### 基本信息

- 原书名：Dynamics of Surface Waves in Coastal Waters

### 内容简介

物理书籍

Wave motion is one of the broadest scientific subjects in nature, especially water waves in the near-shore region which present more richness and complexity of variability with respect to deep-water waves. Dynamics of Surfaee Waves in Coastal Waters Wave-Current-Bottom Interactions develops Se 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. .

This booklays a new foundation for coastal ocean engineering and includes numerous theories and concepts (generalized wave actions in particular), making it beneficial to physical oceanographers and engineers. The book has detailed illustrations and stimulating examples showing how the theory works, and up-to-date techniques, all of which make it accessible to a wide variety of readers, especially senior undergraduate and graduate students in fluid mechanics, coastal and ocean engineering, physical oceanography and applied mathematics. ...

### 作译者

Huang is a professor of fluid mechanics and coastal surface wave dynamics at Shanghai University. He was an undergraduate student in irrigation and water conservancy engineering at the Shihezi Institute of Agriculture (1982-1986), and received his Master of engineering in experimental mechanics in 1993 and his PhD in coastal engineering in 1998, both at Tianjin University. He was a National Science Foundation Postdoctoral Fellow at the State Key Laboratory of Estuarine and Coastal Research, the East China Normal University (1998-2000). He had previously taught at the Xinjiang Shihezi Secondary Specialized School of Land Reclamation and Cultivation (1986-1990), and Tianjin University (1993-1998). ..

Huang's research interests focus on mechanics and symmetry, Hamiltonian mechanics, the dynamics of coastal and ocean surface waves, and applied mathematics.

Among Huang's honors and recognitions are: the first recipient of the Second Prize in Natural Science of the Ministry of Education of China in 2002 (No. 2002-063), a recipient of the National Excellent Doctoral Dissertation of China in 2004 (No. 2004028), and the Special Bonus of the State Council of China in 2004 (No. (02) 9310004). ...

### 目录

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

References

2 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

References

3 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

References

4 The Mild-Slope Equations

### 前言

Wave motion surrounds us--from the most secret, profound waves of quantum mechanics 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 as thoroughly as deep-water waves due to a complicated seabed topography on the former but not on the latter. Therefore, in conjunction with the effects of ubiquitous ambient currents, wave-current-bottom interactions make up the most fundamental, widespread dynamical mechanism in coastal waters manifesting itself as refraction, diffraction, scattering, and resonant wave interactions involved in energy exchanges.

Apparently, it is essential to obtain a full, clear explanation and description of coastal waves for the development of broad offshore, coastal and harbor engineering, and also for having a better understanding of the evolutionary mechanism of deep-water waves. In fact, a commanding view on long-term investigating water waves is to wholly and uniformly treat and describe deep- and shallow-water waves, thus promoting the present rapid exploration and development of global oil and gas fields in deep waters of the oceans.

The aforementioned views, ideas, judgments, all that I have thought and done over the last ten years, were compiled by me in this book. The book consists of nine chapters and appendices from A to H, depicting the fundamental paradigms of weakly nonlinear water waves.

Chapter 1 makes a concise, historical review of water wave theories with the emphasis on current mild-slope equations and Boussinesq-type equations. An outline of three kinds of fundamental formulations of the surface water wave problems then follows.

Chapter 2, on the Liu-Dingemans evolution equations, gives a modification to that, and extensions of that, from third- to fourth-order with stability analysis, and from pure waves to wave-current interactions.

Chapter 3 deals with resonant wave-current-bottom interactions, concentrating on subharmonic resonance concerning the modulated wave groups and second-order long waves.

Chapter 4 is dedicated to six kinds of the mild-slope equations depending on the variation of ambient currents and bottom topography. In particular, a new type of conservative quantity, the product of phase velocity and group velocity, is put forward, and an operator indicating wave-current interaction is introduced to develop a hierarchy of the mild-slope equations. ..

Chapter 5 addresses linear gravity waves over rigid, porous bottoms by formulating two different models involving the mild-slope equations and the general variation of the wave continuity.

Chapter 6 leads to a type of nonlinear unified equations suitable for an uneven bottom, containing four kinds of major equations and theories as special cases.

Chapter 7, taking into account the Coriolis force and moving bottoms, bears on a generalized mean-flow theory for waves on currents, thus creating three new kinds of wave actions.

Chapter 8, on Hamiltonian stratified wave-current interactions, covers three kinds of stratified fluid systems with a number of the canonically conjugate variables.

Chapter 9 is the longest and devoted to short-crested waves (SCWs), perhaps the simplest genuinely three-dimensional water waves. The incompatibility involving standing waves and SCWs is found and effectively solved. Then, linear, first-, second- and third-order theories for pure gravity and capillary-gravity SCWs with or without ambient currents are respectively established in great detail, involving wave forces essential to engineering applications.

This book is aimed at researchers and graduate students specializing in coastal and ocean engineering, physical oceanography, fluid mechanics and applied mathematics, and at all those who wish to obtain a proper understanding of coastal dynamic processes.

Naturally, this book will not always stay "up-to-date" in terms of this research, but it can make a basic contribution to coastal wave investigations. Practically, what the monograph, acting as a courier, wants to become is nothing but my first battle call for the two great things not sought or conjectured by Immanuel Kant in 1788: the starry heavens above me and the moral law within me. ...

Hu Huang

Shanghai

April 2009

### 序言

I am happy to express my gratitude to my PhD and postdoctoral advisers, Professors Xireng Zhou and Dejun Li at Tianjin University and Professor Pingxing Ding at the East China Normal University, for their invaluable support, to Professor Hong Zhang at Shanghai Library for keeping me abreast with the latest foreign books, to Jianbo Liu at the Higher Education Press for her constructive suggestions and cheerfully putting up with my long delayed writing, to Jie Jin at the Shanghai University Library for her warm-heartedly delivering valuable literature to me at my requests, to my student Zhengzhi Deng for his editing and typing the bulk of the manuscript, and to all my students for their continued assistance.

My sincere appreciation is also extended to librarians, classmates and staff for their kind help. ..

The monograph has been financed by the National Natural Science Special Foundation of China for the Publishing of Scientific Achievement Monograph (Grant No. 50424913), the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200428), the Scientific Research Innovation Project of the Shanghai Education Committee (Grant No. O8YZ05), the Open Foundation of the State Key Laboratory of Ocean Engineering at the Shanghai Jiao Tong University (Grant No. 0501), and the Shanghai Leading Academic Discipline Project (Grant No. Y0103). ...