Environmental Fluid Dynamics

Dedication

Preface

Acknowledgments

Chapter 1. Physical Quantities, Dimensional Analysis, Scaling and Bulk Conservation Equations

1.1 Physical Quantities

1.2 Dimensional Analysis

1.3 Fluid Properties

1.4 Flow Domains, Scaling and Modeling

1.5 Dynamic Similarity

1.6 Hydrostatic Pressure

1.7 Pressure Forces on a Surface

1.8 Control Volumes

1.9 Introduction to the Kinematics of Flow

1.10 Bulk Conservation of Mass

1.11 Bulk Conservation of Momentum

1.12 Bulk Conservation of Energy

1.13 Solving Problems Using the Conservation Laws

Chapter 2. Equations of Motion: Axiomatic Approach

2.1 Conservation of Mass

2.2 The Stress Tensor

2.3 Conservation of Linear Momentum

2.4 Conservation of Angular Momentum and the Symmetry of the Stress Tensor

2.5 Conservation of Energy

2.6 The Second Law of Thermodynamics

2.7 The Navier–Stokes Constitutive Equations

2.8 Some Thermodynamic Considerations

2.9 The Temperature Equation

2.10 The Solute Equation

2.11 Shallow Layer Approximations

2.12 The Vorticity Equation

2.13 Introduction to Some Statistics Concepts

2.14 Mean Momentum and Transport Equations for Turbulent Flow

2.15 Turbulent Kinetic Energy and Transport Equations

2.16 Scaling the Equation of Motion: Limiting Cases

References

Chapter 3. Some Exact Solutions

3.1 Fundamental Scales and Processes

3.2 Plane Couette Flow

3.3 Plane Poiseuille Flow

3.4 Superposition of Plane Flows

3.5 Unsteady Parallel Flow: Diffusion of Vorticity

3.6 Oscillating Boundary Layer

3.7 Natural Convection in a Long Cavity

3.8 Natural Convection in a Sloping Cavity

Chapter 4. Effect of Viscosity

4.1 Flow Around a Sphere at Low Reynolds Number

4.2 Porous Media Flow

4.3 Boundary Layer Flow

4.4 Adverse and Favorable Pressure Gradients

4.5 Flow Around a Cylinder with Increasing Reynolds Number

4.6 Flow Around a Cylinder with Circulation

4.7 Flow About a Cylinder in an Accelerating Flow

4.8 Forces on a Cylinder in a Combined Flow Regime

4.9 Shallow Viscous Flows

References

Chapter 5. Fundamentals of Hydraulics

5.1 Simple Jets

5.2 Simple Plume

5.3 Buoyant Jet

5.4 Round Buoyant Jet Discharging into a Stratified Shear Flow

5.5 Scales in Turbulent Flows

5.6 Turbulent Flow in a Smooth Pipe

5.7 Turbulent Flow in a Rough Pipe

5.8 Classification of Open Channel Flow

5.9 Uniform Flow

5.10 Velocity Profile in a Wide Channel with Uniform Flow

5.11 Hydraulic Jump and Specific Energy

5.12 Gradually Varied Flow

References

Chapter 6. Environmental Hydraulics

6.1 Gradually Varied Two Layer Flow

6.2 Rapidly Varied Two Layer Flow: Internal Hydraulic Jump

6.3 Surface Layer Hydraulics

6.4 Meteorological Boundary Layer

6.5 Gravity Current Hydraulics

6.6 Selective Withdrawal

6.7 Unsteady Sink Flow in a Linearly Stratified Fluid Contained in a Horizontal Duct: Shear Waves

References

Chapter 7. Mixing in Environmental Flows

7.1 Turbulence in a Stratified Shear Flow

7.2 The Kinematics of Dispersion

7.3 Fundamental Solution of the Diffusion Equation

7.4 Shear Dispersion

7.5 Longitudinal Dispersion in a Pipe

References

Chapter 8. Surface Waves

8.1 2D Long Surface Waves

8.2 Linear Surface Waves

8.3 Reflection and Transmission of Surface Waves

References

Chapter 9. Environmental Flows

9.1 Long Internal Waves: Two-layer Case

9.2 Internal Wave Modes

9.3 Plane Internal Kelvin Wave

9.4 Poincaré Waves in a Two-Layer System

9.5 Geostrophic Motion in a Two-layer system

9.6 Geostrophic Flow in a Continuously Stratified Fluid

9.7 Wedderburn and Lake Numbers

9.8 Three-Layer Forced Motions

9.9 Linear Waves in a Stratified Fluid

9.10 Internal Waves and Internal Modes

9.11 Internal Waves in a Domain at Variable Depth

9.12 Reflection from a Sloping Wall

Reference

Appendix 1. Mathematical Preliminaries

Index