Free-surface flow: shallow-water dynamics

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Content: Intro Title page Table of Contents Copyright Dedication Prologue References Chapter 1: Basic Concepts Abstract 1.1. Introduction 1.2. Surfaces in Three-Dimensional Space 1.3. Initial and Boundary-Value Problems 1.4. Classification of Partial Differential Equations Problems References Chapter 2: Air-Water Interface Abstract 2.1. Introduction 2.2. Surface Tension 2.3. Free Surface Boundary Conditions 2.4. Simple Viscous Flows With a Free Surface 2.5. Transfer Processes at the Air-Water Interface 2.6. Atmospheric Surface Layer 2.7. Storm Surge. 2.8. Large Scale Interface DisturbancesProblems References Chapter 3: Gravity Waves Abstract 3.1. Introduction 3.2. Small-Amplitude Gravity Waves 3.3. Two-Dimensional Oscillatory Waves 3.4. Airy's Theory for Gravity Waves 3.5. Dispersion of Non-sinusoidal Waves 3.6. Superposition of Linear Gravity Waves 3.7. Seiches 3.8. Mass Transport by Gravity Waves 3.9. Progressive Wave Energy 3.10. Group Velocity 3.11. Wave Refraction 3.12. Wave Diffraction 3.13. Wave Breaking Problems References Chapter 4: Shallow-Water Approximation Abstract 4.1. Introduction. 4.2. Shallow-Water Equations4.3. Waves in Shallow Water 4.4. Dispersion Relations for Nonlinear Waves 4.5. Higher-Order Long-Wave Approximation 4.6. The Boussinesq Equations 4.7. Long Waves in Trapezoidal Channels 4.8. The Serre Equations 4.9. The Korteweg-De Vries Equation 4.10. Hamiltonian Approach to Water Waves Problems References Chapter 5: Tidal Forcing Abstract 5.1. Introduction 5.2. Equilibrium Theory of Tides 5.3. Dynamic Theory of Tides 5.4. Harmonic Analysis and Tide Prediction Problems References Chapter 6: Long Waves Abstract 6.1. Introduction. 6.2. Flow in One-Dimensional Channels6.3. Integral Relations 6.4. The Saint-Venant Equations 6.5. Energy Considerations in an Open Channel 6.6. Vector Representation 6.7. Further Simplifications 6.8. Linearized Equations 6.9. Symmetric Equations 6.10. Steady, Non-uniform Flow 6.11. Shallow-Water Flow in Two Space Dimensions Problems References Chapter 7: Channel Transitions Abstract 7.1. Introduction 7.2. Regimes of Steady Flow 7.3. Nearly-Horizontal Flow 7.4. Transitions in Geometry and Bathymetry 7.5. Flow Under a Vertical Sluice Gate 7.6. Flow Over a Smooth Bottom Ridge. 7.7. The Specific Energy7.8. Critical Velocity and Gravity Wave Speed 7.9. The Froude Number 7.10. Critical Flow in Channels of Arbitrary Cross-Sectional Shape 7.11. Subcritical Flow Over a Smooth Ridge 7.12. Flow Through a Smooth Transition in Width 7.13. Downstream Control -- Formation of a Hydraulic Jump 7.14. The Specific Force 7.15. Fluid Force on Transition Structures 7.16. Other Rapidly-Varied Flow Transitions Problems References Chapter 8: Channel Bed Resistance Abstract 8.1. Introduction 8.2. Uniform Flow in a Sloping Channel 8.3. Logarithmic Velocity Profiles.