uvg txyyh huhv txy A short channel ( 0.7 4 L where L is a channel length, and is a wave length) has an inflow at the mid-channel and outflow at both shoals A long channel ( 0.7 4 L ) has an inflow at both shoals and outflow at the midchannel. This sub -tidal circulation pattern is caused by a change in tidal wave characteristics from a progressive wave to a standing wave. Pritchard (1952) Salinity and flow characteristics in the Chesapeake Bay Observation Chesapeake Bay, USA The salinity on the right side, when looking into the estuary, was higher than on the left due to the Coriolis effect The Chesapeake Bay has a traditional two way circulation: inflow from the bottom and outflow from the surface.

PAGE 31

31 Table 2 1 Continued Pritchard (1956) The relative important momentum terms in the James River estuary. Observation James River, USA N/A The James River estuary has a pattern of the two layer circulation likely the Chesapeake Bay. The longitudinal momentum budget in the James River is mainly balanced between the pressure and the eddy frictional term The Coriolis term is primarily balanced with the lateral pressure gradient term in the lateral direction. Scully et al. (2005) Wind -induced straining (Wind enhances stratification) Observation York River Estuary, Virginia, USA Observation period: Spring 2002 and winter 2003-2004 Bottom mounted RDI -ADCP: (1200 kHz, 1 Hz sampling interval, bin size: 0.5 m, 25 day collection) Mooring two InterOcean S4 current and conductivity sensors (6 and 3 m above bed), Three YSI -CTD The York River Estuary can be classified in a partially mixed estuary. The alongchannel wind plays a larger role in straining the alongchannel density gradient; down-estuary winds enhance the alongchannel density gradient, and it increases the vertical stratification. It is opposit e to previous studies (Simpson et al. 1990, 1991; Sharples et al. 1994), which explain the wind open provides energy to mix away estuarine stratification. Scully & Friedrichs (2007) Inflow from the shoal and outflow from the channel Observation York Ri ver estuary, Virginia, USA Observation period: the winter of 2003/2004 Four Sontek -ADVs, Sontek -ADP: (1500 kHz, bin size: 0.25 m) Bottom mounted RDI -ADCP: (1200 kHz, bin size: 0.5 m) Three YSI 6000-CTDs Two YSI 6600-CTDs The residual along-channel circula tion is seaward over the channel and landward over the shoal in the York River estuary opposi ng to the traditional concept, inflow through the channel and outflow through shoals. This untraditional pattern is caused by lateral tidal asymmetries; the relati vely strong stratification remains in the deep channel than in the shoal, in which relatively well mixed condition exists, during end of ebb, and this retards flood in the deep channel than in the shoal. Valle Levinson & Lwiza (1995) The lateral flow patt ern in the lower Chesapeake Bay under low river flow condition Observation Chesapeake Bay, USA Observation period: October 6 -7, 1993 Towed RDI -ADCP (600 kHz broad band, bin size: 0.5 m) Sea -Bird CTD The semidiurnal tide is dominant. The flow has a maximum over the channel. The lateral gradients of the flow have maximum values in sharp bathymetry change regions The net inflow occurs in the channel and the net outflow over shoals. A lateral baroclinic counter -rotating circulation converging near surface ov er the channel exists.

PAGE 32

32 Table 2 1 Continued Valle Levinson et al. (2003) Transverse flow structures depending on the Ekman number Observation & Analytical model James River Estuary and Chesapeake Bay, USA Observation period: Novemb er 1996: James River Estuary, May 12-13, 1997: Chesapeake Bay, October 5-6, 1993: Chesapeake Bay Governing equations: 2 2 2 2,v o v ogu fvg zA xxz gv fug zA yyz ,where f = 1*10 4 /s, A v = constant This study is the extension of the Kasai et al. s study in 2000, which does not explain the asymmetric nature of exchange flows. Kasai et al. (2000) ignored the initial sea level slop, and Valle Levinson et al. found it should be prescribed to get asymmetric flow. The Earth s rotation effect can not be ignored under the low fric tional condition (low Ekman number), even in the relatively narrow estuary. Lateral flows switch surface flow to the right and bottom flow to the left when the frictional effects are large (high Ekman number). Valle Levinson et al. (2007) Bathymetry, riv er discharge, wind, and tidal forcing effects on a wide plume Observation & Analytical model Chesapeake Bay, USA Observation period: September 23-26, 1996, November 12-15, 1996, and May 12-15, 1997 Towed RDI -ADCP: (600 kHz, Hz sampling interval, bin si ze: 0.5 m, averaged into 30 seconds ensembles) SeaBird SBE21 thermosalinograph: (1/10 Hz sampling interval) EMP -2000 CTD Seabird SBE25 (CTD) Governing equations: 2 2 2 2,v o v ogu fvg zA xxz gv fug zA yyz ,where f = 1*10 4 /s, A v = constant The Chesapeake Bay outflow plume can be referred as a wide plume (Ke > 1). The bathymetry can control the outflow plume, surface salinity field, mean flows and the volume fluxes. Analytical solutions which have the dynamical balance among pressure gradient, Coriolis acceleration and friction, could well support observation results. Valle Levinson (2008) Density induced flow patterns depending on the Ke and the Ek Numerical Model (ROMS) N/A T he exchange flow has a horizontally sheared pattern, which means that the inflow and out flow is located in the channel and over shoals respectively, under high frictional conditions (Ek > 1) independently of the width of the basin (Ke) U nder a weak friction (Ek -> 0) and in a wide (Ke > 2) basin, the flow pattern is changed to horizontally s heared. Simply, a wide estuary is likely to have the horizontally sheared flow pattern, and a narrow estuary is likely to have the vertically sheared flow pattern.

PAGE 33

33 Table 2 1 Continued Winant (2007) The Coriolis and frictional effects in a semi enc l osed tidal basin Analytical model N/A Governing equations: 22 22 22 22 2 21 2 1 2 0, where 2 ()2 ,, 2 ()v uu fv tkxz vf v u tkyz uvw xyz L Bwidth A T k LLength gH H T A v = constant The lateral circulation, with rotation, had a shape of clockwise and anti clockwise during flood and ebb periods respectively. Winant (2 008) The Coriolis and frictional effect s on residual tidal flow Analytical model N/A Governing equation: 22 22 22 22 2 21 2 1 2 0, where 2 ()2 ,, 2 ()vuuu u uvwfv xyzkxz vvvf v uvwu xyzkyz uvw xyz L Bwidth A T k LLength gH H T Flow patterns are different depending on the bottom frictional strength and the Coriolis effect. The tidally averaged inflow and outflow region at a cross section is changed depending on axial positions of the cross section in the basin.

PAGE 34

34 Table 2 1 Continued Winant (2004) Winds induced flow pattern in an long basin Analytical model N/A N/A A xial velo cities are in the same direction with the wind direction at both shoals and opposite direction at the mid-channel T he lateral circulation is to the right of the wind at the surface and compensating return flow near the bottom T he axial velocity distribut ion is similar to the results of Csanady (1973) and Wong (1994) for the case without rotation if rotation is set to be small T he largest lateral and vertical velocities are located in both shoals. Wong (1994) Bathymetry and wind effect on the transverse variability of flows. Observation & analytical model Delaware Bay, USA Observation period: April 2224, 1992 Neil -Brown CTD Ten CTD stations (dx = 1.8 km) across the estuary mouth Three drifters are released to see the residual surface flows. Governing equations: 2 2 2 20 0 for wind circulation,v o vgu gHAxxx u gA xx The highsalinity inflow is concentrated in the deeper channel and the low -salinity outflow is located in both shoals contradicting the conventional two-layer gravitational circulation: the low salinity at the surface and high salinity at the bottom. The analytical model, which has a balance between the pressure gradient and the vertical shear stress, results show that the outflow locates at both shoals and the inflow locates at the channel in a triangular channel. I f the wind effect was applied on the triangular channel, the current flows in the direction of the wind on both shoals and opposite on the channel ; this result is well agreed with Csanady s (1973) result. Abbreviations: N/A = not available, ROMS = Regiona l Ocean Modeling System, SPEM = The S coordinate Primitive Equation Model (the predecessor of ROMS), POM = Princeton Ocean Model, f = Coriolis acceleration, Si = fresh water inflow salinity (psu), So = sea water salinity (psu), vi = fresh water inflow velocity, i = fresh water density anomaly, Ah = horizontal diffusion coefficient, Av = vertical diffusion coefficient, B.C. = boundary condition Ke = Kelvin number, Ek = Ekman number, Ri = Richardson number, R 1 = internal Rossby radius.

PAGE 35

35 Table 2 2 Summary of studies in the fresh water plume dynamics Source (year) Subject Method Location Instruments/Parameters/Governing equations Summary Chao & Boicourt (1986) O nset of the estuarine plume Numerical model (Bryan -Cox three dimensional primitive equation model) N/A Flat bottom (h = 15 m dx = dy = 3 km ) Five vertical layers No tides f = 7.27 105/s Si = 0, So = 35 Ah = 109 m2/s Av = 1 & 5 104 m2/s Quadratic bottom friction (Cd = 0.01 & 0) All closed boundary An anti -cyclonic turning zone w ith upwelling exists within the bulge. C yclonic surface current s with downwelling occur at the fresh water plume front. Chao (1988 a) C lassification of estuarine plumes Numerical model N/A Flat & sloping bottom ( dx = 4 km, dy = 3 km, dz = 2.5m ) No tid es f = 7.27 105/s Si = 0, So = 35 Ah = 109 m2/s Av = 1 104 m2/s Quadratic bottom friction (C d = 0.01) Chao just added sloping bottom at the previous study Chao and Boicourt (1986). He classified estuarine plumes in 4 types: supercritical, subcriti cal, diffusive -supercritical, and diffusive-subcritical Chao (1988 b) W ind effect on the estuarine plume Numerical model N/A Flat & sloping bottom (dx = km, dy = km, dz = m ) No tides f = 7.27 105/s Si = 0, So = 35 Ah = 109 m2/s Av = 1 104 m2/s Q uadratic bottom friction (Cd = 0.01) Wind stress = 0.5 dyne/cm 2 Chao added wind effect s on the previous study (Chao, 1988 a ). D ownwelling-favorable winds can elongate the plume along the shore The Ekman drift can be considerably retarded by the sea level setup or setdown by cross -shelf winds C ross shelf winds are less effective in driving the local circulation. Chapman & Lentz (1994) D ynamics of a density front and the role of the density advection in the bottom boundary layer N umerical model (SPEM) N/A Sloping shelf ( slope = 1/1000) No tides f = 104/s vi = 0.2 m/s, i = -1.0 kg/m3o = 0 kg/m3 Av = 0.001 m2/s Linear bottom friction (r = 0.0005 m/s) Total simulation time: 120 days, dt = 288 s Free -slip for side walls North: wall, South: radiation, East: ? T he advection of density in the bottom boundary layer might p lay a major role in the circulation on continental shelves.

PAGE 36

36 Table 2 2 Continued Csanady (1984) Surface -to bottom plume over a uniformly sloping bottom Analytical model N/A N/A The intensity of the residual circulation is highly related to the river inflow and bottom slope. Garvine, (1987) Earth s rotation effects on surface trapped plumes A layer model N/A N/A Plumes with small rotation effect have strong boundary fronts, while plumes with strong rotation effect have weak bound ary fronts setting up coastal currents. Garvine (1995) Plume scale classification depending on the Ke Scaling analysis N/A N/A He divides the plume characteristic into two groups: small Ke and large Ke. Small Ke refers to small scale discharges which ha ve relatively fast flow s with narrow river mouths Large Ke refers to largescale discharges which have relatively slow flow s Kourafalou et al. (1996) River plume classification by Richardson number Numerical model (POM) N/A Estuary: 20 km (length) 15 km (width) dx = dy = 5 km, 11 layers No tides f = 1.0*104/s Si = 0, So = 35, Horizontal diffusion: Smagorinsky diffusion formula Turbulent closure (Mellor -Yamada 2.5) L og law R adiation B.C. They proposed a plume classification scheme based on the bulk Richardson number (Ri). Ri > 1: a s upercritical plume which has a wide bulge of plume and coastal current meandering. Ri < 1: a s ubcritical plume, which has a small bulge O Donnell (1990) Plume shapes depending on ambient currents Numerical mod el The Connecticut River, USA Radially symmetric fresh water source Plume shapes are sensitive to the magnitude and the direction of ambient currents. Plumes spread out more offshore under low ambient currents than under high ambient currents, which hav e a direction of left to right to the fresh water discharge in northern hemisphere.

PAGE 37

37 Table 2 2 Continued Oey & Mellor (1993) Plume structures in large estuaries Numerical model (POM) N/A Estuary: 39 km (length) 15 km (width) Flat b ottom shelf: 20 m (120 km 700 km) dx = dy = 3 km, dz = 2 m No tides Turbulent closure (Mellor -Yamada 2.5) Radiation B.C. & sponge layer Extension works of Chao and Boicourt (1986) and Garvine (1987) s study. Weaver & Hsieh (1987) Off -shore canyon effects on plumes Numerical model (GFDL Bryan Cox primitive equation model) Bass Strait, Australia The shelf circulation becomes more energetic and barotropic than without a submarine canyon when a channel extends offshore. Both two cases, with and without a channel at the offshore, have same two layer residual flow patterns at the mouth, inflow from the bottom and outflow from the surface. The reverse estuary has more potential energy, which can be converted to kinetic energy and produce a stronger continental shelf circulation, than normal estuaries. Wright (1989) L ocation of fronts Observation & Analytical model Labrador Shelf USA Governing equations: 0 0 0 01 11 1 1 0H o xb H oo bb H o bb H o xyp fV dz x pdzHp x p fU dzrv y pdzrv y UV Slow cross shelf migration for a near shore front and more rapid migrat ion across the outer shelf exist Fronts are most often observed either near -shore or near the shelf break since the continental slope tends to act as a barrier to the crossshelf exchange. Yankovsky & Chapman (1997) Prediction of the type of plume Nume rical model (SPEM) N/A Domain: 80 km 400 km L inearly increasing depth (slope = 1/1000 ~ 3/1000) dx = 2.5 km, dy = 1.25 km vi = 0.1 ~ 0.5 m/s, i = 2.5 ~ 0.5 kg/m3 0.04 m/s alongshelf current f = 104/s Av = 0.001 m2/s R adiation B.C. & sponge layer hb < ho: a surface advected plume. hb > ho & 0 < yb < ys: an intermediate plume. hb > ho & yb > ys: a bottom advected plume where hb: t he depth of which plume remains attached to the bottom. ho: depth at an estuary mouth yb: distance of bottom boundary layer ys: distance of surface boundary layer

PAGE 38

38 CHAPTER 3 CONSERVATION LAWS OF FLUID MOTION AND BOUNDARY CONDITIONS The gov erning equations of fluid flow represent mathematical statements of the conservation lows of physics ( Versteeg and Malalasekera, 1995) Generally, three types of conservation laws of physics are used: (1) mass conservation, (2) momentum conservation, and ( 3) energy conservation. We will derive general mass and momentum conservation equations in this chapter. 3 .1 Mass C onservation in T hree D imensions (3D) S uch a small element of fluid with sides xy and z (F igure 3 1) will be considered to derive mass conservation equations. The rate of increase of mass in a fluid element (the change of mass in unit volume in unit time) should equal to net rate of flow of mass into a fluid element (total in of mass minus total out of mass in unit volume in unit time). The rate of increase of mass in the fluid element is xyzxyz tt (3 1) Next we have to concern the net rate of flow of mass into a fluid element which is given by the product of density, velocity component normal to the face and area of the face (Figure 32). The net rate of flow of mass into a fluid element is

PAGE 39

39 11 () 22 11 + 22 11 + 22 uu inoutu xyzu xyz xx vv vyxzvyxz yy ww wzxywzx zz yuvw xyz xyz (3 2) Combine Equation (3 1) and (3 2) the rate of increase of mass in a fluid element and the net r ate of flow of mass into a fluid element together and divide by xyz then we have the final form of mass conse rvation equations for compressible fluid. 0, or 0 uvw txyz divu t (3 3) Equation (3 3) can be called the unsteady th ree dimensional mass conservation equation for a compressible fluid For an incompressible fluid, the density is constant in time and location, and Equation (3 3) becomes t 0 0 uvw xyz uvw xyz (3 4) which is called the three dimensional mass conservation equation for an incompressible fluid Normally, sea water in the shallow area such as in an estuary is concerned as an incompressible fluid, and Equation (3 4) is used for continuity equation.

PAGE 40

40 3 .2 Momentum E quation in T hree D imensions (3D) We ca n derive momentum equations from Newton s second law ( Fma ) 112233(), () ,if is constant ,introduce to make 'per unit volume' momentumPmvPmvmvmv dPdmv F dtdt dv mm dt ma DuDvDw m DtDtDt DuDvDw DtDtDt (3 5) where D Dt is a total derivative of a property which can be written as D uvw Dttxyz (3 6) Thus x y and z momentum equation can be written as x-momentum: Duuuuuu uvw ugradu Dttxyzt (3 7) y-momentum: Dvvvvvv uvw ugradv Dttxyzt (3 8) z-momentum: Dwwwwww uvw ugradw Dttxyzt (3 9) Also we can derive momentum equations from the mass conservation equation (continuity equation).

PAGE 41

41 continuity equation introducing a property (), which has t o be conserved divu t divu t divuudiv tt uvw uvw ttxyzxyz u t uvw vw xyztxyz D Dt (3 10) Equation (3 10) is a property s conservation equation. If we replace to u then it will be the x momentum equation. From the Equation (3 5) we just figured out right term of the equation. Now we have to think about left term ( F ) We distinguish two types of forces on fluid particles: surface forces pressure force viscous force body forces gravity force centrifugal force Coriolis fo rce Surface force s in x component s due to pressure and viscous are shown in Figure ( 3 3). The net stress (force per unit area) in the x direction exerting on the fluid is the sum of all the components in Figure (33).

PAGE 42

42 11 11 22 22 11 22 11 22xx xx xx xx yx yx yx yx zx zx zx zxpp pxpxyz x xyz xxxx y yxz yy z zx zz yx xx zxy p xyz xxyz (3 11) Th e n et stress in the x direction per unit volume can be obtained dividing Equation (3 11) by xyz Same way, we can get the net stress in the y and z direction per unit volume. x-direction:yx xx zxp xxyz (3 12) y-direction:xyyyzyp yxyz (3 13) z-direction:yz xz zzp zxyz (3 14) Above equations include only surface stresses. To get final form of momentum equations, we have to include body force terms and combine with Equations (3 7) ~ (3 9) then we have ,x-momentum: yx xx zx xbodyDup F Dtxxyz (3 15) ,y-momentum: xyyyzy ybodyDvp F Dtyxyz (3 16) ,z-momentum: yz xz zw zbodyDwp F Dtzxyz (3 17) Above equations are the final form s of momentum equations.

