In this book linear and nonlinear theories of wave modification are considered. There are chapters focusing on linear wave scattering, nonlinear dispersive long waves and parabolic modelling, the interaction of waves with tidal and other currents, the trapping of wave energy in the vicinity of particular topographical features, and the mechanisms by which waves change the bed profile through sediment transport.
In a recent paper Chen and Saffman showed that periodic gravity waves in water of infinite depth are not unique. They presented explicit computations for new families of waves which they termed irregular waves. In the present paper the authors give conclusive numerical evidence that periodic gravity waves in water of arbitrary uniform depth are not unique. Explicit computations of irregular waves in water of finite depth are presented. In addition, they show that Chen and Saffman's bifurcation point for an irregular wave of class 2 is not unique. Results suggest the existence of an infinite number of such bifurcation points.
The study of internal gravity waves provides many challenges: they move along interfaces as well as in fully three-dimensional space, at relatively fast temporal and small spatial scales, making them difficult to observe and resolve in weather and climate models. Solving the equations describing their evolution poses various mathematical challenges associated with singular boundary value problems and large amplitude dynamics. This book provides the first comprehensive treatment of the theory for small and large amplitude internal gravity waves. Over 120 schematics, numerical simulations and laboratory images illustrate the theory and mathematical techniques, and 130 exercises enable the reader to apply their understanding of the theory. This is an invaluable single resource for academic researchers and graduate students studying the motion of waves within the atmosphere and ocean, and also mathematicians, physicists and engineers interested in the properties of propagating, growing and breaking waves.
