Water Wave Mechanics for Engineers and Scientists

The following sections are included:

• Contents

• Preface

The following sections are included:

• Introduction

• Characteristics of Waves

• Historical and Present Literature

The following sections are included:

• Introduction

• Review of Hydrodynamics
  • Conservation of Mass
  • Surface Stresses on a Particle
  • The Translational Equations of Motion

• Review of Vector Analysis
  • The Dot Product
  • The Cross Product
  • The Vector Differential Operator and the Gradient
  • The Divergence
  • The Curl
  • Line Integrals
  • Velocity Potential
  • Stream Function
  • Streamline
  • Relationship between Velocity Potential and Stream Function

• Cylindrical Coordinates

• The Bernoulli Equation

• References

• Problems

The following sections are included:

• Introduction

• Boundary Value Problems
  • The Governing Differential Equation
  • Boundary Conditions

• Summary of the Two-Dimensional Periodic Water Wave Boundary Value Problem

• Solution to Linearized Water Wave Boundary Value Problem for a Horizontal Bottom
  • Separation of Variables
  • Application of Boundary Conditions
  • Summary of Standing Waves
  • Progressive Waves
  • Waves with Uniform Current U₀
  • The Stream Function for Small-Amplitude Waves

• Appendix: Approximate Solutions to the Dispersion Equation

• References

• Problems

The following sections are included:

• Introduction

• Water Particle Kinematics for Progressive Waves
  • Particle Velocity Components
  • Particle Displacements

• Pressure Field Under a Progressive Wave

• Water Particle Kinematics for Standing Waves
  • Velocity Components
  • Particle Displacements

• Pressure Field Under a Standing Wave

• Partial Standing Waves

• Energy and Energy Propagation in Progressive Waves
  • Potential Energy
  • Kinetic Energy
  • Energy Flux

• Transformation of Waves Entering Shallow Water
  • The Conservation of Waves Equation
  • Refraction
  • Conservation of Energy
  • Waves Breaking in Shallow Water

• Wave Diffraction
  • Diffraction Due to Wave–Structure Interaction

• Combined Refraction–Diffraction

• References

• Problems

The following sections are included:

• Introduction

• Asymptotic Long Waves

• Long Wave Theory
  • Continuity Equation
  • Equations of Motion
  • The Energy and Energy Flux in a Long Wave

• One-Dimensional Tides in Idealized Channels
  • Co-oscillating Tide
  • Channels with Variable Cross Sections

• Reflection and Transmission Past an Abrupt Transition
  • Seiching

• Long Waves with Bottom Friction
  • Standing Waves with Frictional Damping
  • Progressive Waves with Frictional Damping

• Geostrophic Effects on Long Waves
  • Amphidromic Waves in Canals

• Long Waves in Irregular-Shaped Basins or Bays

• Storm Surge
  • Bathystrophic Storm Tide

• Long Waves Forced by a Moving Atmospheric Pressure Disturbance

• Long Waves Forced by a Translating Bottom Displacement

• References

• Problems

The following sections are included:

• Introduction

• Simplified Theory for Plane Wavemakers in Shallow Water

• Complete Wavemaker Theory for Plane Waves Produced by a Paddle
  • Planar Wave Energy Absorbers
  • Three-Dimensional Wavemakers

• Cylindrical Wavemakers

• Plunger Wavemakers

• References

• Problems

The following sections are included:

• Introduction

• Wave Height Distributions
  • Single Wave Train
  • Wave Groups
  • Narrow-Banded Spectra: The Rayleigh Distribution
  • The Rayleigh Probability Density Function

• The Wave Spectrum
  • Spectral Analysis
  • Fourier Analysis
  • Complex Series Representations
  • Covariance Function
  • Power Spectrum
  • The Continuous Spectrum

• The Directional Wave Spectrum

• Time-Series Simulation

• Examples of Use of Spectral Methods to Determine Momentum Flux
  • Measurement of S_xy in Shallow Water

• References

• Problems

The following sections are included:

• Introduction

• Potential Flow Approach
  • Steady Flow Term
  • Unsteady Flow

• Forces Due to Real Fluids
  • The Morison Equation
  • Total Force Calculation
  • Methodology for Determining Drag and Inertia Coefficients
  • Wave Forces on Pipelines Resting on the Seafloor
  • Relative Importance of Drag and Inertia Force Components
  • Maximum Total Force on an Object

• Inertia Force Predominant Case
  • Rigorous and Approximate Analytical Methods for Wave Loading on Large Objects
  • Numerical Methods for Wave Loading on Large Object of Arbitrary Shapes
  • Analytical Methods for Impulsive Loading on a Large Circular Cylinder
  • Forces Due to Impulsive Motions of Large Structures of Arbitrary Shape

• Spectral Approach to Wave Force Prediction

• References

• Problems

The following sections are included:

• Introduction

• Waves Over Smooth, Rigid, Impermeable Bottoms
  • Laminar Boundary Layer
  • Turbulent Boundary Layers

• Water Waves Over a Viscous Mud Bottom
  • Water Wave Region
  • Mud Region

• Waves Over Rigid, Porous Bottoms

• References

• Problems

The following sections are included:

• Introduction

• Mass Transport and Momentum Flux
  • Eulerian Mass Transport
  • Lagrangian Mass Transport

• Mean Water Level

• Mean Pressure

• Momentum Flux

• Summary

• References

• Problems

The following sections are included:

• Introduction

• Perturbation Approach of Stokes
  • Linear Equation and Boundary Conditions
  • Nonlinear Boundary Conditions
  • First-Order Perturbation Equations
  • Second-Order Perturbation Equation

• The Stream Function Wave Theory
  • Formulation and Solution

• Finite-Amplitude Waves in Shallow Water
  • The Solitary Wave
  • Cnoidal Wave Theory

• The Validity of Nonlinear Wave Theories

• References

• Problems

The following sections are included:

• Introduction

• Required Equipment
  • Wave Tank
  • Wave Gages and Recording Equipment
  • Velocity Sensor
  • Pressure Sensor
  • Wave Forces

• Experiments
  • Experiment 1: Wave Length, Profile, and Group Velocity as a Function of Wave Period, Water Depth, and Wave Height
  • Experiment 2: Wave Profiles and Particle Trajectories as Functions of Wave Height, Water Depth, and Wave Period; Progressive and Standing Waves
  • Experiment 3: Pressure Variations as a Function of Wave Height, Water Depth, and Wave Period; Progressive and Standing Waves
  • Experiment 4: Wave Height Transformation in Shoaling Water; Wave Breaking
  • Experiment 5: Wave Reflection from Beach; Comparison with Miche's Theory
  • Experiment 6: Wave Reflection from a Partial Vertical Barrier; Comparison with Approximate Theory
  • Experiment 7: Wave Forces on Cylinders and Spheres
  • Experiment 8: Plane Wavemaker
  • Experiment 9: Approximate Wavemaker Theory for a Perfectly Reflecting "Beach"

• References

The following sections are included:

• Subject Index

• Author Index