PAGE 43

43 3 .3 Navier Stokes E quations for a Newtonian F luid Navier Stokes equations for a Newtonian fluid, in which the shearing stress is linearly related to the rate of shearing strain ( dudu dydy ) can be obtained by introducing the rate of strain, 2,2,2xx yy zz xyyx zxxz uvw xyz uv xy uw zx (3 18) where is the dynamic viscosity of the fluid. Substitute Equations (3 18) into momentum equations (x momentum only) then we have ,2yx xx zx xbody xbodyDup F Dtxxyz puuvuw F xxxyyxzzx puuu xxxyyzz uv xxyx w zx ,, since last terms are too smallxbody xbodyF p divgraduF x (3 19) In the same way Navier Stokes equations can be written as

PAGE 44

44 ,x-momentum: xbodyDup divgraduF Dtx (3 20) ,y-momentum: ybody Dvp divgradvF Dty (3 21) ,z-momentum: zbodyDwp divgradwF Dtz (3 22) 3 .4 Reynolds A veraged Navier Stokes E quations (RANS) Until now, we just thought about laminar flow, but most of the flow in estuary/ocean fields is turbulent flow. In this reason, we have to change these equations to turbulent equations. Reynolds averaged Navier Stokes equations are timeaveraged equations of motion for fluid flow. First we define the mean of a flow pr operty as follows 01 ()ttdt t (3 23) These mean properties are the same properties that are the observed data from such as ADCP. If we introduce d the Coriolis term, these equations for incompressible flow can be written as 222 2221oouuuvuwupuuvuwuuuu fv txyzxxyzxyz (3 24) 222 2221oovuvvvwvpuvvvwvvvv fu txyzyxyzxyz (3 25) 222 222 1 oowuwvwwwpuwvwwwwww g txyzzxyzxyz (3 26) In the flow of high Reynolds number, the laminar diffusion terms (the last terms in t he above equations), which are much smaller than turbulent diffusion terms, can be

PAGE 45

45 negligi ble If we used eddy viscosity assum ption (Closure), Equation (3 24) can be rewrit ten as 22 22 22 21 2 1HHV o HHV o HHVuuuvuwu txyz p uuvuw fvAA A xxxyyxzzx puuu fvAAA xxyzz uvw AAA xxyzx 22 221 ignoring last termsHV opuuu fvA A xxyzz (3 27) since 2,2,2 HHV H V V uvw uuAvvAwwA xyz uv uvvuA yx uwuwwuA zx vw vwwvA zy (3 28) where HA and VA are horizontal and vertical turbulent eddy viscosities. In the same manner, y and z momentum equations can be written as 22 221HV ovuvvvwvp vv v fuA A txyzyxyzz (3 29) 22 221HV owuwvwwwp www gA A txyzzxyzz (3 30)

PAGE 46

46 If boundary layer approximation was applied to Equation (3 30) the equation can be reduced to well known hydrostatic equation p g z (3 31) Most of the ocean circulation model s use Reynold saveraged Navier Stokes equations that we derived in here.

PAGE 47

47 x z y x z y x z y x z y Figure 3 1 F luid element for conservation laws x z y 1 2 u ux x 1 2 u ux x (x,y,z ) 1 2 w wz z 1 2 w wz z 1 2 v vy y 1 2 v vy y x z y x z y 1 2 u ux x 1 2 u ux x (x,y,z ) 1 2 w wz z 1 2 w wz z 1 2 v vy y 1 2 v vy y Figure 3 2 Mass flows in and out of a fluid element

PAGE 48

48 x z y 1 2 p px x 1 2 p px x (x,y,z ) 1 2xx xxx x 1 2xx xxx x 1 2yx yxy y 1 2yx yxy y 1 2zx zxz z 1 2zx zxz z x z y x z y 1 2 p px x 1 2 p px x (x,y,z ) 1 2xx xxx x 1 2xx xxx x 1 2yx yxy y 1 2yx yxy y 1 2zx zxz z 1 2zx zxz z Figure 3 3 Surface forces i n the x direction.

PAGE 49

49 CHAPTER 4 INTRODUCTION OF OCEA N CIRCULATION MODELS 4 .1 General Feature s of Several Coastal Ocean Models Many kinds of ocean circulation models such as the Prin ce ton Ocean Model (POM), the Regional Ocean Model ing System (ROMS), the Unst ructured Tidal Residual Intertidal Mudflat Model (Un TRIM ) the EulerianLagrangian finite difference/finite volume model (ELCIRC) the Curvi linear grid Hydrodynamics in 3D (CH3D) the Finite Volume Community Ocean Model ( FVCOM ) etc. are being used for coas tal simulation and prediction. Each model has their own features, advantages and disadvantages to apply for some specific problems. Each of these models includes a free surface and predicts the 3D fields of ocean currents, temperature and salinity. The P rinceton Ocean Model (POM), which was originally developed by Alan Blumberg and George Mellor (Blumberg and Mellor 1987) is probably the most widely used of all Baroclinic coastal ocean models and has been applied to a wide range of coastal problems ( Mart in et al., 1998) This model uses staggered Arakawa C grids (Arakawa and Lamb, 1977), curvilinear orthogonal horizontal grids, and vertical staggered grids with sigma grid s ( Mellor, 2004) The POM uses the leapfrog time differencing with an Asselin tempor al filter to eliminate time splitting and mode splitting an explicit treatment of the surface waves using a smaller time step than that used for the internal mode. POM solves vertical mixing implicitly and use s the Mellor Yamada Level 2.5 turbulence sch eme to calculate vertical mixing ( Martin et al ., 1998 ; Ezer et al 2002; Mellor, 2004) The Regional Ocean Model ing System (ROMS), which has been originally developed by Dale Haidvogel s ocean modeling group at Rutgers University named S -

PAGE 50

50 Coordinate Rutgers University Model (SCRUM) is a member of threedimensional, freesurface, terrainfollowing numerical models that solve the Reynolds averaged Navier Stokes equations using the hydrostatic and Boussinesq assumptions (Haidvogel et al., 2000; Shchepetkin a nd McWilliams 2005) T h e ROMS uses time splitting scheme, which has the external mode (solve vertically integrated twodimensional momentum equations) and the internal mode (solve three dimensional momentum equations) which technique is common to many fr ee surface ocean models. Due to using mode splitting ROMS as well as POM has to follow Courant Friedrichs Lewy (CFL) computational stability condition (Courant et al., 1967) Even though the ROMS solves the same primitive equations on similar numerical gr ids, it provides users more options in many cases which gives more flexibility than the POM. In this reason, ROMS users may need numerical model simulation experience s to use those options correct ly (Ezer et al., 2002). The major features of ROMS are (a) the use of primitive equations with potential temperature, salinity, and an equation of state, (b) the use of the Arakawa C grid in horizontal (c) the use of a generalized sigma coordinate system in the vertical, called an S coordinate by Song and Hai dvogel (1994) (d) the use of a mode splitting (barotropic and baroclinic modes) (e) the use of 4th order in horizontal and vertical advection, (e) the u se of finite difference (FD) scheme in the horizontal and vertical. The Curvilinear Hydrodynamics in 3 Dimensions (CH3D) is a coastal, b aroclinic model that is being used by the Coastal Engineering Research Center (CERC) of the U.S. Army Corps of E n gineers (Johnson et al. 1991). This model was initially developed by Peter Sheng of the University of Florida. The major features of CH3D are (a) the use of a boundary fitted curvilinear grid to more accurately resolve the complex

PAGE 51

51 shoreline and geometry, (b) the use of terrain following vertical grid to accurately represent the varying bottom, (c) the use of a r obust turbulence closure model for vertical turbulent mixing, (d) the use of highly accurate advective schemes, QUICKEST and Ultimate QUICKEST ( Sheng et al. 2008) The Unstructured Tidal Residual Intertidal Mudflat Model (UnTRIM) was developed by Vincenzo Casulli (Trenton University, Italy) following its earlier, structuredgrid version, TRIM (Casulli and Cheng, 1992). UnTRIM is a semi implicit finite difference ( volume) model based on the threedimensional shallow water equations as well as on the three dimensional transport equation for salt, heat, dissolved matter, and suspended sediments (Casulli and Lang, 2004). The model does not use the mode splitting method, which separates the external mode from the internal mode, but solves them together with a t ime implicit method. However, it uses a nonconservative EulerianLagrangian method (ELM) for the advection terms in the momentum equations and the linear advectiondiffusion equations that produces nonconservation problem in mass, momentum, heat and sali nity for long term simulation (Lee, 2000). The major features of UnTRIM are (a) the use of unstructured orthogonal grid to obtain an efficient finite difference model for the threedimensional shallow water equations (Casulli, 2000), (b) it can be applied for hydrostatic or nonhydrostatic problems, (c) terms that control the numerical stability are treated implicitly, and the remaining terms explicitly, which is called semi implicit finite differences method (Casulli, 2004), (d) the Eulerian Lagrangian met hod is used to discretiz e advection, Coriolis and horizontal friction terms.

PAGE 52

52 The EulerianLagrangian F inite D ifference/ F inite Volume Model ( ELCIRC) has been developed, ins pired by the UnTRIM formulation, but it was independently coded and with expanded process representation. Like UnTRIM, ELCIRC solves the shallow water equations using a semi implicit Eulerian Lagrangian finite volume/finite difference method reliant on horizontally unstructured grids and unstreteched z coordinates (Zhang et al. 2004). T he ELCIRC uses a semi implicit scheme in the barotropic pressure gradient term in the momentum equation and the flux term in the continuity equation to achieve computational efficiency and it uses fully implicit scheme for the vertical viscosity term and the bottom boundary condition; all other terms are treated explicitly ( Zhang et al. 2004) This model does not use mode splitting method solving the normal component of the horizontal momentum equation simultaneously with the depthintegrated continuity eq uation. The ELCIRC uses the finite volume method in vertical, finite difference method in horizontal. The Finite Volume Community Ocean Model ( FVCOM ) is the unstructured grid, finite volume coastal ocean model, which uses threedimensional (3D) primitive equation (Chen and Liu, 2003). The major features of FVCOM are (a) using the Mellor and Yamada level 2.5 turbulent closure model, (b) using a sigma coordinate in vertical, and unstructured triangular grid in horizontal, (c) using finite volume method, whic h has advantages of both finitedifference method (numerical efficiency and code simplicity) and finiteelement method (grid flexibility) Even though there are many significant features which users have to know to use th ose models, Table 41 shows diffe rences among given models. More detailed

PAGE 53

53 comparison between POM and ROMS FVCOM and ROMS were studied by Ezer et al. (2002) and Huang et al. (2007) respectively 4 .2 Governing Equations of Regional Ocean Model System ( ROMS ) Three simplifying assumptions s ued for deriv ing governing equations are (1) the flow is incompressible (2) the vertical pressure distribution satisfies the hydrostatic approximation, and (3) using Boussinesq approximations. The governing dynamical equations in flux form, Cartesian hor izontal coordinates and sigma vertical coordinates take the t raditional form (Haidvogel et al 200 8 ): x momentum equation, 0()()()() ''zzzzz zz zHuuHuvHuHuH p vu fHv Hguw txys xxsHs (4 1) y momentum equation, 0()()()() ''zzzzz zz zHvuHvvHvHvH p vv fHu Hgvw txys yysHs (4 2) z momentum equation, 001 0zpg H s (4 3) continuity equation, ()()() 0zzzHuHvH txys (4 4) scalar transport terms, ()()()() ''zzzz source zHCuHCvHCHC C cwC txyssHs (4 5)

PAGE 54

54 equation of state, (,) fCp (4 6) where (,,,) uxyst (,,,) vxyst and (,,,) xyst are the components of velocity in the horizontal ( x y ) and vertical (scaled sigma coordinate, s ) directions respectively. t is the time, (,) xy is the freesurface elevation, (,) hxy is the bottom depth, and zH is the vertical stretching factor. (,) fxy is the Coriolis parameter defi ned as 2sin() where is the rotational speed of the earth and is the latitude g is the gravitational acceleration, p is the pres sure, and 0are total and reference densities, and is the molecular viscosity C is a tracer quantity (for example, salt, temperature, and suspendedsediment), and sourceC is a tracer source/sink terms. An over bar represents a time average, and a prime ( ) represents turbulent fluctuations. In the momentum equation (4 1) horizontal turbulent diffusion ( uuuv xy ) and horizontal laminar diffusion terms ( 22 22 zuu Hxy ) are neglected (for x momentum) These equations are closed by parameteriz e the Reynolds stresses and turbulent tracer fluxes as:

PAGE 55

55 M uw uwK zx (4 7) M vw vwK zy (4 8) HcwK z (4 9) where MK is the vertical eddy viscosity for momentum and HK is the vertic al eddy diffusivity for tracers. 4 .3 Vertical Boundary Conditions of ROMS The boundary conditions (momentum only) at the free surface ( ,, zxyt ) can be prescribed as follows: ,,x Mwu Kxyt z (4 10) ,,y Mwv Kxyt z (4 11) D wuv Dttxyt (4 12) where x w and y w are the wind stress in x and y directions at the free surface. The boundary conditions at the bottom ( zhxy ) can be pres cribed as follows: ,,x Mbu Kxyt z (4 13) ,,y Mbv Kxyt z (4 14) 0 wvh (4 15) where x b and y b are the bottom stress in x and y directions at the bed.

PAGE 56

56 4 4 Op en Boundary Conditions There are several combinations of open boundary conditions (OBC s ) in ROMS. D ifferent OBC s can be chosen for free surface, vertically integrated velocity (M2~ ) and full three dimensional velocity (M3~) field. 4 .4. 1 Free Surface Open Boundary Conditions There are 5 types of free surface open boundary condition options: (1) FSCHAPMAN (Chapman condition), (2) FSGRADIENT ( z ero gradient condition), (3) FSRADIATION ( r adiation condition), (4) FSNUDGING ( p assive/active nudging term ), and (5) FSCLAMPED ( clamped condition). T h e Chapman boundary condition is modified version of Flather B C. Flather B C uses fixed depth ( h ), but Chapman BC uses ( 0h ). The Chapman boundary condition considers gravity wave propagation (Mori, 2007) and can be written as 0()0 gh tx (4 16) The g radient B C is zero gradient condition at the boundary ; this condition is one of the passive open boundary conditions which allow information exit the model domain without reflection (Carter and Merrifield, 2007) 0 x (4 17) If we rewrote this equation in differential notation, it can be 11 1,, nn IjIj (4 18) The radiation boundary condition is based on the transport equation at the boundary It can be prescribed as

PAGE 57

57 0xycc txy (4 19) Clamped condition for free surface is just rigid BC to match given external condition. boundarygiven (4 20) where given should be given externally. The clamped boundary condition sometimes referred as Dirichlet BC in the classical manner. This BC is generally used only when tidal forcing is the sole forcing both at the boundary and within the model domain. The reason for this restriction is that surface waves generated by other forcing within the model domain will reflect from the boundary back into the interior when a clamped B C is used. Theses reflections can severely or catastrophically degrade the model solution in the interior of the domain. With a clamped B C, the normal b aroclinic velocity at the boundary is calculated by the model hence, data for this field at the boundary are not needed. Note that tidal simulations with a clamped B C can provide a means for calculating the tidal velocities at the boundary that are needed for using the Flather radiation B C The clamped B C for surface elevation is generally only useful for tidal forcing because it reflects outward propagating disturbances back into the interior, which can disrupt the solution. Even for tidal forcing, use of a clamped B C requires a longer time for the tidal solution to settle down to a steady tidal cycl e than when using the Flather B C. This is because of the time required to dissipate transient tidal signals generated during the spinup and reflected a t the boundary by the clamped B C.

PAGE 58

58 T he advantage of the clamped BC for forcing tides is that the normal velocity at the boundary is not needed, i.e., the BC is on the elevation and the normal velocity is calculated by the model. Because of this, the clamped BC can be used to calculate tidal velocities at the boundary, which can then be used in a more general simulation with the Flather BC. This procedure is useful since tidal velocity data from an external source tends to be less reli able than tidal elevation data. 4 .4. 2 Vertically Integrated Velocity B oundary Conditions There are 6 types of M2 momentum boundary conditions in ROMS : (1) M2FLATHER ( 2D momentum Flather condition), (2) M2GRADIENT ( 2D momentum Gradient condition), (3) M2RA DIATION ( 2D momentum Radiation condition), (4) M2REDUCED ( 2D reducedphysics), (5) M2NUDGING ( 2D passive/active nudging term ), and (6) M2CLAMPED ( 2D Clamped condition). M2 Flather boundary condition which is the extension of a radiation boundary condition, was originally proposed by Flather (1976). Radiation conditions are a popular class of passive OBCs, which are based on the propagation of a quantity through a boundary: 0 c tn (4 21) which gives 0nc v nH (4 22) Finally, integrating across the boundary gives

PAGE 59

59 ,1()ext ext nbn bg vv H (4 23) where ext means external mode, which means a user has to define those values n denotes the outward normal, and the overbar denotes the vertical average. The Flather condition can be thought of as applying an adjustment to the externally prescribed normal velocity based on the difference between modeled and externally prescribed surface elevation (Carter and Merrifield, 2007) The Flather BC is appropriate for barotropi c flows. The Flather condition imposes the value of the incoming characteristic of the shallow water equation, and hence the tidal wave can propagate cleanly through the outgoing boundary. M2Gradient boundary condition and FS Gradient condition is same as FS Gradient condition and FS radiation condition respectively M2 Reduced boundary condition is good for use i f the only surface elevation is provided as an external forcing. This option calculates M2 velocity components from pressure gradient of hydro st atic pressure. M2REDUCED option is quite similar to M2FLATHER condition. M2 Clamped boundary condition is same as FS Clamped condition. For the gravity wave celerity, FSCHAPMAN and M2FLATHER combination is good to use B oth surface elevation and tidal curr ents should be specified externally in this combination If only surface elevation was provided, M2REDUCED can be used for calculating tidal currents internally

PAGE 60

60 CHAPTER 5 MODEL VERIFICATION W ITH ANALYTICAL SOLUT IONS Before applying to real simulations, it is importan t to compare results of the model with analytical solutions to understand how the model works, what the weakness and strength of the model is and what the limitation of the model is In this chapter, results of the ROMS simulation will be c ompared to several analytical solutions. Six preliminary tests were performed, and Table 5 1 shows the summary of all simulations performed in this section for verifying ROMS model. 5 .1 WindI nduced Setup To make governing equati on simple, we can assume that (1) advection is not important, (2) diffusion is not important, (3) Coriolis term can be ignored, (4) so the only propagation term is important in the wind induced setup case. Figure 5.1 shows the schematic diagram of this problem. With these assumptions, t wo dimensional vertically integrated momentum and continuity equations can be written as 1sxbx oU gH tx (5 1) 0 U tx (5 2) where U is the vertically integrated velocity, H is the total depth, is the surface elevation, sx and bx are the surface stress (wind stress) and bottom stress in x direction respectively. If we assume that bottom stress can be ignored ( 0bx ) and steady state ( 0 U t ), equation (5 1) will b e reduced as

