海岸水域表面波動力學(xué)

前言

Wave motion surrounds us——from the most secret, profound waves of quantummechanics to the grand waves of the ocean surface.   Ocean waves, or water waves, may be divided into deep- and shallow- water（coastal） waves. From an advance point of view, coastal waves are not studied asthoroughly as deep-water waves due to a complicated seabed topography on theformer but not on the latter. Therefore, in conjunction with the effects of ubiqui-tous ambient currents, wave-current-bottom interactions make up the most fun-damental, widespread dynamical mechanism in coastal waters manifesting itselfas refraction, diffraction, scattering, and resonant wave interactions involved inenergy exchanges.Apparently, it is essential to obtain a full, clear explanation and descriptionof coastal waves for the development of broad offshore, coastal and harbor en-gineering, and also for having a better understanding of the evolutionary mech-anism of deep-water waves. In fact, a commanding view on long-term inves-tigating water waves is to wholly and uniformly treat and describe deep- andshallow-water waves, thus promoting the present rapid exploration and devel-opment of global oil and gas fields in deep waters of the oceans.The aforementioned views, ideas, judgments, all that I have thought and doneover the last ten years, were compiled by me in this book. The book consists ofnine chapters and appendices from A to H, depicting the fundamental paradigmsof weakly nonlinear water waves.

內(nèi)容概要

Dynamics of Surface Waves in Coastal Waters Wave-Current-Bottom Interactions develops the typical basic theories (e,g. mild-slope equation and shorecrested waves) and applications of water wave propagation with an emphasis on wave-current-bottom interactions and Hamiltonian systems. In recent times, the interest in water wave propagation has accelerated because of rapid developments in global coastal ocean engineering.

書籍目錄

1  Preliminaries  1.1  Water Wave Theories in Historical Perspective    1.1.1  The Mild-Slope Equations    1.1.2 The Boussinesq-Type Equations  1.2  The Governing Equations  1.3  Lagrangian Formulation  1.4  Hamiltonian Formulation  References2  Weakly Nonlinear Water Waves Propagating over Uneven Bottoms  2.1  Modified Third-Order Evolution Equations of Liu and Dingemans  2.2  Fourth-Order Evolution Equations and Stability Analysis  2.3  Third-Order Evolution Equations for Wave-Current Interactions  References3  Resonant Interactions Between Weakly Nonlinear Stokes Waves and Ambient Currents and Uneven Bottoms  3.1  Introduction  3.2  Governing Equations and WKBJ Perturbation Expansion  3.3  Subharmonic Resonance  3.4  Dynamical System  References4  The Mild-Slope Equations  4.1  Introduction  4.2  Three-Dimensional Currents over Mildly Varying Topography  4.3  Two-Dimensional Currents over Rapidly Varying Topography  4.4  Three-Dimensional Currents over Rapidly Varying Topography  4.5  Two-Dimensional Currents over Generally Varying Topography  4.6  A Hierarchy for Two-Dimensional Currents over Generally Varying Topography  References5  Linear Gravity Waves over Rigid, Porous Bottoms  5.1  Introduction  5.2  A Rapidly Varying Bottom  5.3  Generally Varying Bottom  References6  Nonlinear Unified Equations over an Uneven Bottom  6.1 Introduction  6.2 Nonlinear Unified Equations  6.3  Explicit Special Cases    6.3.1  Generalized Nonlinear Shallow-Water Equations of Airy    6.3.2 Generalized Mild-Slope Equation    6.3.3  Stokes Wave Theory    6.3.4  Higher-Order Boussinesq-Type Equations  References7  Generalized Mean-Flow Theory  7.1  Introduction  7.2  Governing Equations and Boundary Conditions  7.3  Averaged Equations of Motion  7.4  Generalized Wave Action Conservation Equation and Its Wave Actions  References8  Hamiltonian Description of Stratified Wave-Current Interactions  8.1  Introduction  8.2  Two-Layer Wave-Current Interactions  8.3  n-Layer Pure Waves  8.4  n-Layer Wave-Current Interactions over Uneven Bottoms  References9  Surface Capillary-Gravity Short-Crested Waves with a Current in Water of Finite Depth  9.1  Introduction  9.2 An Incomplete Match and Its Solution  9.3  Linear Capillary-Gravity Short-Crested Waves    9.3.1  System Formulation    9.3.2  Analytical Solutions and Kinematic and Dynamical Variables    9.3.3  Special Cases  9.4  Second-Order Capillary-Gravity Short-Crested Waves  9.5  Third-Order Gravity Short-Crested Waves    9.5.1  The System Equations and the Perturbation Method    9.5.2  Third-Order Solution    9.5.3  Special Cases    9.5.4  Short-Crested Wave Quantities    9.5.5  Short-Crested Wave Forces on Vertical Walls  9.6  Third-Order Pure Capillary-Gravity Short-Crested Waves    9.6.1  Formulation    9.6.2  Solution    9.6.3  Kinematical and Dynamical Variables  ReferencesAppendices  A  γ,μ and v in (2.1.4)  B  ξ(3,1), φ3,1), A(3,2)' ηj, τj, μj, λj and Vj in Chapter 2  C  λ1 and λ2 in (2.3.44)  D  μj in (3.3.22)  E  I23, I33, I35,136 in Chapter 5  F  Coefficients in (9.4.33) and (9.4.34)  G  Coefficients in (9.5.136)-(9.5.138)  H  Coefficients in (9.5.139) and (9.5.140)Subject Index

章節(jié)摘錄

插圖：The third term can be called the bottom wave action, a positive compensation byincluding the effects of moving bottoms and describing a widespread dynamicprocess occurring on the nearshore bottoms （such as coastal evolution and sand-wave migrations）. The fourth term may be considered as the dissipation waveaction, transmitting a full scale effect of the dissipation arising from the originin the viscosity of fluid, determining its nonnegligible dissipative function of thecomplete equation system, and probably having a widespread value of applica-tion. Finally the fifth term vanishes identically [2]. Therefore it can be seen thatthese four kinds of wave actions on the left of equation （7.4.2） reach mutuallya more general form of integration with complement, compatibility and distinc-tion. Bretherton and Garrett [2] had shown the equivalence of equation （7.4.1）for many other types of wave motion in fluid dynamics, so that, （7.4.2） can beregarded as a valuable extension of （7.4.1）, giving rise to a generalized waveaction equation for the dissipative dynamical system in the nearshore region,which will play an important role in dealing with the process of real viscousflow.

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