Table Of Contents:
Preface vii

Introduction 1(10)

A brief historical overview 1(1)

Summary of content 2(7)

References - Chapter 1 9(2)

Hydrodynamic Background 11(38)

Introduction 11(1)

Kinematics of fluid flow 12(5)

Eulerian versus Lagrangian description 12(1)

Streamlines, pathlines, streaklines 13(1)

Vorticity ωi and deformation tensor eij 14(1)

Gauss' theorem, Green's theorems 15(1)

The kinematic transport theorem, Leibniz rule 16(1)

Dynamics of fluid flow 17(7)

Conservation of mass 17(1)

Conservation of momentum 18(2)

Stokes' viscosity law, the Navier-Stokes equations 20(2)

The boundary layer approximation 22(1)

Energy dissipation in viscous flow 23(1)

The Euler equations, irrotational flow 23(1)

Conditions at fixed and moving boundaries 24(4)

Kinematic conditions 25(2)

Dynamic conditions 27(1)

Basic ideas for turbulent flow 28(15)

Reynolds' decomposition of physical quantities 29(1)

Determination of the turbulent mean flow 30(4)

The Reynolds equations 34(5)

Modelling of turbulent stresses 39(4)

Energy flux in a flow 43(2)

Appendix: Tensor notation 45(2)

References - Chapter 2 47(2)

Linear Waves 49(158)

Assumptions and the simplified equations 49(6)

Basic solution for linear waves 55(33)

Solution for φ and η 55(11)

Evaluation of linear waves 66(6)

Particle motion 72(5)

The pressure variation 77(3)

Deep water and shallow water approximations 80(8)

Time averaged properties of linear waves in one horizontal dimension (1DH) 88(14)

Introduction 88(1)

Mass and volume flux 89(3)

Momentum flux---radiation stress 92(5)

Energy density 97(2)

Energy flux 99(1)

Dimensionless functions for wave averaged quantities 100(2)

Superposition of linear waves 102(24)

Standing waves 103(5)

Wave groups 108(5)

Wave spectra 113(13)

Linear wave propagation over uneven bottom 126(28)

Introduction 126(5)

Shoaling and refraction 131(4)

Simple shoaling 135(3)

Determination of the refraction pattern 138(4)

Refraction by ray tracing 142(2)

The geometrical optics approximation 144(7)

Kinematic wave theory 151(3)

Wave modification by currents 154(12)

Introduction 154(1)

Waves on a steady, locally uniform current 155(5)

Vertically varying currents 160(5)

The kinematics and dynamics of wave propagation on current fields 165(1)

Combined refraction-diffraction 166(33)

Introduction 166(2)

The wave equation for linear long waves 168(3)

The mild slope equation 171(8)

Further developments of the MSE 179(10)

The parabolic approximation 189(10)

References -- Chapter 3 199(8)

Energy Balance in the Nearshore Region 207(22)

Introduction 207(1)

The energy equation 207(6)

The energy balance for periodic waves 213(9)

Introduction of dimensionless parameters for 1-D wave motion 213(2)

A closed form solution of the energy equation 215(6)

The energy equation for steady irregular waves 221(1)

The general energy equation: Unsteady wave-current motion 222(5)

The wave action equation 227(1)

References - Chapter 4 228(1)

Properties of Breaking Waves 229(82)

Introduction 229(1)

The highest possible wave on constant depth 230(2)

Qualitative description of wave breaking 232(10)

Analysis of the momentum variation in a transition (Or: Why do the waves break?) 238(4)

Wave characteristics at the breakpoint 242(4)

Experimental results for surfzone waves 246(25)

Qualitative surfzone characteristics 247(1)

The phase velocity c 248(2)

Surface profiles η(t) 250(2)

The surface shape parameter B0 252(2)

The crest elevation ηc/H 254(1)

The roller area 255(3)

Measurements of particle velocities 258(4)

Turbulence intensities 262(1)

The values of Pxx, Bx and D 263(6)

The wave generated shear stress uw ww 269(2)

Surfzone wave modelling 271(16)