PAGE 61

61 sx oxgH (5 3) Now integrate equation (5 3) from 2 L x to xL then we have 22sx xL x oL x gH (5 4) We can assume that surface disturbance at the middle of the basin is zero ( 20L x ), so the final analytical solution can be written as 2sx x oL x gH (5 5) The horizontal grid used for this windinduce d setup test is 5 x 5 x 1 cell with a 10 km by 10 km in x, y direction, and 10 m in depth. A constant wind stress of 0.1 Pa (1 dyne/cm2) is applied in positive x direction. Table 5 2 shows the analytical and numeric al solutions in three locations ( left, middle, and right side of the basin), and Figure 5 2 is the plot of the numerical solution of surface elevation. The result s show that the ROMS result s are well agreed with analytical solutions. 5 .2 Seich e Oscillation Test Any natural basin, closed or open to a larger body of water, will oscillate at its natural frequency if it is excited in some fashion, such as by earthquake motion, impulsive winds, or other effects; this oscillation is called Seiche ( Dean and Dalrymple, 1991, p144) A solution of these standing waves in this basin is coscos 2 H kxt (5 6) 2 l T ngh (5 7)

PAGE 62

62 where (called the wave number)2/ kL (angular frequency)2/ T l width of t he basin, and n is the number of nodes. The grid setup is same as previous windinduced setup case for Seiche oscillation test: 5 x 5 x 1 cells with 10 km by 10 km in x, y direction, and 10 m in depth. Initial disturbance of surf ace elevation is set to 0.4 cm at the boundary of the basin. Analytical solutions and ROMS result s (numerical solution) show that the period o f wave motion equals 33.67 and 33.68 minute respectively : error of 0.03 % in period. Even though there is no additional force s such as surface and bottom friction, water surface elevation is damped by numerical damping ; theoretically, this oscillation has to exist f orever without additional force The result is shown in Figure 5 3 5 .3 Tida l Propagation Tidal simulation is one of the most important applications of coastal and estuarine hydrodynamic model s. Lynch and Gray (1978) derived the analytical solutions for tidally forced estuaries of various geometries and depths. Neglecting the advective terms, diffusion terms, bottom friction and wind surface stress, the one dimensional shallow water equations are 0 U gh tx (5 8) 0 U tx (5 9) where U represent s the vertically integrated velocity which is equal to uh in the x direction, u is the vertically averaged velocity, h is the mean water depth, and is the water surface elevation. A ssuming a closed boundary at xl and an open boundary at

PAGE 63

63 0 x the boundary conditions and initial conditions associated with these equations are: Boundary conditions: 0 ) ( t l U (5 10) 0(0,)sin tat (5 11) Initial conditions: 0(,0) x (5 12) (,0)0 Ux (5 13) where l is the length of an estuary, 0 is the still water level elevation, and a and are the amplitude and frequency of the forcing tide at the open boundary respectively. With th is information, analytical solutions of the onedimensional wave equations are (Liu, 1988) : 0 22 0cos() 2 (,) sin sinsin cos ()nn n naklx a xt t kxt kl lckk (5 14) 22 0sin() 2 (,) cos coscos cos ()nn n nacklx a Uxt t kxt kl lkk (5 15) where

PAGE 64

64 222kc (5 16) 222 nnkc (5 17) 2 k L (5 18) (21) 2nn k L (5 19) and w ave length ( L ) can be calculated from L cwherecgh T To compare the numerical solution with a linear analytical solution, a rectangular basin shown in Figure 5 4 with constant water depth of 10 meters is considered. Assume that a periodic tide with amplitude of 50 centimet ers and a period of 12.42 hrs is forced along the mouth of the basin. The still water level elevation 0 is set to be 0. The physical rectangular basin is discretized with 30 15 co mputational cells and a time step of 30 seconds is used. It is noted that in the numerical computation, extra diffusion is introduced due to the use of the implicit numerical scheme, i.e. = 1. Thus the numerical solution should correspond to the first mode of the analytical solution which corresponding to the f irst terms in the Equation (5 14) and (5 15) If = 0.5, the numerical solution should be compared to the complete Equations (5 14) and (5 15) which incl ude the higher mode solution. In this test cases the result should compared to complete Equations because ROMS only has the explicit method. Figures (5 5 ) to (5 10 ) show the comparison between analytical so lutions and numerical res ults at the three locati ons of the basin in y direction (left boundary, center, and right boundary) with each combination of

PAGE 65

65 boundary conditions shown in Table 53 ANA_M2OBC is used for Case 1 and 2, and velocity is defined as unsteady linear shallow water wave theory ( H / <<1 ) in Equation (5 20) cos() ga ukxt c (5 20) where / ck and the phase speed given by 1/2() cgH is a constant. The results show that the Case 3, which has the combination of FS_Clamped condition and M2_Reduced equation, has the best agreement with analytical solutions. 5 .4 Baroclinic Flow Unlike z level models have difficulties in simulating overflow processes and bottom boundary layer dynamics, the sigma gird (terrainfollowing grid ) has an advantage of their smooth representation of topography and their ability to simulate interactions between flows and topography ( Gerdes, 1993; Beckmann and Doscher, 1977; Winton et al., 1998). However, it has a generic numerical error when calculat ing pressure gradient terms (baroclinic flow) over steep topography (Haney, 1991; Beckmann and Haidvogel, 1993; Mellor et al., 1994, 1998). If there are no additional forces in the initially calm water body, the flow will not be exist ed. However, the flow will be generated in the sigma grid models even though ideally no flow s are expected with zero horizontal density gradient ( ,0 xy ) in the basin. The reason is that the horizontal density gradient in each layer is not equal to zero unlike horizontal density gradient in same vertical location ( Figure 5 11 ). This error may be reduced by using high order or z level interpolation schemes (McCalpin, 1994; Chu and Fan, 1997; Kliem

PAGE 66

66 and Pietrzak, 1999) or parabolic reconstruction schemes ( Shchepetkin and McWilliams, 2003). The horizontal grid used for this baroclinic flow test is 5 x 5 x 5 cell with a 10 km by 10 km in x, y direction, and vertically varying in depth ( Figure 5 12) Initial salinity is set to zero in the surface and 80 (psu) in the maximum depth. Density gradient in x, y direction is zero, but vertical density variation exists in vertical sigma layers. No additional forcing is applied in this system. The results show that the max imum axial and vertical velocities are 5.4 and 0.14 cm/s respectively ; this is generated by density gradient in vertical sigma layers 5 .5 WindDriven Flow in an Elongated, Rotating Basin Winant (2004) developed the analytical solution for 3D homogeneou s flow in an elongated and rotating basin. The winddriven circulation in closed rectangular sloping basin is treated as linear steady st ate and barotropic model on a f plane. To get an analytical solution, a rectangular closed b asin with length of 2 L and the width of 2 W on a f plane was co nsidered as shown in Figure 5 13. For ROMS simulation, L and W are given by 10 km and 5 k m respectively. The bathymetry of this basin is given by 2(,)5.038.3*(1(/5000)),50005000 hxy y y (5 21) The Coriolis acceleration is given by 7.2722 105 /s ( =30 ), and the lateral mixing is ignored. Mellor Yamada level 2.5 closure model is used for the vertical turbulent mixing of momentum while Winant (2004) used constant vertical eddy viscosity. Figure 5 14 (right panel) shows that the ROMS result, and it has a quite similar flow pattern compared to Winant s (2004) result which have positive axi al velocities at the shoal and

PAGE 67

67 negative at the middle of the basin; viewer is looking into the basin, and wind blows into the basin. The di fference could be arised by vertical eddy viscosity term, which is previously mentioned. 5 6 Residual Tidal Circulation Winant (2007) developed analytical solution for a three dimensional residual circulation driven by tides in a semi enclosed basin; Wina nt discussed two cases, with and without earth s rotation. The basin the bathymetry of which follows Equation (5 21) is 200 k m long and 1 0 km wide Coriolis acceleration for the E arth s rotation case is given by 7.2722 105 /s ( =30 ), and lateral mixi ng is ignored. Three types of frictional effects are considered: (1) low friction ( = 0.1, or AV = 0.0011), (2) medium friction ( = 0.5, or AV = 0.0267), and (3) high friction ( = 1.0, or AV = 0.1069). Quadratic bottom friction law is used for the ROMS simulation with Cd = 0.0025. T ides, which have 50 cm amplitude and 12 hour period, with clamped condition are imposed at the left tidal boundary. Without rotation ( 0 f ) the pattern of Eulerian mean velocities with three different va lues of is illustrated in Figure 5 15. For low friction case ( 0.1 ), ROMS result has a good agreement with analytical solution at each location. Inflow locates at the bottom at the mouth of the basin, and it varies as where we are looking at. However, the results of ROMS show little different with an analytical solution as frictional effect incre ases For the high frictional effect case, inflow and outflow patterns have poor agreem ent at the closed end of the basin.

PAGE 68

68 Table 5 1 Summary of the model verification tests Part Process Purpose 5.1 Wind induced setup To verify wind effect 5.2 Seiche To verify tidal oscillation 5.3 Tidal propagation To verify linear propagation 5.4 Baroclinic flow To verify baroclinic effect 5.5 Wind driven flow in an elongated, rotating basin To verify wind and Coriolis effect 5.6 Residual tidal circulation To verify tidal effect Table 5 2 Comparison between analytical and numerical solutions (ROMS) () xkm ()Analyticalcm () ROMScm Error (%) 1.0 0.408 0.41 0.49 5.0 0.0 4.16*10 5 0.0 9.0 0.408 0.41 0.49 Table 5 3 List of open boundary conditions for numerical tests Case FS M2 M3 Given Condition Case 1 Chapman Flather Gradient ANA_FSOBC & ANA_M2OBC Case 2 Clamped Flather Gradient ANA_FSOBC & ANA_M2OBC Case 3 Clamped Reduced Gradient ANA_FSOBC C ase 4 Clamped Reduced Gradient ANA_FSOBC & FSOBC_REDUCED Case 5 Chapman Reduced Gradient ANA_FSOBC & FSOBC_REDUCED Case 6 Chapman Reduced Radiation ANA_FSOBC & FSOBC_REDUCED

PAGE 69

69 sxX = 0 X = L Initial surface Modified surface by wind sxX = 0 X = L Initial surface Modified surface by wind Figure 5 1 Schematic diagram of windinduced setup problem 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Surface Elevation: Numerical Solution dayEta [cm] Left Center Right Figure 5 2 RO MS results for windinduced setup at three different locations

PAGE 70

70 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Surface Elevation: Numerical Solution dayEta [cm] Figure 5 3 ROMS results of Seiche test x y l = 60 Km b = 30 Km Closed Boundary Closed BoundaryClosed Boundary Open Boundary x y l = 60 Km b = 30 Km Closed Boundary Closed BoundaryClosed Boundary Open Boundary Figure 5 4 Schematic diagram of a rectangular basin for the tidal propagation test

PAGE 71

71 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -1 0 1 Numerical sol. vs. Analytical sol. (x = 0km) dayEta [m] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -1 0 1 Numerical sol. vs. Analytical sol. (x = 30km) dayEta [m] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -2 0 2 Numerical sol. vs. Analytical sol. (x = 60km) dayEta [m] Figure 5 5 Case 1: Free surface Chapman and M2 Flather condition with ANA_FSOBC and ANA_M2OBC. Line: Analytical Solution, Circle: Numerical Solution

PAGE 72

72 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -0.5 0 0.5 Numerical sol. vs. Analytical sol. (x = 0km) dayEta [m] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -1 0 1 Numerical sol. vs. Analytical sol. (x = 30km) dayEta [m] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -2 0 2 Numerical sol. vs. Analytical sol. (x = 60km) dayEta [m] Figure 5 6 Case 2: Free surface Clamped and M2 Flather condition with ANA_FSOBC and ANA_M2O BC. Line: Analytical Solution Circle: Numerical Solution

PAGE 73

73 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -0.5 0 0.5 Numerical sol. vs. Analytical sol. (x = 0km) dayEta [m] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -2 0 2 Numerical sol. vs. Analytical sol. (x = 30km) dayEta [m] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -2 0 2 Numerical sol. vs. Analytical sol. (x = 60km) dayEta [m] Figure 5 7 Case 3: Free surface Clamped and M2 Reduced with ANA_FSOBC. Line: Analytical Solution Circle: Numerical Solution

PAGE 74

74 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -0.5 0 0.5 Numerical sol. vs. Analytical sol. (x = 0km) dayEta [m] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -2 0 2 Numerical sol. vs. Analytical sol. (x = 30km) dayEta [m] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -2 0 2 Numerical sol. vs. Analytical sol. (x = 60km) dayEta [m] Figure 5 8 Case 4: Free sur face Clamped and M2 Reduced with ANA_FSOBC and FSOBC_REDUCED. Line: Analytical Solution Circle: Numerical Solution

PAGE 75

75 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -1 0 1 Numerical sol. vs. Analytical sol. (x = 0km) dayEta [m] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -2 0 2 Numerical sol. vs. Analytical sol. (x = 30km) dayEta [m] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -2 0 2 Numerical sol. vs. Analytical sol. (x = 60km) dayEta [m] Figure 5 9 Case 5: Free surface Chapman and M2 Reduced with ANA_FSOBC and FSOBC_REDUCED. Line: Analytical Solution C ircle: Numerical Solution

PAGE 76

76 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -1 0 1 Numerical sol. vs. Analytical sol. (x = 0km) dayEta [m] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -2 0 2 Numerical sol. vs. Analytical sol. (x = 30km) dayEta [m] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -2 0 2 Numerical sol. vs. Analytical sol. (x = 60km) dayEta [m] Figure 5 10. Case 6: Free surface Chapman and M2 Reduced with ANA_FSOBC and FSOBC_REDUCED. Line: Analytical Solution Circle: Numerical Solution

PAGE 77

77 1 3 5 7 9 1 3 5 7 9 Figure 5 11. Left panel: Lower grid has higher density and there is no horizontal density gradient. In this case no flow is expected. Right panel: Black dotted lines indicate vertical layers and red dotted lines are Isopycnal (lines of constant density). In this case, flow will be generated even though no horizontal density gradient exists. X Y Z S a l t 8 0 7 5 7 0 6 5 6 0 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 0 5 T I M E = 9 9 6 d a y Figure 5 12. Left Panel: Initial salinity condition for baroclinic flow test. Right Panel: Salinity distribution and velocity vector after 9.96 day simulation.

PAGE 78

78 Figure 5 13. 3D view of the coordinate system for model domain. Figure source: Winant (2004). u 0 3 5 0 3 0 2 5 0 2 0 1 5 0 1 0 0 5 0 0 0 5 0 1 0 1 u 0 3 5 0 3 0 2 5 0 2 0 1 5 0 1 0 0 5 0 0 0 5 0 1 0 1 Figure 5 14. Left panel shows Winan t s (2004) result at the middle of the basin, and right panel shows ROMS result The axial velocity is negative in the shaded area, which has an opposite directional flows to the wind direction. White line in the right panel indicates the line of zero value of axial velocity. Vertical velocity is 500 times exaggerated.

PAGE 79

79 Figure 5 15. Tidal r esidual velocities at different axial positions in the nonrotating (f=0) basin. The first, third, and fifth panel are the analytical solutions, and the second, fourth, and sixth panel are the numerical results. The axial velocity is negative in the shaded area.

PAGE 80

80 CHAPTER 6 THE EFFECT OF BATHYM ETRY ON ESTUARY/OCEAN EXCHANGE Several model verification problems were tested and compared to analytical solutions with ROMS (version 3.1) in Chapter 5. The main objectives of those simulations were to understand th e structure, strengths and weakness es of the model. Through previous tests, I figured out what boundary conditions and coefficients were adequate for this study. In this chapter, I will explore how bathymetr y which includes channel shapes in the estuary, maximum channel depth, estuary width, slope of the shelf, extension of the channel toward the shelf, and the offshore channel direction, affect s the hydrodynamics at the estuary/ocean transit ion, with and without wind effects. 6.1 Model Grids and Descript ion After several tests, an idealized model grid (200 km by 220 km) was chosen to study bathymetr ic effect s on estuary/ocean exchange flow s. S pecific cases have different domains. The domain i s an estuary 100 km long, which is long enough to remove transient effects of the upper river boundary, and 20 km wide, which is wide enough to examine lateral variations of the flow in the estuary; some cases have different width s. The distance between an estuary mouth and the tidal forcing boundary is 100 km to remov e noise from such boundary. The domain is divided into 400 by 440 horizontal grids (each grid has a size of 500 m by 500 m) and 20 vertical layers. The grid size should be less than the internal Rossby radius (Drijfhout, 1989) or even 1/3 of it (Lindow, 19 97) The grid size prescribed here is small enough to satisfy these criteria. Figure 6 1 shows the horizontal view of the basic model domain. Twenty one types of bathymetry were used to see the effect of bathymetry on estuary/oc ean exchange dynamics A detailed description of various model

PAGE 81

81 configurations is shown in Table 6 1 The river discharge, which has a constant 2 cm/s flow, is imposed at the western end of the estuary in each case, and the tidal oscillation boundary with 50 cm tidal amplitude and period of 12 hour is located at the eastern boundary of the domain. A clamped condition for the free surface and a reduced option for the M2 field are used at the eastern boundary. At the northern and sou thern boundary, zero gradient condition for free surface (the M2 field) and tracer is used. A f ourthorder centered advection scheme is used for the horizontal and vertical advection momentum term s. In the tracers field such as salinity, temperature and suspended solid s, a fourthorder centered horizontal and vertical advection scheme is used. The Mellor Yamada level 2.5 turbulence closure model is used as a vertical mixing scheme for momentum and tracers. Horizontal diffusion terms for momentum and tracers are ignored since horizontal diffusion terms in estuarine dynamics are relatively smaller than other terms The l ogarithmic bottom friction law is used, with a bottom roughness of 2 cm A free slip condition is used for the side walls. Coriolis accelerat ion term is set to 7.25 x 105 /s, which means the estuary is assumed to be located at 30 degree s in the northern hemisphere, for the entire domain. Initial temperature and salinity are set to 20 and 3 5 psu over the entire domain. The time step used in the model simulation is 60 seconds for the baroclinic mode (internal mode, 3D) and 6 seconds for the barotropic mode (external mode, 2D). A f orty day spinup time is applied to each simulation to remove the transient effect s of the initial condition. Quasi steady state is reached after 40 day spinup.

