ابراهيم صالح محمد المعتاز

Ioannis Tsanis, , Jian Wu, Huihua Shen and Caterina Valeo, "Environmental Hydraulics: Hydrodynamic and Pollutant Transport Models of Lakes and Coastal Waters (Developments in Water Science), Elsevier Science Publishing Company, 2007.

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Book Outline

Preface

Chapter 1.

Introduction

1.1. Enviromental Hydraulics

1.2. Methodology¹

1.2.1. Field Studies

1.2.2. Laboratory Experiments

1.2.3. Numerical Modelling

Chapter 2.

The Mathematical Theory of Circulation Models

2.1. Governing Equations

2.2. Basic Assumptions

2.2.1. Incompressible Approximation

2.2.2. Hydrostatic Approximation

2.2.3. Boussinesq Approximation

2.3. Turbulence Closure

2.3.1. Turbulence Parameterization

2.3.2. Boussinesq's Eddy Viscosity²

2.3.3. Prandtl's Mixing Length

2.3.4. One-Equation, or k−L₀ Model of Turbulence

2.3.5. Two-Equation or k−ε Model of Turbulence

2.3.6. Large Eddy Simulation

Continuity equation

Momentum equation

Temperature equation

2.4. Boundary and Initial Conditions

2.4.1. Boundary Conditions at the Surface (z=ζ)

2.4.2. Boundary Conditions at the Bottom

2.4.3. Lateral Boundary Conditions

2.4.4. Open Boundary Conditions

2.4.5. Initial Conditions

2.5. Circulation Theory

2.5.1. Long-Wave Theory

2.5.2. Shear-Induced Countercurrent Flow Theory

2.6. Model Considerations

2.6.1. Baroclinic Terms

2.6.2. Advection Terms

2.6.3. Bottom Shear Stress Terms

2.6.4. Rigid-Lid Approximation

2.7. Finite Difference Method

Chapter 3.

The Vertically Integrated Two-Dimensional Models

3.1. Governing Equations

Continuity equation

Momentum equations

3.2. Numerical Methods

3.2.1. Explicit Method

Momentum equation in the x-direction

Momentum equation in the y-direction

Continuity equation

3.2.2. ADI Method

Double-sweep method

3.2.3. Operator-Splitting Method

First fractional step

Second fractional step

First fractional step

Second fractional step

3.3. Numerical Experiments

3.3.1. Computational Conditions

3.3.2. Horizontal Circulation

3.3.3. Comparison of Numerical Methods

Chapter 4.

Three-Dimensional Circulation Models

4.1. A Vertical–Horizontal Splitting 3D Model

4.1.1. Model Equations in the σ-Coordinate System

4.1.2. Fractional Step Method for the 3D Model³

4.1.3. Grid Discretization and Finite Difference Representation

4.1.4. Numerical Scheme for the Advection Step

4.1.5. Implicit Scheme for the Vertical Eddy Diffusion Step

4.1.6. Numerical Scheme for the Temperature Equation

4.2. An External Internal 3D Model (Princeton Model)

4.3. An Operator-Splitting 3D Model

4.3.1. First Fractional Step

Momentum equation

Temperature equation

Momentum equation

Temperature equation

Temperature equation

4.3.2. Second Fractional Step

4.3.3. Third Fractional Step

4.4. Control Volume 3D Model (IDOR)

4.4.1. Momentum Equation

Temporal difference

Spatial difference

Advective terms

Pressure term

Coriolis and Diffusive Terms

4.4.2. Equation of Temperature

Advective terms

Diffusive terms

Production term

4.4.3. Continuity Equation

4.4.4. Calculation Procedures

Implicit scheme

Explicit scheme

4.4.5. Numerical Experiments with the IDOR 3D Model

Non-stratified cases

Computational conditions

Simulation results and discussions

Stratified cases

Computational conditions

Simulation results and discussions

4.5. Fully Three-Dimensional Model

4.5.1. Approximation of Hydrostatic Pressure

4.5.2. Procedure of Numerical Calculation

4.5.3. Numerical Example

4.6. Large Eddy Simulation Model

4.6.1. An Application of the LES Model

4.6.2. Comparison of LES and Non-LES Analysis

Chapter 5.

Quasi-Three-Dimensional Circulation Models

5.1. Q3D Model⁴

5.2. Vertical Eddy Viscosity Distribution

5.3. Vertical–Horizontal Integrating (VHI) 3D Model

5.3.1. Model Development

Condition 1

Condition 2

Condition 3

5.3.2. Characteristics of the VHI3D Model

5.3.3. Model Verifications with Analytical and Laboratory Data

Comparisons with analytical solutions

Verification with laboratory data

Sensitivity study of parameters

5.3.4. Model Comparison in a Simplified Basin

Computational conditions

Simulated results and model comparison

Chapter 6.

