Water Wave Propagation Over Uneven Bottoms Linear Wave Propagation

The primary objective of this book is to provide a review of techniques available for the problems of wave propagation in regions with uneven beds as they are encountered in coastal areas. The view taken is that the techniques should be useful for application in advisory practice. However, effort is put into a precise definition of the underlying physical principles, so that the validity of the methods used can be evaluated. Both linear and nonlinear wave propagation techniques are discussed. Because of its length, the book comes in two parts, part 1 covering primarily linear wave propagation, and part 2 covering on nonlinear wave propagation.

The primary objective of this book is to provide a review of techniques available for the problems of wave propagation in regions with uneven beds as they are encountered in coastal areas. The view taken is that the techniques should be useful for application in advisory practice. However, effort is put into a precise definition of the underlying physical principles, so that the validity of the methods used can be evaluated. Both linear and nonlinear wave propagation techniques are discussed. Because of its length, the book comes in two parts: Part 1 covers primarily linear wave propagation, and Part 2 covers nonlinear wave propagation. Contents: Basic EquationsWave Propagation FormulationThe Mild-Slope EquationPractical Aspects of Linear Wave Propagation ModelsBoussinesq-Type Models for Uneven BottomsKdV-Type ModelsHarmonic GenerationNonlinear Wave Propagation of Stokes' Waves over Uneven Bottoms keywords:

Waves in Oceanic and Coastal Waters describes the observation, analysis and prediction of wind-generated waves in the open ocean, in shelf seas, and in coastal regions with islands, channels, tidal flats and inlets, estuaries, fjords and lagoons. Most of this richly illustrated book is devoted to the physical aspects of waves. After introducing observation techniques for waves, both at sea and from space, the book defines the parameters that characterise waves. Using basic statistical and physical concepts, the author discusses the prediction of waves in oceanic and coastal waters, first in terms of generalised observations, and then in terms of the more theoretical framework of the spectral energy balance. He gives the results of established theories and also the direction in which research is developing. The book ends with a description of SWAN (Simulating Waves Nearshore), the preferred computer model of the engineering community for predicting waves in coastal waters.

This book is intended as an introduction to classical water wave theory for the college senior or first year graduate student. The material is self-contained; almost all mathematical and engineering concepts are presented or derived in the text, thus making the book accessible to practicing engineers as well.The book commences with a review of fluid mechanics and basic vector concepts. The formulation and solution of the governing boundary value problem for small amplitude waves are developed and the kinematic and pressure fields for short and long waves are explored. The transformation of waves due to variations in depth and their interactions with structures are derived. Wavemaker theories and the statistics of ocean waves are reviewed. The application of the water particle motions and pressure fields are applied to the calculation of wave forces on small and large objects. Extension of the linear theory results to several nonlinear wave properties is presented. Each chapter concludes with a set of homework problems exercising and sometimes extending the material presented in the chapter. An appendix provides a description of nine experiments which can be performed, with little additional equipment, in most wave tank facilities.

This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models.

In Part I of this report, a time dependent form of the reduced wave equation of Berkhoff is developed for the case of water waves propagating over a bed consisting of ripples superimposed on an otherwise slowly varying mean depth which satisfies the mild slope assumption. The ripples are assumed to have wavelengths on the order of the surface wave length but amplitudes which scale as a small parameter along with the bottom slope. The theory is verified by showing that it reduces to the case of plane waves propagating over a non-dimensional, infinite patch of sinusoidal ripples, studied recently by Davis and Heathershaw and Mei. We then study two cases of interest--formulation and use of the coupled parabolic equations for propagation over patches of arbitrary form in order to study wave reflection, and propagation of trapped waves along an infinite ripple patch. In the second part, we use the results of Part 1 to extend the results for weakly-nonlinear wave propagation to the case of partial reflection from bottoms with mild-sloping mean depth with superposed small amplitude undulations. Keywords include: Combined refraction-diffraction, Linear Surface Waves, Shallow and intermediate water depths, and Wave reflection.

This is the first book on explosion-generated water waves. It presents the theoretical foundations and experimental results of the generation and propagation of impulsively generated waves resulting from underwater explosions. Many of the theories and concepts presented herein are applicable to other types of water waves, in particular, tsunamis and waves generated by the fall of a meteorite. Linear and nonlinear theories, as well as experimental calibrations, are presented for cases of deep and shallow water explosions. Propagation of transient waves on dissipative, nonuniform bathymetries together with laboratory simulations are analyzed and discussed.