PAGE 82

82 6.2 Salinity and F low P atterns at the E stuary/ O cean T ransition D epending on B athymetries Tidally averaged salinity distributions after 40 day spinup at the estuary/ocean transition (the estuary mouth ) with dif ferent bathymetries are shown in Figure 6 2 to Figure 6 4 Six cases, which include different channel shapes (rectangular or triangular), shelf shapes (flat or sloping), extension of the channel toward sh elf, and channel direction at the shelf (straight or downshelf, in a Kelvinwave sense, turning or upshelf turning), are chosen to explore bathymetry effects: jw0110000.h jw0110100.h jw0110600.h jw0111100.h jw0111600.h and jw0111900.h The o nly difference among these cases is the bathymetry Other given conditions such as tidal amplitude and period at the boundary, magnitude of Coriolis acceleration and freshwater discharge rate per unit area are equal. Each case shows that the river plume t urns right due to the Coriolis effect I f the Coriolis effect is turned off, the plume will spread out radially toward the open ocean over a flat shelf. However, each case has different patterns of tidally averaged salinity and flow distribution depending on the shape of the bathymetry. Tidally averaged salinity distribution patterns at the estuary mouth are shown in Figure 6 2 Even though the estuary has the same rectangular shape, Figure 6 2 a and b, the salinity distribution pattern can be different depending on the bathymetry of the shelf. With a sloping shelf, salinity at the estuary mouth can be higher than with a flat shelf. T his can be explained from the different tidal impact s on the estuary mou th for flat and sloping shelves, even though both cases have the same remote tidal characteristics and freshwater inflow. In the case of the flat shelf ( Figure 6 2 a ) the tidal amplitude at the estuary mouth is 0.31 m, and it is s maller than 0.55 m in the case of the sloping

PAGE 83

83 shelf ( Figure 6 2 b ) This is due to tidal damping by bottom friction over the flat shelf and wave setup over the sloping shelf For this reason, a quantit atively similar salinity patt ern to Figure 6 2 a can be located upestuary in the case of the sloping shelf ( Figure 6 4 a and b ) In both cases, high and low salinity regions are located in the right and left side of the channel res pectively while looking into the estuary. The case of the sloping shelf, jw0110100.h has more vertically well mixed conditions throughout the estuary mouth than the case of the flat shelf because stronger tidal mixing occurs with sloping shelf. C omparing the salinity pattern in the case of the rectangular channel with a sloping shelf ( Figure 6 2 b) and the triangular channel with a sloping shelf ( Figure 6 2 c), the minimum salinity region is loca ted in the left upper corner of the channel due to Coriolis effect in the rectangular channel. However, the lowest salinity at the estuary entrance is located ~7 km right from the left boundary in the triangular channel case T hese two cases have similar tidal amplitude at the estuary mouth. These distributions result in vertically stratified salinity pattern to the left of the channel and in lateral variations of salinity on the right of the channel. On the other hand, the rectangular channel displays lat erally varying salinity patterns in the entire cross section. If the channel i s extended offshore ( Figure 6 2 d), the low salinity region influences a wider area than without an extended channel ( Figure 6 2 c). The extended channel can keep the higher salinity in the thalweg near the bottom, separating lower salinity at the surface T h is makes the estuary more vertically stratified than without the offshore channel. Comparing the rectangular channel and the triangular channel ( Figure 6 2 a and d), salinity is more vertically stratified in the triangular channel than in the

PAGE 84

84 rectangular channel. In addition, the minimum salinity region is shifted from the very left top of the channel (in the rectangular channel) to the 5 km from the left bank over the triangular channel. The s alinity pattern at the estuary mouth can be steered by an extension of the channel toward the shelf or the channel shape. H owever, it is less affected by the offshore channel direction. All three cases : straight channel downshelf ( right ) turning, and upshelf ( left ) turning channel, have similar qualitative and quantitative salinity patterns at the estuary mouth ( Figure 6 2 d, e, and f ). The only appreciable difference is that the higher salinity region leans more to the right with the right turning channel This is depicted by the 32 psu contour line in Figure 6 2 e which is located more to the right than in Figure 6 2 d and f. Tidally averaged along channel and cross channel velocities at the estuary mouth are shown in Figure 6 3 Contour represents axial velocity (u), and vectors represent lateral and ver tical velocities (v and w). Vertical velocities are 100 times exaggerated to show vertical circulation, and positive and negative values mean outflow from the estuary and inflow to the estuary respectively. The w hite contour represents the zero isotach in the residual axial velocity. Rectangular channel with a flat shelf ( Figure 6 3 a) and a sloping shelf ( Figure 6 3 b) have a similar two layer circulation pattern: outflow at the surface and inflow at th e bottom. Both cases have the maximum outflow at the surface on the left edge of the estuary. R esidual cross estuary flows have the opposite direction o n both sides, heading toward the center of the estuary. The flow pattern at the triangular channel with a sloping shelf ( Figure 6 3 c) has the maximum outflow and inflow at middle of the

PAGE 85

85 crosssection thus the vertical along channel velocity gradient is largest in the middle of the channel ( Figure 6 6 ) Th e region of the inflow reaches to the surface at both left and right shoals, and it has a similar pattern to that of Kasai s (2000) result. In addition, ADCP data near the mouth of Chesapeake Bay (ValleLevinson et al., 2007) showed a similar pattern ( Figure 6 20). If the channel i s extended toward the shelf ( Figure 6 3 d), the flow pattern changes to a vertically sheared twolayer pattern, and the maximum outflow is locate d in the middle of the channel as in the short channel ( Figure 6 3 c). However, the magnitude of the maximum outflow is reduced, and the maximum outflow region is not constrained to the middle of the channel as in the sloping shelf case. Both right and left turning channel s have similar flow patterns ( Figure 6 3 e and f). These two cases have laterally asymmetric two layer flow patterns T he maximum outflow is located at the surface on the left, and the maximum inflow is located in the middle of the channel. This flow pattern is similar to a combination of the rectangular and triangular channel s. The right turning channel has more tilted inflow and outflow interface than the left turning channel having more concentrated outflow at the l eft surface. This is due to the competi tion between Coriolis force and centrifugal force Coriolis and centrifugal force are in the same direction in the right turning channel but act in the opposite direction in the left turning channel. Not only at the estuary mouth, but also at an adjacent region, salinity and flow patterns should be discussed to determine bathymetry effects. All of these cases have the same channel width 20 km, which is wide enough to develop lateral variations in flow patterns. Figure 6 4 shows along channel salinity and flow patterns at three different cross sections: north, center and south. In the case of the rectangular channel

PAGE 86

86 with flat shelf, net flows are outward toward the open sea at both shoals, and net flows are opposite in the surface and the bottom at the center in the estuary mouth region ( Figure 6 4 a ) However, the flow field depicts a two layer circulation pattern everywhere inside the estuary. Comparing the flat shel f and sloping shelf cases same values of salinity regions in the flat shelf case are located about 8 km inside the mouth in the sloping shelf case. Both cases have vertically well mixed salinity conditions throughout the estuary. T he t riangular channel wi th sloping shelf show s strong two layer circulation in the mid dle of the channel, and vertical stratification is stronger than in the middle of the rectangular channel ( Figure 6 4 c and Figure 6 5 ) Over both shoals, more well mixed conditions persist than in the rectangular channel cases. If the triangular channel i s extended offshore, vertical stratification increases dramatically in the mid channel ( Figure 6 4 d and Figure 6 5 ). Both right and left turning channel results show the same effects as those with the extended straight channel which consist of strengthening stratification in the mid channel as it extends offshore ( Fig ure 6 4 e and f). Comparing the right turning channel to the left turning channel, the right turning channel has weaker stratification throughout the estuary ( Figure 6 5 ) 6.3 Salinity and F low P atterns D epending on E stuary W idt hs Traditionally it has been recognized that a basin s width is an important factor to determine whether Coriolis effects on an estuary exchange flow are appreciable or not. Several studies have been focused on this (e.g. Garvine 1995; ValleLevinson 2008) To see the effects of estuary widths on salinity and flow patterns, five different widths of channel with same 15 m depth at the thalweg are designed: 1, 2, 6, 10 and 20 km. All other parameters and boundary conditions are set to be equal. All five cases have sloping shelf with same bottom slope of 1/1000. The salinity distribution in the narrow

PAGE 87

87 estuary has the vertically stratified and laterally well mixed patterns ( Figure 6 7 a). The maximum salinity lies on the channel bottom throughout the cross channel and the minimum salinity on the surface in the mid channel, which indicates the Earth s rotation effects do not affect much on this narrow estuary system. If channel width was doubled to 2 km ( Figure 6 7 b) isohalines are tilted little bit toward the right shoal especially for the maximum salinity region; however, the minimum salinity region is not changed much lying on the middle of the surface. When channel width increased from 2 km to 6 km, dramatic salinity pattern change happens ( Figure 6 7 c). The maximum isohaline lies on the right side bed paralleling to the bottom, and the minimum salinity region moves a little bit left. After this point, width of 6 km, the maximum sal inity region occupies right bottom to surface having vertically w ell mixing and laterally stratified patterns ( Figure 6 7 d and e). Even though the salinity pattern turns into laterally stratified as width increases, vertical stratification increases as width increases in the middle of the channel ( Figure 6 10). Width dependent tidally averaged along channel, lateral and vertical velocities at the estuary mouth are shown in Figur e 6 8 For narrow channels ( Figure 6 8 a and b), it has the traditional two layer circulation pattern, inflow at the bottom and outflow at the surface, even though the Earth s rotation effect is acting on the estuary. Flow patter ns as well as salinity pattern have dramatic changes as channel width increase from 2 km to 6 km ( Figure 6 8 c). The interface of inflow and outflow lies on the right paralleling to the bottom. However, the maximum outflow still l ocates at the surface of mid channel. While the salinity pattern similar from this point, the flow pattern changes again. As the channel width increases, the interface of inflow and outflow follows bottom topography

PAGE 88

88 hugging outflow region into the mid channel. All cases have similar lateral flow directions, heading right from the left shoal and left from the right shoal, and it makes outflows keep in mid estuary. Vertical velocity gradients in three cross sectional locations ( Figure 6 11) show that the inflow region moves to the right side of estuary having vertically well mixed condition as width increases. Along channel salinity and velocity distribution at the three cross section in the narrow estuary ( Figure 6 9 a) shows that it has similar salinity and flow patterns, which have vertically well mixed condition and only outflow exists at the both shoals. Even though flow and salinity patterns are similar in the estuary at both channel sides, there exis ts potential possibility that heavier water intrudes from north side of the estuary rather than through south side. In the mid channel, stronger stratification than in both sides exists at the estuary mouth, but it is destroyed as the cross sectional posit ion moves toward estuary head. In the case of 2 km width, along channel salinity and flow patterns are very similar to those in the 1 km wide estuary ( Figure 6 9 b). In the 6 km width estuary, salinity and flow patterns are similar to in the 1 or 2 km width estuaries, however, vivid lateral salinity variation exists in the estuary as well as in the mouth ( Figure 6 9 c). If the channel width is getting wider, the across channel variation of salinity becomes vivid, and it is likely has sea water intrusion to north side of estuaries ( Figure 6 12 d and Figure 6 4 c). Table 6 2 shows along channel, across channel and vertical density gradients for each case. Along channel density gradients are calculated in three sections and mid depth: north, center, and south of the estuary from 20 km inside of mouth to estuary mouth. Across channel density gradients are calculated in three along channel positions

PAGE 89

8 9 and mid depth: mouth, 10 km inside of mouth, and 20 km inside of mouth. Vertical density gradients are calculated in three across channel positions at the estuary mouth only: north, center, and south. Along channel and across channel density gradients are not changed much at each section and case. However, vertical density gradients in the north side are reduced dramatically, and vertically density gradients increase in the mid channel as channel width increases. These tell us that along channel and across channel density gradients are not changed much depending on channel width even though salinity difference between each side is getting bigger as channel width increases. However, vertical density gradients can be strongly affected by the change of channel width. 6.4 Salinity and F low P atterns D epending on E stuary D epths Not only the channel shape and shelf slope but also the maximum depth in the channel could affect on salinity and flow patterns at the estuary mouth. Figure 6 12 shows the depth dependent salinity distribution and flow patterns at the estuary mouth. Width of the estuary is fixed (20 km), but the maximum channel depth is varying (15 m ~ 55 m). The lowest salinity region is located in the ~ 7 km from t he south boundary with the shallow channel ( Figure 6 12 a), however, the region moves to the south as channel depth increases ( Figure 6 12 b ~ e) The high salinity region is located in the north face of the estuary having vertically well mixed condition within a shallow channel ( Figure 6 12 a). This vertically well mixed condition at the north side of the estuary turns into vertically stratified condition as the channel depth inc rease s ( Figure 6 12 b ~ e). The heavier salinity region, once which was occupied in right side of the estuary from bottom to surface in a shallow estuary, moves down to the

PAGE 90

90 thalweg. The minimum salinity region moves to the left c orresponding to centering the maximum salinity region. Figure 6 13 shows the depth dependent residual velocities at the estuary mouth. Within a shallow channel ( Figure 6 13 a), inflow locates at the both shoals and bottom, and outflow at the mid surface of the channel. We can not see this flow pattern in Wong s (1994) or Kasai s (2000) study. However, this pattern exists in the lower Chesapeake Bay, which has the similar bathymetry to JW0110600.h (about 20 km wide and 20 m deep); Figure 6 15 shows the similar results as simulated. As a channel depth increases to 25 m at the thalweg, the inflow region at the left shoal turns into outflow region while inflow still remains at the r ight shoal ( Figure 6 13 b). If a channel depth increased, the remained inflow region at the right shoal also disappear s having a vertically sheared flow pattern, and the maximum outflow occurs at the surface of left shoal. Figure 6 14 explains how strong vertical stratification could be developed in the mid channel as channel depth increases, and correspondingly salinity intrusion could be maximized. In addition, the maximum magnitude of inflow and outflow in the deep channels increases compared to the shallower channels. The results can be summarized as that (1) the maximum outflow centers in the middle of the channel in the shallow estuary ( Figure 6 13 a and b), (2) it leans to the left as depth increases ( Figure 6 13 c, d, and e), and (3) Laterally sheared flow pattern changes to vertically sheared pattern as depth increases. We may find the reason why flow pattern changes dramatically as a channel dept h increases in the lateral bottom slope; in these cases lateral bottom slope increases from 1/1000 to 5/1000. In the channel with a higher lateral bottom slope, heavier water is concentrated toward

PAGE 91

91 thalweg, and it adjusts lighter outflow at the surface mak ing traditional two way circulation, lighter water at the top and heavier water at the bottom; increasing bottom slope suppresses inertial force by Coriolis, and it makes the salinity distribution pattern from laterally sheared to vertically sheared. 6.5 N onD imensionalized N umber and M omentum A nalysis Flow patterns at the estuary depending on estuary width and depth can be summarized by two well known nondimensionalized numbers: Kelvin and Ekman number. Many studies (e.g. ValleLevinson 2003, 2007, 2008; Lerczak and Geyer 2004; Winant 2007; Chao and Boicourt 1986; Chao 1988 a, b; Chapman and Lentz 1994; Yankovsky and Chapman 1997) have been done setting vertical eddy viscosity as constant in whole domain, however it should have cross sectionally and verti cally different values in real world. In this reason, Ekman number, which is given by 2/vAfH and it is the ratio between friction and Coriolis acceleration, has to have spatial variability too. Figure 6 16 shows the vertically averaged vertical eddy viscosity (Av) and local Ekman number at the estuary mouth for JW0110700.h which has the sloping shelf and maximum depth of 50 m at the thalweg. Vertical eddy viscosity has higher value in the middle of channel and Ekman number has lower value because Ekman number is in inverse proportion to square of depth. Figure 6 18 shows the spatial variability of Ekman number for JW0110200.h and it has higher values in both shoals and lower values in the thalweg throughout entire estuary. Not only Ekman number but also Kelvin number should be concerned to be compared to other studies. Kelvin number is the ratio between the width of a basin and internal Rossby radius, and internal Rossby radius also varies spatially in the estuary

PAGE 92

92 (e.g. Alenius et al. 2003). Normally internal Rossby radius has the shape of parabola which is the normal shape of bathymetry in the estuary, because it is proportional to square root of depth. Figure 6 18 shows spatial variability of internal Rossby radius at the mouth for two cases: (a) wide estuary (JW0110600.h), (b) narrow estuary (JW0110600.h). In both cases bathymetries are symmetric with respect to thalweg, but R1 is not symmetric in t he wide estuary ( Figure 6 18 a); it has the higher value at the left side than the right side of the estuary. That indicates stratification is stronger at the left side than the right side of the estuary. Wide estuary has the significant asymmetry of R1, but narrow estuary does not ( Figure 6 18 a and b), which tells us a narrow estuary tends to have less chance of an asymmetry of stratification. To compare the results with previous studies, cross sectionally averaged Ekman number and Kelvin number are calculated; cross sectionally averaged R1 is used. Ekman, internal Rossby and Kelvin number for each case are summarized in Table 6 3 It shows that the dominant factor determining t hose numbers is the channel depth if the channel width is fixed. That means channel depth, which can be thought as bottom slope when the width of the basin is fixed, rules those numbers and flow patterns. ValleLevinson s results (2008), which shows the re sidual flow patterns in terms of the Kelvin and Ekman numbers ( Figure 6 19), and results of this study have a good agreement in some point, and does not in some point. ValleLevinson s results (2008) show that the qualitative flow pattern does not change much as a lateral channel slope changes, however, results of this study does. The difference can be found from the way to approach this problem. ValleLevinson fixed Kelvin and Ekman number whatever the bathymetry shape is, and it gives similar flow patterns. However, in this study those

PAGE 93

93 nondimensionalized numbers are not fixed but vary, and it gives significant different flow patterns respecting the channel shape. Not only the nondimensionalized numbers but also tidally averaged along channel momentum balance can show us why the flow should have the specific pattern, and what term is most dominant to create the pattern. Tidally averaged along channel momentum terms for shallow and deep channel cases in three sections are shown in Figure 6 20. It shows that the lateral advection term is comparable to other terms at the surface of both shoals in shallow estuary. However, cross sectionally averaged along channel momentum balance ( Figure 6 21) shows that the pressure gradient term is the dominant in all cases, and the lateral advection term becomes important as depth increases. 6. 6 Plume D ynamics Tidally averaged salinity distributions at each domain i n three dimensional are shown in Figure 6 22, and salinity iso surfaces of 20, 25, 30, and 34 psu are shown in Figure 6 23. Every case has identical tidal boundary and magnitude of fresh water inflow rate per unit area (2 cm/s). However, all cases have different plume shapes except having right turning shape to the direction of fresh water flow due to Coriolis effect. Some studies (e.g. Yankovsky and Chapman 1997; O Donnell 1990; Garvine 1987) put the some amount of along shelf current to prevent plume bulge toward the left side, however, it is not used for all of these cases: only Coriolis force would affect on right turning plume. With the rectangular channel and flat shelf, fresh water plume front, which can be recognized as iso surface of salinity 34 psu, can be located at the north side of the shelf. However, with a sloping shelf, plume front can not be located in the north side of shelf but inside of estuary at the north side. That means plume tends to

