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Table of Contents
Preface; Acknowledgements; Contents; 1 Introduction; 1.1 Aim and Scope; 1.2 Hydrostatic and Non-hydrostatic Free Surface Flows; 1.3 Historical Background; 1.4 Non-hydrostatic Flows and Environmental Mechanics; 1.5 Methodology; References; 2 Vertically Integrated Non-hydrostatic Free Surface Flow Equations; 2.1 Introduction; 2.2 Vertically Integrated Equations in Continuum Mechanical Description; 2.2.1 Basic Conservation Laws; 2.2.2 Depth-Integrated Continuity Equation; 2.2.3 Depth-Integrated Momentum Equations in Horizontal Plane
2.2.4 Non-hydrostatic Stresses in z-Direction and Vertical Velocity Profile2.3 Shallow Flow Approximation and Depth-Averaged Equations; 2.4 Simplified Forms of Non-hydrostatic Extended Flow Equations; 2.4.1 RANS Model for River Flow; 2.4.2 One-Dimensional Water Waves Over Horizontal Topography; 2.4.3 Turbulent Uniform Flow on Steep Terrain; 2.4.4 Flows Over Curved Beds; 2.4.5 Enhanced Gravity; 2.4.6 Non-hydrostatic Model Including Friction Effects; 2.5 Sediment Transport and Movable Beds; 2.5.1 Introduction; 2.5.2 Non-hydrostatic Unsteady Free Surface Flow with Bed-Load Sediment Transport
2.6 Numerical Methods for Boussinesq-Type Models2.6.1 Unsteady Flow Simulations; 2.6.2 Steady Flow Simulations; 2.7 Higher-Order Equations; 2.7.1 Fawer-Type Equations; 2.7.2 Moment Equations; References; 3 Inviscid Channel Flows; 3.1 Introduction; 3.2 Potential Flow Theory; 3.2.1 Fundamentals; 3.2.2 Conservation Laws; 3.2.3 Flow Net; 3.3 Picard Iteration; 3.3.1 General Aspects of Iterative Solutions; 3.3.2 Second-Order Velocity Field; 3.3.3 Third-Order Velocity Field; 3.4 Approximate Treatment of Flow Net Geometry; 3.4.1 Velocity Profile; 3.4.2 Extended Equations
3.7.5 Determination of Velocity and Pressure Distributions3.8 Free Overfall; 3.8.1 Picard Iteration; 3.8.2 Curvilinear Flow at the Brink Section; 3.8.3 Moment of Momentum Method; 3.8.4 Two-Dimensional Solution; 3.8.5 Flow Net; 3.9 Transition from Mild to Steep Slopes; 3.9.1 Picard Iteration; 3.9.2 Two-Dimensional Solution; 3.9.3 Flow Net; 3.10 Flow Over Round-Crested Weirs; 3.10.1 Picard Iteration; 3.10.2 Dressler's Theory; 3.10.3 Two-Dimensional Solution; 3.10.4 Flow Nets; 3.11 Sharp-Crested Weir; 3.11.1 Critical Flow; 3.11.2 Profile of High Dams; 3.12 Critical Flow Over Weir Profiles
2.2.4 Non-hydrostatic Stresses in z-Direction and Vertical Velocity Profile2.3 Shallow Flow Approximation and Depth-Averaged Equations; 2.4 Simplified Forms of Non-hydrostatic Extended Flow Equations; 2.4.1 RANS Model for River Flow; 2.4.2 One-Dimensional Water Waves Over Horizontal Topography; 2.4.3 Turbulent Uniform Flow on Steep Terrain; 2.4.4 Flows Over Curved Beds; 2.4.5 Enhanced Gravity; 2.4.6 Non-hydrostatic Model Including Friction Effects; 2.5 Sediment Transport and Movable Beds; 2.5.1 Introduction; 2.5.2 Non-hydrostatic Unsteady Free Surface Flow with Bed-Load Sediment Transport
2.6 Numerical Methods for Boussinesq-Type Models2.6.1 Unsteady Flow Simulations; 2.6.2 Steady Flow Simulations; 2.7 Higher-Order Equations; 2.7.1 Fawer-Type Equations; 2.7.2 Moment Equations; References; 3 Inviscid Channel Flows; 3.1 Introduction; 3.2 Potential Flow Theory; 3.2.1 Fundamentals; 3.2.2 Conservation Laws; 3.2.3 Flow Net; 3.3 Picard Iteration; 3.3.1 General Aspects of Iterative Solutions; 3.3.2 Second-Order Velocity Field; 3.3.3 Third-Order Velocity Field; 3.4 Approximate Treatment of Flow Net Geometry; 3.4.1 Velocity Profile; 3.4.2 Extended Equations
3.7.5 Determination of Velocity and Pressure Distributions3.8 Free Overfall; 3.8.1 Picard Iteration; 3.8.2 Curvilinear Flow at the Brink Section; 3.8.3 Moment of Momentum Method; 3.8.4 Two-Dimensional Solution; 3.8.5 Flow Net; 3.9 Transition from Mild to Steep Slopes; 3.9.1 Picard Iteration; 3.9.2 Two-Dimensional Solution; 3.9.3 Flow Net; 3.10 Flow Over Round-Crested Weirs; 3.10.1 Picard Iteration; 3.10.2 Dressler's Theory; 3.10.3 Two-Dimensional Solution; 3.10.4 Flow Nets; 3.11 Sharp-Crested Weir; 3.11.1 Critical Flow; 3.11.2 Profile of High Dams; 3.12 Critical Flow Over Weir Profiles