Narrow Results

The nearshore potential vorticity balance of Bowen and Holman (1989) is expanded to include the forcing from wave group induced radiation stresses. Model results suggest that the forcing from these radiation stresses can drive oscillations in the longshore current that have a spatial structure similar to linear shear instabilities of the longshore current. In addition, the forced response is nearly resonant when the forcing has scales (k,σ) similar to the linearly most unstable mode. Thus, we suggest that wave groups may provide an initial perturbation necessary for the generation of shear instabilities of longshore currents and also act as a source of vortical motions on beaches where linear instabilities are completely damped.

Data from the SUPERDUCK (1986) field experiment were analyzed for the presence of spatially coherent wave groups. The analysis confirms that wave groups with periods and longshore spatial structures comparable to the observed shear wave motions were sometimes present on this open coast. This indicates that wave groups with the required spatial and temporal structure to initiate the low frequency oscillations in the longshore current can exist.

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

The following sections are included:

• Contents

• Preface

Smoothed particle hydrodynamics (SPH) is used to simulate both two and three-dimensional cases of wave breaking. A combined SPH-LES type scheme or sub-particle scale (SPS) scheme is used to capture coherent turbulent structures. Results are presented for weakly plunging breaking waves. The 2-D numerical results show that a highly turbulent bore is produced propagating up the beach while generating reverse breaking that precipitates a downbursting-like phenomenon. The initial application of the 3-D scheme to the same problem is presented but the resolution is insufficient to detect reliably coherent turbulent structures. Nevertheless, even the 3-D results suggest the existence of eddies whose primary axis of rotation is near-vertically oriented.

The Smoothed Particle Hydrodynamics (SPH) method is applied to simulate oscillatory flow, sediment suspension, deposition, and mobile bed mechanics. The sediment suspension is simulated with concentration model. The result shows that it can reproduce the phase lag between stream velocity and sediment concentration, which was verified by experiment data. The SPH method is promising and should be able to be used for coastal processes.

Smoothed particle hydrodynamics (SPH) is being used to model fluid flows, including free surface waves; however, the method assumes an compressible fluid. Most water wave theories are based on the assumption of incompressibility, which is reasonable for water. Here we develop a linear wave theory for waves on a compressible fluid. The effect of the fluid compressibility on wave number is examined to determine how much error is induced by an assumption of compressibility and also how these effects might be avoided. The dispersion relationship for a free surface wave on a compressible fluid is determined and the results are compared to incompressible free surface wave theory.

Tsunamis waves generated by landslides are simulated in the present work using a 3D Smoothed Particle Hydrodynamics (SPH) numerical model. Some improvements, able to enhance the numerical model stability and accuracy, are presented here. An experimental study on tsunamis waves generation due to a rigid body sliding down an inclined ramp is here considered. The 3D-SPH model shows a good agreement between observed water level oscillations and simulated ones, thus demonstrating the model's ability in the study of flow fields generated by impacts of bodies with the water. The application of the implemented numerical model to a real case tsunamis event is finally presented.

A model for sediment suspension is developed for the Smoothed Hydrodynamics Hydrodynamics (SPH) method. A sub-particle scheme is included into the scheme in order to capture the turbulence structure of the flow, in the same way as the sub-grid method is used for the hydrodynamic turbulence. The hydrodynamics part of the SPH model is validated by experiment data of the run-up of solitary wave. The SPH sediment part is validated by experiment data of oscillatory flow above wave-generated ripples. The comparisons show very good agreement.