PAGE 94

94 spread out more radially in the flat shelf than in the sloping shelf ( Figure 6 27 ) In the flat shelf, plume front is vertically very stiff having vertically well mixed condition. However, iso surface of 34 has wider surface in t he sloping shelf case, which can be thought as surface trapped plume. In the case of the rectangular channel with a flat shelf, the plume distance, which equals salinity of 34 psu, reaches 33.5 km offshore and 16 km south from the middle of the estuary mouth. In the case of the rectangular channel with a sloping shelf, however, the plume distance reaches 20.5 km offshore and 19 km south from the middle of the estuary mouth. That tells us that fresh water plume with a sloping shelf can not reach farther than in a flat shelf, and it turns easily to the right ( Figure 6 27) The maximum salinity intrusion in the flat shelf case, which equals salinity of 20 psu, occurs at the north side of the channel bottom and it reaches 24 km from the estuary mouth, however, it intrudes 31 km from the estuary mouth in the sloping shelf case; Table 6 4 shows summarized plume and salinity intrusion distance from the estuary mouth for each case. If the channel shape changes from rectangular to triangular, plume can spread more offshore kept in a mid channel; plume width is 24.5 km in this case. Shapes of iso surfaces tell us that south side of the channel and mid channel are the main pathways of fresh water in the rectangular and triangular channel cases respectively. If the triangular channel was extended toward a shelf and the shelf was flat, fresh water plume can reach all the way east boundary captured in the main channel ( Figure 6 22 d; Figure 6 23 d, d 1 ; Figure 6 27). Even though it has the large plume surface, plume front cannot move to north beyond the edge of the channel, and it is released to the south after moving far offshore covering wide are a of the south shelf. One of the

PAGE 95

95 dramatic changes comparing to short channels is the width of iso surfaces. Iso surface of salinity 20 lies on the top of the entire estuary, and other s lie underneath, which tells us extending channel can make strong vertic al stratification in the estuary. Only right turning channel can make a lower salinity region near the coast and high salinity region at the offshore in south shelf; all other cases have step by step salinity increase from the coast to offshore at the south shelf. In this case low salinity plume can reach to the south boundary following the underneath channel and hugging higher salinity region into the coast and mid channel. Normally we can not expect left turning plume at the shelf, except wind blows over the shelf, or along shelf currents that are in opposite direction to Coriolis exist. However, fresh water plume can be turned left if left turning underneath channel exists at the shelf ( Figure 6 22 f and Figure 6 23 f, f 1). Then why does plume front locate near the underneath channel shoulders? We can find the reason from the flow curtain effect. Figure 6 26 shows the along shelf salinity and velocities (left panel), and along shelf velocity contour (right panel) at the three different sections. In every section, strong vertical velocities and along shelf velocities locate near the channel shoulders, and it prevents lateral mixing between outside and inside of the channel; it acts as a barrier. In this reason, if there existed a channel or large depth change, plume front can be formed around that area, which has sudden change of bathymetry. Channel depth dependent plume shapes are shown in Figure 6 24. If the maximum channel depth increased, plume width grows having more surface trapped plume type. In addition, flat fresh water lies on the surface corresponding to flat heavy

PAGE 96

96 water lying underneath as channel depth increases. On the other hand, there is the limitation for heavy water intrusion into the estuary. If the estuary was narrow, plume can be spread out radially rather than having short right turning region even though the Earth s rotation effect affect on the estuary. The ratio of left turning p lume distance and off shore plume distance to the estuary width is getting smaller as the estuary width increase even though left turning plume distance is comparable to the narrow estuary ( Figure 6 25), and finally the plume front can not be located over the north boundary of the estuary after channel width reaches to the sudden width ( Figure 6 25 e, e 1). When comparing iso surfaces of salinity in each case, same iso surface line locates in similar locat ion from the estuary mouth. Table 6 4 shows the plume and salinity intrusion distance from the estuary mouth. It tells us that the plume width increase as channel depth and width increases even though fresh water inflow per unit area is identical. In addition, existence of extended channel at the shelf can generate wider plume than without channel. In sum, (1) in all cases with an extended channel, plume fronts are always formed near the channel edge, (2) plume width at the shelf and shape can be modulated not only by channel shape but also by channel direction at a shelf, (3) salinity intrusion is affected by channel depth rather than channel width, and plume shape is vice versa. 6. 7 The Effect of W inds Wind stress is one of the most important factors with river discharge, tidal oscillation, bathymetry, and bottom friction on the estuary circulation dynamics. Bowman (1978) noted plume direction in the Hudson River, which could be directed to either to the left or to the right of t he river mouth, was controlled by the wind direction.

PAGE 97

97 In this study, weak wind stress (| w|=0.01 Pa) and four wind directions (upwelling, downwelling, offshore, and onshore winds) were considered. Detailed combinations of scenario are described in Table 6 1 Every wind induced simulation was conducted for 10 days after 40 day spinup. To examine the effect of wind, ideal s inusoidal wind stresses, which have a period of 8 day and wind stress amplitude of 0.01 Pa, were applied over the entire area of the model domain from second day to fifth day. Figure 6 28 shows that given wind stress of 0.01 Pa for 4 days after 40 day spinup. Figure 6 29 represents the top view of iso surface s salinity of 20, 25, 30, and 34 psu; alphabet s and numbers denote the type of bathymetry and wind direction respectively. If southerly winds, which can be called as upwelling favorable winds, blew over the estuary which has a rectangular channel and flat shelf ( Figure 6 29 a 1), the plume front initially having very sharp and vertically stiff face changes to wider and vertically flat shape. Isosurface of 34 lies widely under iso surface of 30 having vertically stratified condition especially at the shelf. In this case, surface fresh water plume at the southern part of the shelf can be easily transported offshore, correspondingly, salinity at the bottom near the shore line increases. If northerly winds, which can be called as downw elling favorable winds, were applied ( Figure 6 29 a 2), plume front becomes more sharp and vertically stiff. In this case, the fresh water plume is easily trapped near the southern shore line. Off shore winds make a similar effect with upwelling favorable winds to the plume generating vertically stratified plume front at the southern shelf area, and onshore winds make a similar effect with downwelling favorable winds. In the case of rectangular channel with a sloping shelf ( Figure 6 29 b),

PAGE 98

98 the effect of winds on the shape of plume is less effective than in the flat shelf case. However, it also shows similar pattern; upwelling favorable and off shore winds generate wider flat plume front, and downwelling favorable and onshore winds generate stiff plume front. In the case of triangular channel with a sloping shelf ( Figure 6 29 c), iso surface of 30 spread out more southerly than in the normal case ( Figure 6 23 c) even though upwelling favorable winds push surface water to the north. It might be possible that the heavier bottom water intrudes into the estuary balancing offshore surface Ekman transport by upwelling favorable winds, and lighter water corresponding to heavier water intrusion spread out and flow south due to the Coriolis effect. Comparing to the rectangular channel case, the plume with the triangular channel case is more responsible to the winds. In the extended channel case ( Figure 6 29 d), we can see how onshore winds are effective to transport surface plume to the north; it is more effective than southerly winds in this specific case. Not only offshore plume but also flows and salinity pattern in the estuary can be affected by onshore winds. South and north turning channel cases ( Figure 6 29 e and f) show how underneath channel can effectively prevent plume movement by winds. T he plume distance and salinity intrusion from the estuary mouth for each case are shown in Table 6 5 Figure 6 30, Figure 6 31, and Figure 6 32. Each case shows that the maximum plume distance from the estuary mouth can be existed under upwelling favorable winds except the left turning channel case. Normally upwelling favorable winds generate upwelling and corresponding salinity intrusion occurs near the estuary mouth. However, all cases have maximum salinity intrusion under neutral case rather than under windy conditions. It is because that mixing effect by winds is larger

PAGE 99

99 than the upwelling process in the estuary. If the wind stress was larger than these cases or river discharge was small, upwelling effect on salinity intrusion into the estuary can be significant.

PAGE 100

100 Table 6 1 Description of JW0000000.h file Main options Detailed turn on/off options 1. River discharge 0 = 2 cm/s 2. Tides 0 = OFF, 1 = ON 3. Coriolis 0 = OFF, 1 = ON 4. Bathymet ry 00 = Rectangular & no slop shelf & 20 km wide & 10 m 01 = Rectangular & sloping shelf & 20 km wide & 10 m 02 = Triangular & sloping shelf & 1 km wide & 15 m 03 = Triangular & sloping shelf & 2 km wide & 15 m 04 = Triangular & sloping shelf & 6 km wide & 15 m 05 = Triangular & sloping shelf & 10 km wide & 15 m 06 = Triangular & sloping shelf & 20 km wide & 15 m 07 = Triangular & sloping shelf & 20 km wide & 25 m 08 = Triangular & sloping shelf & 20 k m wide & 35 m 09 = Triangular & sloping shelf & 20 km wide & 45 m 10 = Triangular & sloping shelf & 20 km wide & 55 m 11 = Triangular & no slop shelf & 20 km wide & 15 m 12 = Triangular & no slop shelf & 20 km wide & 35 m 13 = Parabola & no slop shelf & 20 km wide & 15 m 14 = Parabola & no slop shelf & 20 km wide & 35 m 15 = Parabola & no slop shelf & 20 km wide & 55 m 16 = Parabola & no slop shelf & 20 km wide & 15 m 17 = Parabola & no slop shelf & 20 km wide & 35 m 18 = Parabola & no slop shelf & 20 km wide & 55 m 19 = Parabola & no slop shelf & 20 km wide & 15 m 20 = Parabola & no slop shelf & 20 km wide & 35 m 21 = Parabola & no slop shelf & 20 km wide & 55 m 6. Wind stress 0 = OFF 1 = 0.01 Pa (weak wind) 7. Wind direction 0= No wind, 1 = 0 2 = 45 3 = 90 4 = 135 5 = 180 6 = 225 7 = 270 8 = 315

PAGE 101

101 Table 6 2 Density gradients: along channel (d( )/km), cross channel (d( )/km), and vertical (d( )/m). jw0110200 (1 km) jw0110300 (2 km) jw0110400 (6 km) jw0110500 (10 km) jw0110600 (20 km) d dx North 0.455 0.424 0.447 0.489 0.419 Center 0.475 0.444 0.440 0.438 0.445 South 0.462 0.428 0.440 0.464 0.493 d dy Mouth 0.109 0.087 0.367 0.383 0.259 10 km 0.342 0.295 0.489 0.390 0.336 20 km 0.275 0.128 0.343 0.331 0.335 d dz North 0.220 0.373 0.141 0.005 0.004 Center 0.171 0.1 99 0.282 0.304 0.335 South 0.221 0.284 0.321 0.178 0.217 Table 6 3 Ekman, internal Rossby radius, and Kelvin number depending on the cases. Ek R 1 (km) Ke Channel type dependent JW0110000.h 0.3143 4.788 4.18 JW0110100.h 0.7296 3.3 54 5.96 JW0110600.h 0.8776 3.842 5.20 JW0111100.h 0.2281 8.818 2.27 JW0111600.h 0.1610 11.234 1.78 JW0111900.h 0.1698 11.462 1.74 Depth dependent JW0110600.h (10 m) 0.8776 3.842 5.20 JW0110700.h (20 m) 0.9110 5.041 3.97 JW0110800.h (30 m) 0.43 45 9.000 2.22 JW0110900.h (40 m) 0.1866 11.991 1.67 JW0111000.h (50 m) 0.0961 13.180 1.52 Width dependent JW0110200.h (1 km) 0.5790 4.178 0.24 JW0110300.h (2 km) 0.5472 4.432 0.45 JW0110400.h (6 km) 0.6078 4.578 1.31 JW0110500.h (10 km) 0.7627 4 .230 2.36 JW0110600.h (20 km) 0.8776 3.842 5.20

PAGE 102

102 Table 6 4 Plume and salinity intrusion distance from the estuary mouth. The location of plume front (salinity = 34 psu), and salinity intrusion (salinity = 20 or 30 psu) are calculated from the estuary mouth. M inus value in y direction means that plume or given salinity locates south from the middle of estuary. The sign, indicates that the plume front or salinity intrusion can be reach either left or right boundary. Plume distance from mouth Salinity intrusion from mouth Salinity (psu) X (km) Y (km) X (km) Y (km) Channel type dependent jw0110000.h 33.5 16.0 24.0 10.0 34 & 20 jw0110100.h 20.5 19.0 31.0 10.0 34 & 20 jw0110600.h 24.5 14.0 29.5 10.0 34 & 20 jw0111100.h 7.5 15.5 0 34 & 30 jw0111600.h 59.0 48.5 12.5 2.5 34 & 30 jw0111900.h 74.0 8.0 18.0 4.5 34 & 30 Depth dependent JW0110600.h (10 m) 24.5 14.0 29.5 10.0 34 & 20 JW0110700.h (20 m) 45.0 7.5 57.0 1.5 34 & 20 JW0110800.h (30 m) 53.0 13.5 8.0 34 & 20 JW0110900.h (40 m) 55.0 11.0 9.5 34 & 20 JW0111000.h (50 m) 51.5 1.0 9.5 34 & 20 Width dependent JW0110200.h (1 km) 12.0 3.225 22.0 0.6 34 & 20 JW0110300.h (2 km) 14.5 2.275 24.5 0.05 34 & 20 JW0110400.h (6 km) 17.5 2.7 23.0 0.9 34 & 20 JW0110500.h (10 km) 25.5 2.8 24.0 6.0 34 & 20 JW0110600.h (20 km) 24.5 14.0 29.5 10.0 34 & 20

PAGE 103

103 Table 6 5 Plume distance and salinity intrusion from the estuary mouth for each case. Plume front is defined by salinity of 34 ps u, and salinity intrusion distance is calculated at the location of 20 and 30 psu. In the cases of triangular and sloping shelf, plume fronts reach eastern boundary. Plume distance from mouth Salinity intrusion from mouth Salinity (psu) X (km) Y (km) X (km) Y (km) Rectangular & flat shelf jw0110000.h 33.5 16.0 24.0 10.0 34 & 20 jw0110011.h 35.0 19.0 20.5 10.0 jw0110013.h 37.0 14.0 20.0 10.0 jw0110015.h 44.5 13.0 19.5 9.5 jw0110017.h 38.5 18.5 20.5 10.0 Rectangular & sloping shelf jw01 10100.h 20.5 19.0 31.0 10.0 34 & 20 jw0110111.h 20.5 20.5 23.5 10.0 jw0110113.h 23.5 12.5 23.5 10.0 jw0110115.h 28.5 16.5 23.0 10.0 jw0110117.h 23.0 20.5 23.5 10.0 Triangular & sloping shelf jw0110600.h 24.5 14.0 29.5 10.0 34 & 20 jw0 110611.h 26.5 15.0 23.5 1.0 jw0110613.h 29.0 4.5 23.5 10.0 jw0110615.h 34.0 5.5 23.0 10.0 jw0110617.h 29.5 13.0 18.5 10.0 Triangular & extended jw0111100.h 7.5 15.5 0 34 & 30 jw0111111.h 9.5 9.0 1.5 jw0111113.h 8.5 6.5 1.0 j w0111115.h 8.0 7.5 1.0 jw0111117.h 8.5 9.5 1.0 Right turning jw0111600.h 59.0 48.5 12.5 2.5 34 & 30 jw0111611.h 60.0 46.0 8.5 6.5 jw0111613.h 60.5 42.0 5.0 8.0 jw0111615.h 62.5 36.0 4.5 9.5 jw0111617.h 60.5 42.0 7.0 8.0 Left tu rning jw0111900.h 74.0 8.0 18.0 4.5 34 & 30 jw0111911.h 77.5 2.5 18.0 5.0 jw0111913.h 77.0 3.0 13.5 4.0 jw0111915.h 77.5 2.5 15.5 4.5 jw0111917.h 78.0 5.5 18.5 3.5

PAGE 104

104 River Land Land 100 Km 100 Km220 Km River Land Land 100 Km 100 Km220 Km 100 km100 km 220 km 100 km 20 km 100 km 10 m 73 m 100 km100 km 220 km 100 km 20 km 100 km 100 km100 km 220 km 100 km 20 km 100 km 10 m 73 m River Land Land 100 Km 100 Km220 Km River Land Land 100 Km 100 Km220 Km River Land Land 100 Km 100 Km220 Km River Land Land 100 Km 100 Km220 Km River Land Land 100 Km 100 Km220 Km River Land Land 100 Km 100 Km220 Km River Land Land 100 Km 100 Km220 Km a) b) c) d) River Land Land 100 Km 100 Km220 Km River Land Land 100 Km 100 Km220 Km 100 km100 km 220 km 100 km 20 km 100 km 10 m 73 m 100 km100 km 220 km 100 km 20 km 100 km 100 km100 km 220 km 100 km 20 km 100 km 10 m 73 m River Land Land 100 Km 100 Km220 Km River Land Land 100 Km 100 Km220 Km River Land Land 100 Km 100 Km220 Km River Land Land 100 Km 100 Km220 Km River Land Land 100 Km 100 Km220 Km River Land Land 100 Km 100 Km220 Km River Land Land 100 Km 100 Km220 Km a) b) c) d) Figure 6 1 Model domains and bathymetries. a) T he gener al bathymetry for nonextended triangular channel cases. b) T he bathymetry for the rectangular channel with a sloping shelf case. c) T he bathymetry for the extended triangular channel case. d) T he bathymetry for the extended right turning channel. The bathymetry for the extended left turning channel is not shown, but it is exactly same as d) except channel turned into north boundary.