Particle Trajectory Models and Pollutant Transport Models

6.1. Particle Trajectory Models

6.1.1. A Second-Order Lagrangian Trajectory Model

6.1.2. A Random-Walk Approach

6.2. Numerical Schemes for the 2D Pollutant Transport Models

6.2.1. Explicit Scheme

6.2.2. First-Order Upwind Scheme

6.2.3. McCormack Two-Step Scheme

6.2.4. Quick Scheme

6.2.5. Sharp Scheme

6.2.6. Comparison of Numerical Schemes

6.3. Numerical Schemes for the 3D Pollutant Transport Model

Chapter 7.

Numerical Analysis of Coarse-Fine Grid Model

7.1. An Approach to Modelling Nearshore Areas⁵

7.2. Algorithm for Coupling the Coarse and Fine Grids

7.3. Applications of the Coarse-Fine Grid Model to Hamilton Harbour

7.3.1. Introduction

7.3.2. Horizontal Mixing Times in Hamilton Harbour

7.3.3. A Nested-Grid Model of Hamilton Harbour

7.3.4. Circulation Modelling in the Three Nearshore Areas

7.3.5. Remedial Measures

7.4. Toronto Waterfront⁶

7.4.1. Coarse-Grid and Fine-Grid Model Comparisons

7.5. Lake Biwa

7.5.1. A Comparison with a Uniform Grid Model

Chapter 8.

Model Verifications With Analytical Solutions And Laboratory Data

8.1. Pollutant Transport and Residence Time in a Model Basin⁷

8.1.1. A Physical Model of Windermere Basin

8.1.2. Numerical Modelling of Circulation Pattern

8.1.3. Numerical Modelling of Dye Transport

8.1.4. Numerical Study of Residence Time

8.1.5. Numerical Tracer Test

8.1.6. Methods of Increasing Residence Time

8.2. Study of Wind-Induced Flows⁸

8.2.1. Model Comparison with Analytical Solutions

Analytical solution for steady laminar flow

A new analytical solution for steady shear-induced turbulent flow

8.2.2. Model Verification with Experimental Data

8.2.3. Numerical Experiments

Effect of eddy viscosity

Effect of vertical discretization

Developing shear-induced turbulent flow

Wind-induced set-up

Seiche

Chapter 9.

Model Applications to the Great Lakes

9.1. General Circulation in the Great Lakes

9.1.1. Wind-Induced Circulation Patterns

9.1.2. Wind-Induced Set-Up in Lake Ontario

9.2. Bacterial Transport of the St. Clair River in Sarnia⁹

9.2.1. Circulation and Pollutant Transport in Sarnia Bay

9.2.2. Duration of the Aftereffects of Bacteria Releases

9.2.3. Sensitivity Analysis

9.2.4. Model Verification

9.2.5. Remedial Measures

9.3. Toronto Waterfront Receiving Water Study¹⁰

9.3.1. Field Study

9.3.2. Model Results

Case 1 (July 17–20)

Case 2 (September 19–22)

9.4. Hamilton Harbour Study

9.4.1. Verification with Current Meter Data

9.4.2. Verification with Drogue Data

9.4.3. Verification with Water-Level Data

9.5. Cootes Paradise Study

9.5.1. Current Patterns and Pollutant Transport

Long-term simulations

9.6. Lake St. Clair Study¹¹

9.6.1. Typical Circulation Patterns

9.6.2. Current-Induced Wave Refraction

9.7. Lake Simcoe Study

9.8. Little Lake and Crary Park Marina Study¹²

9.8.1. Circulation Patterns in Little Lake

9.8.2. Circulation Patterns in the Crary Park Marina

9.8.3. Analysis of Sediment Movement

9.8.4. Results and Discussion

Chapter 10.

Model Applications To Other Lakes And Coastal Waters

10.1. Model Application in Gretan Pelagos (Mediterranean Sea)

10.1.1. Northern Crete Waterfront

10.1.2. Princeton Model versus IDOR Model

10.2. Model Applications to Lake Biwa

10.2.1. Barotropic Flow

10.2.2. Baroclinic Flow

10.2.3. Internal Kelvin Wave

10.2.4. Flows during Destratification Period

10.2.5. Comparison of Numerical Methods

10.2.6. Density Current between the South and North Basins

Computational conditions

10.2.7. Flows Near the Inflow Estuaries

Yasu River

Ane River

Chapter 11.

The Future In Hydrodynamic Modelling

11.1. Environmental Information Systems (EIS)

Appendix.

Documentation of a Two-Dimensional Circulation Model

Inputs

Program Execution

Source Code

Disclaimer

References