Surfzone assumptions 271(3)

Energy flux Ef for surfzone waves 274(5)

Radiation stress in surfzone waves 279(2)

Volume flux in surfzone waves 281(1)

The phase velocities for quasi-steady breaking waves 282(3)

The energy dissipation in quasi steady surfzone waves 285(2)

Further analysis of the energy dissipation 287(8)

Energy dissipation for random waves 287(4)

Energy dissipation with a threshold 291(1)

A model for roller energy decay 292(1)

Advanced computational methods for surzone waves 293(2)

Swash 295(8)

References - Chapter 5 303(8)

Wave Models Based on Linear Wave Theory 311(12)

Introduction 311(2)

1DH shoaling-breaking model 313(1)

2DH refraction models 313(5)

The wave propagation pattern 313(4)

Determination of the wave amplitude variation 317(1)

Wave action models 318(1)

Models based on the mild slope equation and the parabolic approximation 319(1)

References - Chapter 6 320(3)

Nonlinear Waves: Analysis of Parameters 323(18)

Introduction 323(2)

The equations for the classical nonlinear wave theories 325(3)

The system of dimensionless variables used 328(3)

Stokes waves 331(2)

Long waves 333(5)

The Stokes or Ursell parameter 335(1)

Long waves of moderate amplitude 335(1)

Long waves of small amplitude 336(1)

Long waves of large amplitude 337(1)

Conclusion 338(1)

References - Chapter 7 338(3)

Stokes Wave Theory 341(40)

Introduction 341(1)

Second order Stokes waves 342(27)

Development of the perturbation expansion 342(3)

First order approximation 345(1)

Second order approximation 346(3)

The solution for φ2 349(2)

The surface elevation η 351(4)

The pressure p 355(3)

The volume flux and determination of K 358(4)

Stokes' two definitions of the phase velocity 362(2)

The particle motion 364(2)

Convergence and accuracy 366(3)

Higher order Stokes waves 369(5)

Introduction 369(1)

Stokes third order theory 370(1)

Waves with currents 371(1)

Stokes fifth order theory 372(1)

Very high order Stokes waves 373(1)

The stream function method 374(5)

Introduction 374(1)

Description of the stream function method 374(4)

Comparison of stream function results with a Stokes 5th order solution 378(1)

References - Chapter 8 379(2)

Long Wave Theory 381(88)

Introduction 381(2)

Solution for the Laplace equation 383(4)

The Boussinesq equations 387(2)

Boussinesq equations in one variable 389(7)

The fourth order Boussinesq equation 389(3)

The third order Korteweg-deVries (KdV) equation 392(4)

Cnoidal waves -- Solitary waves 396(14)

The periodic case: Cnoidal waves 399(3)

Final cnoidal wave expressions 402(4)

Infinitely long waves: Solitary waves 406(4)

Analysis of cnoidal waves for practical applications 410(15)

Specification of the wave motion 411(4)

Velocities and pressures 415(5)

Wave averaged properties of cnoidal waves 420(3)

Limitations for cnoidal waves 423(2)

Alternative forms of the Boussinesq equations - The linear dispersion relation 425(10)

Equations in terms of the velocity us at the bottom 426(1)

Equations in terms of the velocity us at the MWS 426(1)

The equations in terms of the depth averaged velocity u 427(2)

The equations in terms of Q 429(1)

The linear dispersion relation 430(5)

Equations for 2DH and varying depth 435(2)

Equations with enhanced deep water properties 437(7)

Introduction 437(1)

Improvement of the linear dispersion properties 437(5)

Improvement of other properties 442(2)

Further developments of Boussinesq modelling 444(4)

Fully nonlinear models 445(1)

Extension of equations to O(μ4) accuracy 445(1)

Waves with currents 446(1)

Models of high order 446(1)

Robust numerical methods 446(1)

Frequency domain methods for solving the equations 447(1)

Boussinesq models for breaking waves 448(3)

Eddy viscosity models 449(1)

Models with roller enhancement 449(1)

Vorticity models 450(1)