PAGE 105

105 2 22 62 83 23 02 4 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 8 6 4 2 0j w 0 1 1 0 0 0 0 h 2 83 23 43 0 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 8 6 4 2 0j w 0 1 1 0 1 0 0 h 2 63 43 23 02 8 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 1 0 5 0j w 0 1 1 0 6 0 0 h 1 81 42 02 22 42 62 83 03 21 6 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 1 0 5 0j w 0 1 1 1 1 0 0 h 1 82 02 22 83 03 23 42 62 4 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 1 5 1 0 5 0j w 0 1 1 1 6 0 0 h 2 22 42 62 83 03 23 4 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 1 5 1 0 5 0j w 0 1 1 1 9 0 0 h a) f) e) d) c) b) 2 22 62 83 23 02 4 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 8 6 4 2 0j w 0 1 1 0 0 0 0 h 2 83 23 43 0 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 8 6 4 2 0j w 0 1 1 0 1 0 0 h 2 63 43 23 02 8 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 1 0 5 0j w 0 1 1 0 6 0 0 h 1 81 42 02 22 42 62 83 03 21 6 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 1 0 5 0j w 0 1 1 1 1 0 0 h 1 82 02 22 83 03 23 42 62 4 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 1 5 1 0 5 0j w 0 1 1 1 6 0 0 h 2 22 42 62 83 03 23 4 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 1 5 1 0 5 0j w 0 1 1 1 9 0 0 h a) f) e) d) c) b) Figure 6 2 Tidally averaged s alinity distribution pattern at the estuary mouth with different channel and shelf types. Viewer is looking toward the estuary from the ocean. The salinity contour intervals are 1 psu.

PAGE 106

106 y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 0 0 0 0 h y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 0 2 0 0 h y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 0 1 0 0 h y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 1 1 0 0 h y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 1 6 0 0 h y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 1 9 0 0 h a) f) e) d) c) b) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 0 0 0 0 h y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 0 2 0 0 h y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 0 1 0 0 h y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 1 1 0 0 h y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 1 6 0 0 h y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 1 9 0 0 h a) f) e) d) c) b) a) f) e) d) c) b) Figure 6 3 Tidally averaged along channel velocities (contour) across channel and vertical velocities (vectors) at the es tuary mouth. Vertical velocities are 100 times exaggerated. White line represents that the location of the residual axial velocities has zero value, which means it is the interface between inflow and outflow. Reference velocity vector of 10 cm/s is located in the left top.

PAGE 107

107 1 6 3 4 2 2 3 0 2 6 Z ( m ) 8 0 1 0 0 1 2 0 8 6 4 2 0C e n t e r 3 4 2 6 2 2 3 0 Z ( m ) 8 0 1 0 0 1 2 0 8 6 4 2 0 2 5 N o r t h 1 8 3 4 2 2 3 0 26 X ( k m ) Z ( m ) 8 0 1 0 0 1 2 0 8 6 4 2 0S o u t h Figure 6 4 (a) jw0110000.h. Along channel salinity distribution and velocity vectors (u and w) for three sections: north, center, and south. North and south face are the same as right and left side of channel respec tively when we are looking into the estuary. Only estuary mouth region (70 ~ 130 km in the x axis) is shown, and the estuary mouth is denoted by blue dashed line at the 100 km of x axis The unit of reference vector is cm The salinity contour intervals are 2 psu. Vertical velocity is 100 times exaggerated.

PAGE 108

108 2 2 3 4 2 6 3 0 Z ( m ) 8 0 1 0 0 1 2 0 1 5 1 0 5 0 2 5 N o r t h 2 2 3 0 3 4 1 8 2 6 Z ( m ) 8 0 1 0 0 1 2 0 1 5 1 0 5 0C e n t e r 3 0 3 4 2 6 2 2 1 8 X ( k m ) Z ( m ) 8 0 1 0 0 1 2 0 1 5 1 0 5 0S o u t h Figure 6 4 Continued. (b) jw0110100.h.

PAGE 109

109 2 2 2 6 3 0 3 4 Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0 2 5 N o r t h 1 8 2 2 3 0 2 6 3 4 Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 2 0 1 5 1 0 5 0C e n t e r 1 8 2 2 2 6 3 0 3 4 X ( k m ) Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0S o u t h Figure 6 4 Continued. (c) jw0110600.h

PAGE 110

110 1 6 2 8 3 0 3 2 Z ( m ) 8 0 1 0 0 1 2 0 1 5 1 0 5 0C e n t e r 2 6 2 8 3 0 3 4 3 4 Z ( m ) 8 0 1 0 0 1 2 0 4 2 0 2 5 N o r t h 1 6 2 0 2 2 2 4 X ( k m ) Z ( m ) 8 0 1 0 0 1 2 0 4 2 0S o u t h Figure 6 4 Continued. (d) jw0111100.h.

PAGE 111

111 2 6 2 8 3 0 3 0 3 2 3 2 3 4 X Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 2 0 1 5 1 0 5 0 2 5 N o r t h 2 6 2 8 3 0 3 2 X Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 2 0 1 5 1 0 5 0C e n t e r 1 6 2 0 2 4 2 8 3 2 X ( k m ) Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 2 0 1 5 1 0 5 0S o u t h Figure 6 4 Continued. (e) jw0111600.h.

PAGE 112

112 2 8 3 0 3 0 3 2 3 4 3 2 X Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 2 0 1 5 1 0 5 0 2 5 N o r t h 2 8 3 0 2 6 3 2 X Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 2 0 1 5 1 0 5 0 2 5C e n t e r 2 2 2 4 2 4 2 6 2 6 X Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 2 0 1 5 1 0 5 0 2 5S o u t h Figure 6 4. Continued. (f) jw0111900.h.

PAGE 113

113 Figure 6 5 Vertical salinity gradients in three cross sectional locations depending on the channel shape d(u)/dz 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Rec./Flat Rec./Slope Tri./Slope Tri./Ext. Par./Right Par./Left [1/s] south center north Figure 6 6 Vertical along channel velocity gradients in three cross sectional locations depending on the channel shape. d(S)/dz 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Rec./Flat Rec./Slope Tri./Slope Tri./Ext. Par./Right Par./Left [ppt/m south center north

PAGE 114

114 3 13 3 3 2 Y ( K m ) Z ( m ) 0 0 2 0 4 0 6 0 8 1 1 0 5 0S a l i n i t y ( B = 1 k m ) 3 13 33 2 Y ( K m ) Z ( m ) 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2 1 0 5 0S a l i n i t y ( B = 2 k m ) 2 93 33 23 03 1 Y ( K m ) Z ( m ) 0 1 2 3 4 5 6 1 0 5 0S a l i n i t y ( B = 6 k m ) 2 83 43 33 13 23 02 9 Y ( K m ) Z ( m ) 0 1 2 3 4 5 6 7 8 9 1 0 1 0 5 0S a l i n i t y ( B = 1 0 k m ) 2 63 43 33 13 23 02 9282 7 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 1 0 5 0S a l i n i t y ( B = 2 0 k m ) a) c) b) e) d) 3 13 3 3 2 Y ( K m ) Z ( m ) 0 0 2 0 4 0 6 0 8 1 1 0 5 0S a l i n i t y ( B = 1 k m ) 3 13 33 2 Y ( K m ) Z ( m ) 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2 1 0 5 0S a l i n i t y ( B = 2 k m ) 2 93 33 23 03 1 Y ( K m ) Z ( m ) 0 1 2 3 4 5 6 1 0 5 0S a l i n i t y ( B = 6 k m ) 2 83 43 33 13 23 02 9 Y ( K m ) Z ( m ) 0 1 2 3 4 5 6 7 8 9 1 0 1 0 5 0S a l i n i t y ( B = 1 0 k m ) 2 63 43 33 13 23 02 9282 7 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 1 0 5 0S a l i n i t y ( B = 2 0 k m ) a) c) b) e) d) Figure 6 7 Width dependent tidally averaged salinity distribution pattern at the e stuary mouth Width of channel changes from 1 to 20 km, but maximum depth at the thalweg is fixed to 15 m. Salinity contour intervals are 1 psu.

PAGE 115

115 y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0M e a n v e l o c i t i e s ( B = 2 k m ) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0M e a n v e l o c i t i e s ( B = 1 k m ) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0M e a n v e l o c i t i e s ( B = 6 k m ) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0M e a n v e l o c i t i e s ( B = 1 0 k m ) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0M e a n v e l o c i t i e s ( B = 2 0 k m ) a) b) c) d) e) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0M e a n v e l o c i t i e s ( B = 2 k m ) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0M e a n v e l o c i t i e s ( B = 1 k m ) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0M e a n v e l o c i t i e s ( B = 6 k m ) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0M e a n v e l o c i t i e s ( B = 1 0 k m ) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0M e a n v e l o c i t i e s ( B = 2 0 k m ) a) b) c) d) e) Figure 6 8 Width dependent residual along channel velocities (contour), across channel and vertical velocities (vectors) at the estuary mouth. Vertical velocities are 50 times exaggerated. White line represents that the location of the residual axial velocities has zero value, which means it is the interface between inflow and outflow. Refer ence velocity vector of 10 cm/s is located on the left top.

PAGE 116

116 1 8 2 8 3 2 3 4 2 2 Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0 2 5 N o r t h 1 8 2 2 3 2 2 6 3 4 Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 2 0 1 5 1 0 5 0C e n t e r 2 2 2 8 3 2 3 4 1 8 X ( k m ) Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0S o u t h Figure 6 9 (a) jw0110200.h (1 km) Width dependent along channel salinity distribution and velocity vectors (u and w) for three sections: north, center, and south. North and s outh face are the same as right and left side of channel respectively, when we are looking into the estuary. Only estuary mouth region (70 ~ 130 km in the x axis) is shown, and the estuary mouth is denoted by blue dashed line at the 100 km of x axis. The unit of reference vector is cm The salinity contour intervals are 2 psu. Vertical velocity is 100 times exaggerated.

PAGE 117

117 1 8 2 8 3 2 3 4 2 2 Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0 2 5 N o r t h 1 8 2 2 3 2 2 6 3 4 Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 2 0 1 5 1 0 5 0C e n t e r 2 2 2 8 3 2 3 4 1 8 X ( k m ) Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0S o u t h Figure 6 9 Continued. (b) jw0110300.h (2 km)

PAGE 118

118 1 8 2 8 3 4 3 2 2 2 Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0 2 5 N o r t h 2 2 2 6 3 2 3 4 1 8 X ( k m ) Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0S o u t h 1 8 2 2 3 2 2 8 3 4 Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 2 0 1 5 1 0 5 0C e n t e r Figure 6 9 Continued. (c) jw0110400.h (6 km)

PAGE 119

119 2 0 3 0 3 4 3 4 2 4 Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0 2 5 N o r t h 1 8 2 2 3 2 2 8 3 4 Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 2 0 1 5 1 0 5 0C e n t e r 2 2 2 8 3 2 3 4 1 6 X ( k m ) Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0S o u t h Figure 6 9 Continued. (d) jw01105 00.h (10 km)

PAGE 120

120 d(S)/dz 0 0.1 0.2 0.3 0.4 0.5 0.6 1 km 2 km 6 km 10 km 20 km [ppt/m] south center north Figure 6 10. Vertical salinity gradients in three cross sectional locations depending on channel width. d(u)/dz 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 1 km 2 km 6 km 10 km 20 km [1/s] south center north Figure 6 11. Vertical along channel v elocity gradients in three cross sectional locations depending on channel width.

PAGE 121

121 2 62 83 03 23 4 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 1 0 5 0S a l i n i t y ( h = 1 5 m ) 2 72 93 13 3 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 2 0 1 5 1 0 5 0S a l i n i t y ( h = 2 5 m ) 2 52 72 93 13 3 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 3 0 2 5 2 0 1 5 1 0 5 0S a l i n i t y ( h = 3 5 m ) 2 52 72 93 13 3 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0S a l i n i t y ( h = 4 5 m ) 2 52 72 93 13 3 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0S a l i n i t y ( h = 5 5 m ) a) b) c) d) e) 2 62 83 03 23 4 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 1 0 5 0S a l i n i t y ( h = 1 5 m ) 2 72 93 13 3 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 2 0 1 5 1 0 5 0S a l i n i t y ( h = 2 5 m ) 2 52 72 93 13 3 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 3 0 2 5 2 0 1 5 1 0 5 0S a l i n i t y ( h = 3 5 m ) 2 52 72 93 13 3 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0S a l i n i t y ( h = 4 5 m ) 2 52 72 93 13 3 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0S a l i n i t y ( h = 5 5 m ) 2 62 83 03 23 4 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 1 0 5 0S a l i n i t y ( h = 1 5 m ) 2 72 93 13 3 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 2 0 1 5 1 0 5 0S a l i n i t y ( h = 2 5 m ) 2 52 72 93 13 3 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 3 0 2 5 2 0 1 5 1 0 5 0S a l i n i t y ( h = 3 5 m ) 2 52 72 93 13 3 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0S a l i n i t y ( h = 4 5 m ) 2 52 72 93 13 3 Y ( K m ) Z ( m ) 0 5 1 0 1 5 2 0 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0S a l i n i t y ( h = 5 5 m ) a) b) c) d) e) a) b) c) d) e) Figure 6 12. Depth dependent tidally averaged salinity distribution pattern at the estuary mouth Depth of channel changes from 15 to 55 m at the thalweg, but depth at the shoals and width of channel are fixed. Salinity contour intervals are 1 psu.

PAGE 122

122 y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 0 7 0 0 h ( h = 2 5 m ) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 0 8 0 0 h ( h = 3 5 m ) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 0 6 0 0 h ( h = 1 5 m ) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0 1 0j w 0 1 1 0 9 0 0 h ( h = 4 5 m ) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 1 0 0 0 h ( h = 5 5 m ) a) e) d) c) b) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 0 7 0 0 h ( h = 2 5 m ) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 0 8 0 0 h ( h = 3 5 m ) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 0 6 0 0 h ( h = 1 5 m ) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0 1 0j w 0 1 1 0 9 0 0 h ( h = 4 5 m ) y / B z / H 0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 1u 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 5 0 5 1 0j w 0 1 1 1 0 0 0 h ( h = 5 5 m ) a) e) d) c) b) Figure 6 13. Depth dependent residual along channel velocities (contour), across channel and vertical velocities (vectors) at the estuary mo uth. Vertical velocities are 100 times exaggerated. W h it e line represents that the location of the residual axial velocities has zero value, which means it is the interface between inflow and outflow. Reference velocity vector of 10 cm/s is located on the left top.

PAGE 123

123 2 6 32 3 0 3 4 Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 3 0 2 0 1 0 0C e n t e r 2 2 2 6 3 0 3 2 3 4 Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0 2 5 N o r t h 1 8 2 2 2 6 3 0 3 2 X ( k m ) Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0S o u t h Figure 6 14. (a) jw0110700.h (25m) Depth dependent along channel salinity distribution and velocity vectors (u and w) for three sections: north, center, and south. North and south faces are the same as right and left side of channel respectively, when we are looking into the estuary. Only estuary mouth region (70 ~ 130 km in the x axis) is shown, and the estuary mouth is denoted by blue dashed line at the 100 km of x axis. The unit of reference vector is cm The salinity co ntour intervals are 2 psu. Vertical velocity is 100 times exaggerated.

PAGE 124

124 2 8 3 0 3 2 3 4 X Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 4 0 3 0 2 0 1 0 0C e n t e r 2 0 2 2 2 4 2 6 2 8 3 2 3 0 X ( k m ) Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0S o u t h 3 2 3 2 3 4 3 0 X Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0 2 5 N o r t h Figure 6 1 4 Continued. (b) jw0110800.h (35m)

PAGE 125

125 2 6 3 4 X Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 5 0 4 0 3 0 2 0 1 0 0C e n t e r 3 0 3 2 3 2 3 4 X Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0 2 5 N o r t h 2 4 2 2 3 0 2 6 2 8 X ( k m ) Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0S o u t h Figure 6 1 4 Continued. (c) jw0110900.h (45m)

PAGE 126

126 3 0 3 4 3 2 X Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0 2 5 N o r t h 2 6 3 0 3 4 X Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 6 0 4 0 2 0 0 2 5C e n t e r 2 2 2 6 2 8 2 4 X Z ( m ) 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 0 8 6 4 2 0 2 5S o u t h Figure 6 1 4 Continued. ( e) jw0111000.h (55m)

PAGE 127

127 Figure 6 15. Mean flow patterns at the lower Chesapeake Bay. ValleLevinson et al. (2007).

PAGE 128

128 0 2 4 6 8 10 12 14 16 18 20 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 Vertically averaged vertical eddy viscosity (Av) at the mouth Y (km)Av (m2/s) 0 2 4 6 8 10 12 14 16 18 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Local Ekman number (Ek) at the mouth Y (km)Ek a) b) 0 2 4 6 8 10 12 14 16 18 20 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 Vertically averaged vertical eddy viscosity (Av) at the mouth Y (km)Av (m2/s) 0 2 4 6 8 10 12 14 16 18 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Local Ekman number (Ek) at the mouth Y (km)Ek a) b) Figure 6 16. (a) v ertically averaged vertical eddy vi scosity (Av) (b) local Ekman number (Ek) at the estuary mouth (JW0110700.h).

PAGE 129

129 Spatial variability of Ekman number (Av/fH2) X (km)Y (km) 50 100 150 60 80 100 120 140 160 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Figure 6 17. Spatial variability of Ekman number in the domain for JW0110200.h

PAGE 130

130 0 2 4 6 8 10 12 14 16 18 20 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Internal Rossby Radius (R1) Y(Km)R1 (m) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2000 2500 3000 3500 4000 4500 5000 5500 6000 Internal Rossby Radius (R1) Y(Km)R1 (m) a) b) 0 2 4 6 8 10 12 14 16 18 20 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Internal Rossby Radius (R1) Y(Km)R1 (m) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2000 2500 3000 3500 4000 4500 5000 5500 6000 Internal Rossby Radius (R1) Y(Km)R1 (m) a) b) a) b) Figure 6 18. Cross sectional variability of Internal Rossby Radius at the estuary mouth for (a) J W01106 00.h and (b) JW01102 00.h

PAGE 131

131 a) b) a) b) Figure 6 19. Residual velocities depending on Kelvin and Ekman number at the estuary mouth: (a) moderate slope and (b) steep slop (ValleLevinson, 2008).

PAGE 132

132 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 m/s2Depth(m)Left of Channel Lateral advection Coriolis Vertical diffusion Pressure gradient 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -15 -10 -5 0 m/s2Depth(m)Center of Channel 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 m/s2Depth(m)Right of Channel 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -7 -6 -5 -4 -3 -2 -1 0 m/s2Depth(m)Left of Channel 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -60 -50 -40 -30 -20 -10 0 m/s2Depth(m)Center of Channel 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -7 -6 -5 -4 -3 -2 -1 0 m/s2Depth(m)Right of Channel a) b) 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 m/s2Depth(m)Left of Channel Lateral advection Coriolis Vertical diffusion Pressure gradient 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -15 -10 -5 0 m/s2Depth(m)Center of Channel 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 m/s2Depth(m)Right of Channel 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 m/s2Depth(m)Left of Channel Lateral advection Coriolis Vertical diffusion Pressure gradient 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -15 -10 -5 0 m/s2Depth(m)Center of Channel 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 m/s2Depth(m)Right of Channel 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -7 -6 -5 -4 -3 -2 -1 0 m/s2Depth(m)Left of Channel 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -60 -50 -40 -30 -20 -10 0 m/s2Depth(m)Center of Channel 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -7 -6 -5 -4 -3 -2 -1 0 m/s2Depth(m)Right of Channel 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -7 -6 -5 -4 -3 -2 -1 0 m/s2Depth(m)Left of Channel 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -60 -50 -40 -30 -20 -10 0 m/s2Depth(m)Center of Channel 0 0.2 0.4 0.6 0.8 1 1.2 x 10-4 -7 -6 -5 -4 -3 -2 -1 0 m/s2Depth(m)Right of Channel a) b) Figure 6 20. Vertical profiles of the tidally averaged absolute value of along channel momentum terms at the center and shoals for a shallow (a, jw0110600.h ) and deep (b, jw0111000.h ) estuary.

PAGE 133

133 10 15 20 25 30 35 40 45 50 5 10 15 20 25 30 35 40 45 Momentum balance depth (m)% Lateral advection Vertical diffusion Pressure gradient Coriolis Figure 6 21. Cross sectionally averaged momentum terms for different channel depth

PAGE 134

134 a) f) e) d) c) b) a) f) e) d) c) b) a) f) e) d) c) b) Figure 6 22. 3D salinity distribution for different channel shapes

PAGE 135

135 a) c -1) c) b -1) b) a -1) a) c -1) c) b -1) b) a -1) a) c -1) c) b -1) b) a -1) Figure 6 23. Salinity iso surface of 20, 25, 30, 34 psu Right panel s are the plain views.

PAGE 136

136 d) f-1) f) e -1) e) d -1) d) f-1) f) e -1) e) d -1) d) f-1) f) e -1) e) d -1) Figure 6 23. Continued

PAGE 137

137 a) c -1) c) b -1) b) a -1) a) c -1) c) b -1) b) a -1) a) c -1) c) b -1) b) a -1) Figure 6 24. 3D depth dependent salinity distribution and iso surface

PAGE 138

138 d) e -1) e) d -1) d) e -1) e) d -1) Figure 6 2 4 Continued

PAGE 139

139 a) c -1) c) b -1) b) a -1) a) c -1) c) b -1) b) a -1) a) c -1) c) b -1) b) a -1) Figure 6 25. 3D width dependent salinity distribution and iso surf ac e

PAGE 140

140 d) e -1) e) d -1) d) e -1) e) d -1) Figure 6 2 5 Continued

PAGE 141

141 X ( m )0 0 0 0 0 1 2 0 0 0 0 1 4 0 0 0 0 1 6 0 0 0 0 Y X Z v 0 0 1 0 0 3 0 0 5 0 0 7 0 0 9 0 1 1 0 1 3 0 1 5 0 1 7 0 1 9 0 2 1 0 2 3 0 2 5 0 2 7 0 2 9 0 3 1 2 0 k m s o u t h ( v ) X ( m )0 0 0 0 0 1 2 0 0 0 0 1 4 0 0 0 0 1 6 0 0 0 0 Y X Z v 0 0 1 0 0 3 0 0 5 0 0 7 0 0 9 0 1 1 0 1 3 0 1 5 0 1 7 0 1 9 0 2 1 0 2 3 0 2 5 0 2 7 0 2 9 0 3 1 4 5 k m s o u t h ( v ) X ( m )0 0 0 0 0 1 2 0 0 0 0 1 4 0 0 0 0 1 6 0 0 0 0 Y X Z v 0 0 1 0 0 3 0 0 5 0 0 7 0 0 9 0 1 1 0 1 3 0 1 5 0 1 7 0 1 9 0 2 1 0 2 3 0 2 5 0 2 7 0 2 9 0 3 1 9 0 k m s o u t h ( v ) X ( m )0 0 0 1 2 0 0 0 0 1 4 0 0 0 0 1 6 0 0 0 0 Y X Z 19 0 k m s o u t h ( s a l i n i t y ) X ( m )0 0 0 1 2 0 0 0 0 1 4 0 0 0 0 1 6 0 0 0 0 Y X Z 14 5 k m s o u t h ( s a l i n i t y ) X ( m )0 0 0 1 2 0 0 0 0 1 4 0 0 0 0 1 6 0 0 0 0 Y X Z 12 0 k m s o u t h ( s a l i n i t y ) a) b -1) a -1) b) c -1) c) X ( m )0 0 0 0 0 1 2 0 0 0 0 1 4 0 0 0 0 1 6 0 0 0 0 Y X Z v 0 0 1 0 0 3 0 0 5 0 0 7 0 0 9 0 1 1 0 1 3 0 1 5 0 1 7 0 1 9 0 2 1 0 2 3 0 2 5 0 2 7 0 2 9 0 3 1 2 0 k m s o u t h ( v ) X ( m )0 0 0 0 0 1 2 0 0 0 0 1 4 0 0 0 0 1 6 0 0 0 0 Y X Z v 0 0 1 0 0 3 0 0 5 0 0 7 0 0 9 0 1 1 0 1 3 0 1 5 0 1 7 0 1 9 0 2 1 0 2 3 0 2 5 0 2 7 0 2 9 0 3 1 4 5 k m s o u t h ( v ) X ( m )0 0 0 0 0 1 2 0 0 0 0 1 4 0 0 0 0 1 6 0 0 0 0 Y X Z v 0 0 1 0 0 3 0 0 5 0 0 7 0 0 9 0 1 1 0 1 3 0 1 5 0 1 7 0 1 9 0 2 1 0 2 3 0 2 5 0 2 7 0 2 9 0 3 1 9 0 k m s o u t h ( v ) X ( m )0 0 0 1 2 0 0 0 0 1 4 0 0 0 0 1 6 0 0 0 0 Y X Z 19 0 k m s o u t h ( s a l i n i t y ) X ( m )0 0 0 1 2 0 0 0 0 1 4 0 0 0 0 1 6 0 0 0 0 Y X Z 14 5 k m s o u t h ( s a l i n i t y ) X ( m )0 0 0 1 2 0 0 0 0 1 4 0 0 0 0 1 6 0 0 0 0 Y X Z 12 0 k m s o u t h ( s a l i n i t y ) a) b -1) a -1) b) c -1) c) Figure 6 26. Cross shelf salinity and velocity vectors (left panel ) and along shelf velocity (right panel) at three different positions for jw0111600.h : (a) 20 km (b) 45 km and (c) 90 km south from the estuary mouth. Vertical velocities are 100 times exaggerated.

PAGE 142

142 Plume distance from mouth -60 -40 -20 0 20 40 60 80 100 120 Rec./Flat Rec./Slope Tri./Slope Tri./Ext. Par./Right Par./Left [km] dy dx Figure 6 27. Plume distance from the estuary mouth. 'dx' and 'dy' are the plume widths in x and y direction respectively. 40 41 42 43 44 45 46 47 48 49 50 -8 -6 -4 -2 0 2 4 6 8 10 12 x 10-3 Wind stress (Pa) from 135 degree Time (day)Wind stress (Pa) U V Total Figure 6 28. Given total wind stress of 0.01 Pa on the domain. In this case, southeasterly wind blows over the domain, and it has magnitude of 0.00707 Pa in both u and v components.

PAGE 143

143 a -1) a -4) a -2) a -3) a -1) a -4) a -2) a -3) a -1) a -4) a -2) a -3) Figure 6 29. Salinity iso surface of 20, 25, 30, and 34 psu depending on wind direction: (a 1) upwelling, (a2) downwelling, (a3 ) off shore, and (a4 ) on shore winds. These are for the rectangular and no slop shelf cases.

PAGE 144

144 b -1) b -4) b -2) b -3) b -1) b -4) b -2) b -3) b -1) b -4) b -2) b -3) Figure 6 2 9 Continued. These are for rectangular and sloping shelf cases.

PAGE 145

145 c -1) c -4) c -2) c -3) c -1) c -4) c -2) c -3) c -1) c -4) c -2) c -3) Figure 6 29. Continued. These are for triangular and sloping shelf cases.

PAGE 146

146 d -1) d -4) d -2) d -3) d -1) d -4) d -2) d -3) d -1) d -4) d -2) d -3) Figure 6 2 9 Continued. These are for triangular, no sloping shelf and extended channel cases.

PAGE 147

147 e -1) e -4) e -2) e -3) e -1) e -4) e -2) e -3) e -1) e -4) e -2) e -3) e -1) e -4) e -2) e -3) Figure 6 2 9 Continued. These are for s outh turning channel cases.

PAGE 148

148 f-1) f-4) f-2) f-3) f-1) f-4) f-2) f-3) f-1) f-4) f-2) f-3) Figure 6 29. Continued. These are for north turning channel cases.

PAGE 149

149 Plume distance from mouth (km) 0 10 20 30 40 Normal Upwelling Downwelling Offshore Onshore Figure 6 30. Plume width in x direction depending on wind direction for jw0110600.h Plume distance (south) from mouth (km) 0 5 10 15 Normal Upwelling Downwelling Offshore Onshore Figure 6 3 1 Plume width in y direction depending on wind direction for jw0110600.h Salt intrusion from mouth (km) 0 10 20 30 Normal Upwelling Downwelling Offshore Onshore Figure 6 32. Salinity intrusion from the estuary mouth depending on wind direction for jw0110600.h

PAGE 150

150 CHAPTER 7 SUMMARY AND CONCLUSI ONS The objective of thi s study is to understand the bathymetric effects on winddriven exchange hydrodynamics at an estuary/ocean transition. To achieve thi s objective, three bathymetry types and four wind directions we re used. The first bathymetry type examines morphological (c onfiguration) influences on exchange hydrodynamics. S ix different types of channel configurations are explored: 1) rectangular crosssection and no sloping shelf ; 2) rectangular crosssection and sloping shelf ; 3) triangular crosssection and sloping shel f ; 4) triangular crosssection and straight extended channel ; 5) parabol ic crosssection and right turning channel ; and 6) parabol ic crosssection and left turning channel. The second type of bathymetry examines the influence of width on exchange hydrodynamics. F ive different width s of channel are explored: 1, 2, 6, 10, and 20 km. The third type of bathymetry examines the influence of depth on exchange hydrodynamics. Five different channel depths are explored: 15, 25, 35, 45, and 55 m depth at the thalweg. To study the wind effect on different channel types, four directions of weak winds (| w|=0.01 Pa) were applied to the first type of bathymetry. The numerical experiments outlined above were carried out with ROMS To assess the model performance, six pr eliminary tests we re carried out and compared with analytical solutions: i) wind induced setup, ii) Seiche excitation, iii) tidal propagation, iv) density driven ( baroclinic ) flow, v) wind driven flow in an elongated rotating basin, and vi) residual tidal circulation in an estuary. The fifth and sixth preliminary tests were compared to Winant s (2004, 2007) analytical solutions, which are the only 3D analytical solutions in a basin, and only Huang et al. (2008) conducted comparison tests with Winant s (2004) results using FVCOM and ROMS.

PAGE 151

151 In the first bathymetric type simulations, it is found that the residual salinity, flow, and plume patterns at the estuary mouth can be different depending on the estuarine channel shape and also on the shelf bathymetry. Fo r a sloping shelf, tidal effects at the estuary mouth can be larger than in the case with a flat shelf even under the same river discharge and equal dimensions of the estuary. In this situati on, higher salinity is expected at the estuary mouth compar ed to an estuary connected to a flat shelf; larger tidal boundary effects push the interfacial zone between fresh and ocean water toward upestuary. In the rectangular estuarine channel, the minimum salinity region is located in the left upper part of the estuary, looking into the estuary, due to the Coriolis effect. However, this region is displaced to the right in the triangular channel presumably because of a recirculation around a cape on the left side of the entrance, which causes inflow of coastal waters with relatively higher salinity. The triangular channel also allows the development of relatively larger stratification at the estuary mouth, compared to the rectangular channel The direction of the channel extrusion onto the shelf, upshelf or downshelf as in a Kelvinwave sense, plays a lesser role in affecting the salinity pattern at the estuary mouth. Flow patterns in the rectangular channel have a typical two layer circulation : outflow at the surface and inflow near the bottom regardless of whether t he shelf is flat or sloping which agrees with Wong s (1994) results. However, the maximum outflow region migr ates to the middle of the channel in the triangular crosssection. In the cases of upshelf or downshelf turning channel, the flow patterns ar e sim ilar to a combination of the cases with rectangular and triangular sections.

PAGE 152

152 Exploration of width effects on salinity and flow patterns show s that vertically and laterally well mixed conditions can be found in the narrow estuary but not in the wide estuar y As channel width increase s the maximum salinity region moves to the right bottom of the channel thus increasing lateral variations of salinity. T he flow pattern shows a two layer circulation in the narrow channel. If the channel width increase s, the in flow region moves to the right side of estuary, and at some point the inflow region is found throughout the entire bottom following the b athymetry Al though the inflow region changes with channel width, the maximum outflow region changes little, it is loca ted in the middle of the channel. The study of depth effects on salinity patterns shows that lateral gradients in salinity change to vertical gradients as depth increases. In the shallow channel, the maximum salinity region is found on the right side of t he estuary, but it moves down to the thalweg as channel depth increases augmenting also the vertical stratification. In addition, the inflow region can reach the surface at the both shoals in the shallow estuary unlike the pattern in the deep channel. Thi s pattern can be found in the lower Chesapeake B ay (Valle Levinson et al., 2007), which has similar estuary geometry with this idealized study case. Not only the flow patterns but also the offshore plume can be affected by the channel and offshore bathymetry. Chao (1988 a) studied the sloping shelf effect on river forced estuarine plumes and suggested four types of estuarine plumes according to the shape of surface salinity field. H owever, his study only focused in a rectangular channel. None of previous s tudies have focused on the plume pattern in response to channel shape I n this study, several types of channel have been applied. Even for

PAGE 153

153 identical channel shapes, the plume can extend further offshore with a flat shelf than with a sloping shelf. We can f ind this reason from the law of inertia and the Bernoulli effect; if river water meets a sloping shelf at a estuary mouth, it will have wider interface to diverge, and will meet sea water, which has relatively higher inertia than in a flat shelf. In additi on, the plume front over a flat shelf is vertically upright, and it can spread out more radially than over a sloping shelf. The plume formed over a rectangular channel is narrow er than that formed over a triangular channel. If the triangular channel extends toward the shelf, the plume follows the channel and spreads out further offshore, identical to Weaver and Hsieh s study (1987). In addition, the extended channel enhances vertical stratification over the entire domain influenced by freshwater Usually, t he across shelf salinity gradient is positive in a downshelf of the estuary. However, a negative crossshelf salinity gradient will develop if the channel has the same direction as Coriolis : a relatively higher surface salinity region can be located near t he shore and lower salinity offshore over the channel. F or the cases with extended channel s, it becomes apparent that the freshwater plume tends to follow the channel, and remains constrained by the shoulder s of the channel. T he reason for the constraint may be attributed to flow curtain effects i.e., a vertical velocity or large velocity gradient s around the edge of the channel may act as a barrier and prevent plume expansion. Wright (1989) showed that the fronts were most often observed either near sh ore or near the shelf break in a Labrador Shelf since continental slope tended to act as a barrier to cross shelf exchange, and this can be explained by flow curtain effects also. The f reshwater outflow plume normally turns right (downshelf) on it s direc tion upon entering the coastal ocean. However, it can be spread out radially if the estuary width is

PAGE 154

154 narrow. The plume from the wide estuary cannot be located over the northern side of the estuary, as explained by the internal Rossby radius constraint On e of the important driving forces in the estuarine circulation and plume dynamics is the wind. W inds will act as a mixing source (Simpson et al. 1990, 1991; Sharples et al. 1994) or as a source of vertically differentiated transport, or density straining, and increased stratification (Scully et al. 2005). Upwelling favorable winds enhance the offshore expansion of the surface plume, and correspondingly vertical stratification increases offshore. The p lume near the shoreline downshelf of the estuary mouth becomes thin and wide when upwelling favorable winds blow and heavier offshore water is transported onshore along the bottom. However, the reach of the salinity intrusion shows that upwelling or downwelling winds do not act as much in the estuary as o n the shelf shoreline. While upwelling winds flatten the plume (make isopycnal s horizontal) downwelling favorable winds stiffens the plume vertically (make isopycnal s vertical) Offshore and onshore winds have similar effects to upwelling favorable and downwelli ng favorable winds respectively. The reach of salinity intrusion into the estuary shows shorter intrusions under upwelling favorable winds than under a nowind condition. This indicates that the mixing effect by winds is larger than advection in the estuary in these experiment s. In this study, channel width and depth are vari ed to investigate the effect of channel shape. The results show that vertically sheared flow pattern changes into laterally sheared patterns as width increased and depth decreased. However, no definite criteri on was identified because every estuary has different aspect ratios (depth vs width) and these specific aspect ratios cannot represent all estuaries. To overcome

PAGE 155

155 this problem, the lateral bottom slope and depth at the shoals are taken as relevant parameters of the problem In addition, not only the shelf slope but also along channel bottom slope can be an important criteri on for estuary and freshwater plume dynamics. To study the wind effect on the estuary and plume dynamics, only weak wind stress (|w|=0.01 Pa) was used. Future studies should explore the effects of strong er winds. In addition to the appl ication of various wind stresses, other parameters as river discharge and tidal amplitude will be relevant for estuary/ocean ex change hydrodynamics and should be studied. This study focuses on idealized estuary and shelf cases. However, in the real world, estuaries have much more complex bathymetry, curvature, diverse river impact, tidal and open boundary impacts. Thus, compre hensive studies including each boundary impact and comparison to real data from diverse estuaries are needed to understand estuary/ocean transition dynamics.