Wave breaking modelled by the nonlinear shallow water equations 451(1)

Large amplitude long waves U >> 1: The nonlinear shallow water equations (NSW) 451(3)

References - Chapter 9 454(15)

Boundary Layers 469(46)

Introduction 469(21)

The boundary layer equations. Formulation of the problem 470(3)

Perturbation expansion for u 473(1)

The 1st order solution 474(6)

The 2nd order solution 480(3)

The steady streaming us in wave boundary layers 483(3)

Results for us 486(4)

Energy dissipation in a linear wave boundary layer 490(3)

Turbulent wave boundary layers 493(9)

Rough turbulent flow 497(3)

Energy dissipation in turbulent wave boundary layers 500(2)

Bottom shear stress in 3D wave-current boundary layers 502(11)

Introduction 502(1)

Formulation of the problem 502(2)

The mean shear stress 504(5)

Special cases 509(4)

References - Chapter 10 513(2)

Nearshore Circulation 515(88)

Introduction 515(3)

Depth integrated conservation of mass 518(5)

Separation of waves and currents 520(3)

Conditions at fixed and moving boundaries, II 523(7)

Kinematic conditions 523(1)

Dynamic conditions 524(6)

Depth integrated momentum equation 530(10)

Integration of horizontal equations 531(2)

Integration of the vertical momentum equation 533(7)

The nearshore circulation equations 540(8)

The time averaged momentum equation 540(4)

The equations for depth uniform currents 544(4)

Analysis of the radiation stress in two horizontal dimensions, 2DH 548(9)

Sαβ expressed in terms of Sm and Sp 551(3)

Radiation stress for linear waves in two horizontal dimensions (2DH) 554(3)

Examples on a long straight beach 557(24)

The momentum balance 557(2)

The cross-shore momentum balance: Setdown and setup 559(7)

Longshore currents 566(7)

Longshore current solution for a plane beach 573(6)

Discussion of the examples 579(2)

Wave drivers 581(6)

Conditions along open boundaries 587(13)

Introduction about open boundaries 587(2)

Absorbing-generating boundary conditions 589(9)

Boundary conditions along cross-shore boundaries 598(2)

References - Chapter 11 600(3)

Cross-Shore Circulation and Undertow 603(24)

The vertical variation of currents 603(5)

Introduction 603(2)

The governing equations for the variation over depth of the 3D currents 605(3)

The cross-shore circulation, undertow 608(15)

Formulation of the 2-D problem and general solution 608(2)

Boundary conditions 610(3)

Solution for the undertow profiles with depth uniform νt and α1 613(2)

Discussion of results and comparison with measurements 615(3)

Solutions including the effect of the boundary layer 618(4)

Undertow outside the surfzone 622(1)

Conclusions 622(1)

References - Chapter 12 623(4)

Quasi-3D Nearshore Circulation Models 627(34)

Introduction 627(4)

Governing equations 631(2)

Time-averaged depth-integrated equations 631(1)

Choices for splitting the current 632(1)

Solution for the vertical velocity profiles 633(4)

Calculation of the integral terms: The dispersive mixing coefficients 637(4)

Final form of the basic equations 640(1)

Example: Longshore currents on a long straight coast 641(4)

Applications and further developments of quasi-3D modelling 645(10)

The start-up of a longshore current 645(2)

Rip currents 647(2)

Curvilinear version of the Shorecirc model 649(5)

The nearshore community model, NearCoM 654(1)

References - Chapter 13 655(6)

Other Nearshore Flow Phenomena 661(44)

Infragravity waves 661(20)

Introduction 661(3)

Basic equations for infragravity waves 664(2)

Homogeneous solutions -- Free edge waves 666(7)

IG wave generation 673(8)

Shear instabilities of longshore currents 681(20)

Introduction 681(1)

The discovery of shear waves 681(3)

Derivation of the basic equations 684(4)

Stability analysis of the equations 688(4)

Further analyses of the initial instability 692(4)

Numerical analysis of fully developed shear waves 696(5)

References - Chapter 14 701(4)
Author Index 705(6)
Subject Index 711