PAGE 156

156 LIST OF REFERENCES Alenius, P., A. Nekrasov, and K. Myrberg, 2003: Variability of the baroclinic R ossby radius in the Gulf of Finland. Con t. Shelf Res 23 563 573. Allen, S. E., M. S. Dinniman, J. M. Klinck, D. D. Gorby, A. J. Hewett, and B. M. Hickey, 2003: On vertical advection truncation errors in terrainfollowing numerical models: Comparison to a laboratory model for upwelling over submarine canyons. J. Geophys. Res. 108, 16 pp Arakawa, A., and V. R. Lamb, 1977: Computational design of the basic dynamical processes of the UCLA general circulation model. Methods in Computational Physics, 1 7 Academic Press, 173265. Beckmann, A., and D. B. Haidvogel, 1993: Numerical Simulation of Flow around a Tall Isolated Seamount. Part I: Problem Formulation and Model Accuracy. J. Phys. Oceanogr. 23, 17361753. Beckmann, A., and R. Dscher, 1997: A Method for Improved Representation of Dense Water Spreading over Topography in Geopotential Coordinate Models. J. Phys. Oceanogr. 27, 581 591. Blanton, J. O., G. Lin, and S. A. Elston, 2002: Tidal current asymmetry in shallow estuaries and tidal creeks Cont. Shelf Res. 22, 17311743. Blanton, J., and F. Andrade, 2001: Distortion of tidal currents and the lateral transfer of salt in a shallow coastal plain estuary (O esturio do Mira, Portugal). Estuaries and Coasts 24 467 480. Blumberg, A. F. and G. L. Mellor, 1987: A Description of a ThreeDimensional Coastal Ocean Circulation Model, ThreeDimensional Coastal Ocean Models N. Heaps Ed. American Geophysical Union, New York, NY, 208 pp Bowman, M. J. and R. I. Iverson, 1978: Estuar ine and plu me fronts Oceanic fronts and coastal processes M. J. Bowman and W. F. Esaias Ed. Springer Verlag, Berlin 87104. Bowman, M. J., 1978: Spreading and mixing of the Hudson River effluent into the New York Bight, Hydrodynamics of estuaries and fjords: proceedings of the 9th International Lige Colloquium on Ocean Hydrodynamics J. C. J. Nihoul Ed., Elsevier 378368. Brown, J., and A. Davies, 2010: Flood/ebb tidal asymmetry in a shallow sandy estuary and the impact on net sand transport. Geomorphology 114 431 439. Carter, G. S., and M. A. Merrifield, 2007: Open boundary conditions for regional tidal simulations. Ocean Modelling, 18, 194 209.

PAGE 157

157 Casulli, V., and G. Lang, 2004: Mathematical Model UnTRIM User Interface Description. Casulli, V., and R. A. Walters, 2000: An unstructured grid, threedimensional model based on the shallow water equations. International Journal for Numerical Methods in Fluids 32 331348. Casulli, V., and R. T. Cheng, 1992: Semi implicit finite difference methods for t hreedimensional shallow water flow. International Journal for Numerical Methods in Fluids 15 629 648. Chao, S., 1988 a: River Forced Estuarine Plumes. J. Phys. Oceanogr. 18 72 88. Chao, S., 1988 b: WindDriven Motion of Estuarine Plumes. J. Phys Oceanog r. 18 11441166. Chao, S., 1990: Tidal Modulation of Estuarine Plumes. J. Phys. Oceanogr. 20, 11151123. Chao, S., and W. C. Boicourt, 1986: Onset of Estuarine Plumes. J. Phys. Oceanogr. 16 21372149. Chapman, D. C., and S. J. Lentz, 1994: Trapping of a Coastal Density Front by the Bottom Boundary Layer. J. Phys. Oceanogr. 24, 14641479. Chen, C., H. Liu, and R. C. Beardsley, 2003: An Unstructured Grid, FiniteVolume, Three Dimensional, Primitive Equations Ocean Model: Application to Coastal Ocean and Estuaries. Journal of Atmospheric and Oceanic Technology 20, 159 186. Chu, P. C., and C. Fan, 1997: SixthOrder Difference Scheme for Sigma Coordinate Ocean Models. J. Phys. Oceanogr. 27 20642071. Courant, R., K. Friedrichs, and H. Lewy, 1967: On the partial difference equations of mathematical physics. IBM Journal 215 234. Csanady, G. T., 1973: WindInduced Barotropic Motions in Long Lakes. J. Phys. Oceanogr. 3 429438. Csanady, G. T., 1984: Circulation Induced by R iver Inflow in Well Mixed Water over a Sloping Continental Shelf. J. Phys. Oceanogr. 14, 17031711. de Miranda, L., A. Brgamo, and B. de Castro, 2005: Interactions of river discharge and tidal modulation in a tropical estuary, NE Brazil. Ocean Dynamic s, 55, 430 440.

PAGE 158

158 Dean, R. G., and R. A. Dalrymple, 1991: Water Wave Mechanics for Engineers & Scientists (Advanced Series on Ocean EngineeringVol2) World Scientific Publishing Company. Drijfhout, S. S., 1989: Eddy genesis and the related heat transp ort: a parameter study. Mesoscale/synoptic Coherent Structures in Geophysical Turbulence, J.C.J. Nihoul and E. M. Jamart Eds. Elsevier Oceanography Series, 50. 245 263. Dyer, K. R., 1973: Estuaries: A Physical Introduction, John Wiley & Sons, London. Dyer, K. R., 1998: Estuaries: A Physical Introduction, 2E 2nd ed. John Wiley & Sons, Emery, W. J., W. G. Lee, and L. Magaard, 1984: Geographic and Seasonal Distributions of Brunt Visl Frequency and Rossby Radii in the North Pacific and North Atlant ic. J Phys. Oceanogr. 14, 294 317. Ezer, T., H. Arango, A. F. Shchepetkin, 2002: Developments in terrainfollowing ocean models: intercomparisons of numerical aspects. Ocean Modelling, 4 249 267. Feliks, Y., 1985: On the Rossby Radius of Deformati on in the Ocean. J. Phys. Oceanogr. 15, 16051607. Flather, R. A., 1976: A tidal model of the northwest European continental shelf. Memories Society Royal des Sciences de Liege, 6e serie, 10 141 164. Friedrichs, C., and D. Aubrey, 1988: Nonlinear tidal distortion in shallow well mixed estuaries: a synthesis. Estuarine, Coastal and Shelf Science, 27, 521 545. Garvine, R. W., 1974: Physical Features of the Connecticut River Outflow During High Discharge. J. Geophys. Res. 79, PP. 831 846. Garvine, R. W., 1987: Estuary Plumes and Fronts in Shelf Waters: A Layer Model. J Phys. Oceanogr. 17 18771896. Garvine, R. W., 1995: A dynamical system for classifying buoyant coastal discharges. C ont. Shelf Res. 15, 15851596. Garvine, R. W., 1974: Ph ysical Features of the Connecticut River Outflow During High Discharge. J. Geophys. Res. 79, 831 846. Gerdes, R., 1993: A Primitive Equation Ocean Circulation Model Using a General Vertical Coordinate Transformation 1. Description and Testing of the Mo del. J. Geophys. Res. 98, 14,68314,701. Guo, X., and A. Valle Levinson, 2007: Tidal effects on estuarine circulation and outflow plume in the Chesapeake Bay. C ont. Shelf Res. 27 20 42.

PAGE 159

159 Haidvogel, D. B., and Coauthors, 2008: Ocean forecasting in terrain following coordinates: Formulation and skill assessment of the Regional Ocean Modeling System. J. Comput. Phys. 227 35953624. Haidvogel, D. B., H. G. Arango, K. S. Hedstrom, A. Beckmann, P. Malanotte, and A. F. Shchepetkin, 2000: Model evaluati on experiments in the North Atlantic Basin: simulations in nonlinear terrainfollowing coordinates. D yn. Atmos. Oceans 32 239281. Haney, R. L., 1991: On the Pressure Gradient Force over Steep Topography in Sigma Coordinate Ocean Models. J. Phys. Ocea nogr. 21 610 619. Horrevoets, A. C., H. H. G. Savenije, J. N. Schuurman, and S. Graas, 2004: The influence of river discharge on tidal damping in alluvial estuaries. J. Hydrol. 294 213228. Huang, H., C. Chen, G. W. Cowles, C. D. Winant, R. C. Be ardsley, K. S. Hedstrom, and D. B. Haidvogel, 2008: FVCOM validation experiments: Comparisons with ROMS for three idealized barotropic test problems. J. Geophys. Res. 113 14 pp Humphreys, J., S. Franz, and B. Seaman, 1993: Florida's estuaries: A citi zen's guide to coastal living and conservation. Florida Sea Grant College Program, University of Florida, Sea Grant Extension Bulletin 23. Ingram, R. G., Characteristics of the Great Whale River Plume. J. Geophys. Res. 86 20172023. Jay, D. A., and J D. Musiak, 1994: Internal Tidal Asymmetry in Channel Flows: Origins and Consequences. Mixing in Estuaries and Coastal Seas, Coastal and Estuarine Studies 50 211249. Jay, D. A., and J. D. Smith, 1990: Residual Circulation in Shallow Estuaries 1. Hig hly Stratified, Narrow Estuaries. J. Geophys. Res. 95 711 731. Johnson, B. H., R. E. Heath, B. B. Hsieh, K. W. Kim, and H. L. Butler, 1991: User's Guide for a ThreeDimensional Numerical Hydrodynamic, Salinity, and Temperature Model of Chesapeake Bay. (Computer program manual) Department of the Army, Waterways Experiment Station, Corps of Engineers, Vicksburg, MS. Kasai, A., A. E. Hill, T. Fujiwara, and J. H. Simpson, 2000: Effect of the Earth's rotation on the circulation in regions of freshwater in fluence. J. Geophys. Res. 105 16,96116,969.

PAGE 160

160 Kliem, N., and J. D. Pietrzak, 1999: On the pressure gradient error in sigma coordinate ocean models: A comparison with a laboratory experiment. J. Geophys. Res. 104, 29,781 29,799. Kourafalou, V. H., L. Oey, J. D. Wang, and T. N. Lee, 1996: The fate of river discharge on the continental shelf 1. Modeling the river plume and the inner shelf coastal current. J. Geophys. Res. 101 34153434. Lee, J., 2000: A ThreeDimensional Conservative EulerianLagr angian Model for Coastal and Estuarine Circulation. Thesis, University of Florida Lerczak, J. A., and W. Rockwell Geyer, 2004: Modeling the Lateral Circulation in Straight, Stratified Estuaries*. J. Phys. Oceanogr. 34 14101428. Li, C., and J. O'Don nell, 2005: The Effect of Channel Length on the Residual Circulation in Tidally Dominated Channels. J. Phys. Oceanogr. 35 1826 1840. Lindow, H., 1997: Experimentelle Simulationen windangeregter dynamischere Muster in hochauflosenden numerischen Modell en. Meereswissenschaftliche Berichte, 22. Liu, W., M. Hsu, A. Y. Kuo, and J. Kuo, 2001: The Influence of River Discharge on Salinity Intrusion in the Tanshui Estuary, Taiwan. Journal of Coastal Research 17, 544552. Liu, Y., 1988: Two dimensional fi nite difference model for moving boundary hydrodynamic problems. Thesis, University of Florida. Lynch, D. R., and W. G. Gray, 1978: Analytical solutions for computer flow model testing. ASCE Journal of the Hydraulics Division 104 140 --1428. Manoj, N. T., A. S. Unnikrishnan, and D. Sundar, 2009: Tidal Asymmetry in the Mandovi and Zuari Estuaries, the West Coast of India. Journal of Coastal Research 25, 11871197. Martin, P. J., G. Peggion, and K. J. Yip, 1998: A Comparison of Several Coastal Ocean Mo dels Naval Research Laboratory, Oceanography Division, Stennis Space Center, MS 395295004, McCalpin, J. D., 1994: A comparison of secondorder and fourthorder pressure gradient algorithms in a sigmaco ordinate ocean model. International Journal for Nu merical Methods in Fluids 18 361 383. Mellor, G. L., 1996: Introduction to physical oceanography Springer, 285 pp.

PAGE 161

161 Mellor, G. L., 2004: USERS GUIDE for A THREE DIMENSIONAL, PRIMITIVE EQUATION, MNUMERICAL OCEAN MODEL. Mellor, G. L., L. Oey, and T. Ezer, 1998: Sigma Coordinate Pressure Gradient Errors and the Seamount Problem. J. Atmos. Oceanic Technol. 15 1122 1131. Mellor, G., T. Ezer, and L. Oey, 1994: The Pressure Gradient Conundrum of Sigma Coordinate Ocean Models. J. Atmos. Oceanic Technol. 11 11261134. Mertz, G., Y. Gratton, and J. A. Gagne, 1990: Properties of Unstable Waves in the Lower St. Lawrence Estuary. Atmos Ocean, 28, 230240. Miranda, L. B., A. L. Brgamo, and B. M. Castro, 2005: Interactions of river discharge and tidal modulation in a tropical estuary, NE Brazil. Ocean Dynamics 55, 430 440. Mori, N., 2007: ROMS Memorandum Open Boundary Condition. http://sauron.urban.eng.osaka cu.ac.jp/%7Emori/research/ROMS/roms_obc.pdf ODonnell, J., 2010: The Dynamics of Estuary Plumes and Fronts. Contemporary Issues In Estuarine Physics A. Valle Levinson, Ed., Cambridge University Press. Pattiaratchi, C., 1996: Mixing in estuaries and c oastal seas American Geophysical Union, 524 pp. Pinet, P. R., 2003: Invitation to Oceanography, Third Edition. 3rd ed. Jones and Bartlett Publishers, Inc., Pritchard, D. W., 1952: Salinity Distribution and Circulation in the Chesapeake Bay Estuarine system. J Mar. Res. 11, 106 123. Pritchard, D. W., 1955: Estuarine Circulation Patterns. Amer. Soc. Civ. Eng. 81 Pritchard, D. W., 1956: The Dynamic Structure of a Coastal Plain Estuary. J. Mar. Res. 15, 33 42. Pritchard, D.W., 1967: What is an estuary: physical viewpoint. Estuaries G. H. Lauff, Ed., AAAS Publication 83, Washington, DC, 35. Rossby, C. G., 1938: On the mutual adjustment of pressure and velocity distributions in certain simple current systems, II. J. Mar. Res. I/3, 239 263 Scully, M. E., and C. T. Friedrichs, 2007: The Importance of Tidal and Lateral Asymmetries in Stratification to Residual Circulation in Partially Mixed Estuaries*. J. Phys. Oceanogr. 37, 14961511.

PAGE 162

162 Scully, M., C. Friedrichs, and J. Brubaker, 2005: Co ntrol of estuarine stratification and mixing by wind induced straining of the estuarine density field. Estuaries and Coasts 28, 321 326. Sharples, J., J. H. Simpson, and J. M. Brubaker, 1994: Observations and Modelling of Periodic Stratification in the Upper York River Estuary, Virginia. Estuarine, Coastal and Shelf Science 38, 301 312. Shchepetkin, A. F., and J. C. McWilliams, 2003: A method for computing horizontal pressuregradient force in an oceanic model with a nonaligned vertical coordinate. J. Geophys. Res. 108 34 pp. Shchepetkin, A. F., and J. C. McWilliams, 2005: The regional oceanic modeling system (ROMS): a split explicit, free surface, topography following coordinate oceanic model. Ocean Modelling, 9 347 404. Sheng, Y. P., B. Tu tak, J. R. Davis, and V. Paramygin, 2008: Circulation and Flushing in the Lagoonal System of the Guana Tolomato Matanzas National Estuarine Research Reserve (GTMNERR), Florida. Journal of Coastal Research 55, 9 25. Simpson, J. H., J. Brown, J. Matthews, and G. Allen, 1990: Tidal Straining, Density Currents, and Stirring in the Control of Estuarine Stratification, Estuaries 13, 125132. Simpson, J. H., J. Sharples, and T. P. Rippeth, 1991: A prescriptive model of st ratification induced by freshwater runoff. Estuarine, Coastal and Shelf Science 33, 23 35. Simpson, J., J. Brown, J. Matthews, and G. Allen, 1990: Tidal straining, density currents, and stirring in the control of estuarine stratification. Estuaries and Coasts 13, 125132. Song, Y., and D. Haidvogel, 1994: A semi implicit ocean circulation model using a generalized topography following coordinate system. J. Comput. Phys. 115 228244. Speer, P. E., and D. G. Aubrey, 1985: A study of nonlinear tidal propagation in shallow inlet/estuarine systems Part II: Theory. Estuarine, Coastal and Shelf Science 21 207224. Stewart, R. H., 2009: Introduction to Physical Oceanography Orange Grove Texts Plus. The effect of channel length on the residual circulation in tidally dominated channels. http://cat.inist.fr/?aModele=afficheN&cpsidt=17296980 (Accessed June 4, 2010).

PAGE 163

163 Valle Levinson, A., 2008: Density driven exchange flow in terms of the Kelvin and Ekman numbers. J Geophys. Res. 113. Valle Levinson, A., and K. M. M. Lwiza, 1995: The effects of channels and shoals on exchange between the Chesapeake Bay and the adjacent ocean. J. Geophys. Res. 100 1855118563. Valle Levinson, A., C. Reyes, and R. Sanay, 2003: Effects of Bathymetry, Friction, and Rotation on Estuary Ocean Exchange. J. Phys Oceano gr. 33 2375. Valle Levinson, A., K. Holderied, C. Li, and R. J. Chant, 2007: Subtidal flow structure at the turning region of a wide outflow plume. J. Geophys. Res. 112 18 pp Versteeg, H., and W. Malalasekra, 1996: An Introduction to Computational Fluid Dynamics: The Finite Volume Method Approach 1st ed. Prentice Hall. Weaver, A. J., and W. W. Hsieh, 1987: The Influence o f Buoyancy Flux from Estuaries on Continental Shelf Circulation. J Phys. Oceanogr. 17 2127 2140. Winant, C. D., 2004: Three Dimensional Wind Driven Flow in an Elongated, Rotating Basin. J. Phys. Oceanogr. 34 462476. Winant, C. D., 2007: Three D imensional Tidal Flow in an Elongated, Rotating Basin. J. Phys. Oceanogr. 37 23452362. Winant, C. D., 2008: Three Dimensional Residual Tidal Circulation in an Elongated, Rotating Basin. J. Phys. Oceanogr. 38 12781295. Winton, M., R. Hallberg, a nd A. Gnanadesikan, 1998: Simulation of Density Driven Frictional Downslope Flow in Z Coordinate Ocean Models. J Phys. Oceanogr. 28, 21632174. Wong, K., 1994: On the nature of transverse variability in a coastal plain estuary. J. Geophys. Res. 99 1 4,20914,222. Wright, D. G., 1989: On the Alongshelf Evolution of an Idealized Density Front. J. Phys. Oceanogr. 19, 532 541. Yankovsky, A. E., and D. C. Chapman, 1997: A Simple Theory for the Fate of Buoyant Coastal Discharges*. J Phys. Oceanogr. 27 13861401. Zhang, Y., A. M. Baptista, and E. P. Myers, 2004: A cross scale model for 3D baroclinic circulation in estuary plumeshelf systems: I. Formulation and skill assessment. C ont. Shelf. Res. 24, 21872214.

PAGE 164

164 BIOGRAPHICAL SKETCH Jungwoo Lee was born in 1976 (in the lunar calendar ) and grew up in Hongsung in South Korea. He went to the Environmental Engineering Department of Chungnam National University (CNU), Daejeon, South Korea in March 1995. In February 2003, he completed his undergraduate degree in the Environmental Engineering D epartment of CNU. T h en, he continued his higher study in the graduate school of CNU After received Master of Engineering degree, he entered the University of Florida to study more. He had spent four years as a g raduate research assistant and earned his doctorate from the University of Florida in 2010.