Mandal B.N., De Soumen. Water Wave Scattering

CRC Press, 2015. — 375 p.The theory of water waves is most varied and a fascinating topic. It includes a wide range of natural phenomena in oceans, rivers and lakes. It is mostly concerned with elucidation of some general aspects of wave motion including the prediction of behaviour of waves in the presence of obstacles of some special confi gurations that are of interest to ocean engineers. Unfortunately, even the apparently simple problems appear to be difficult to tackle mathematically unless some simplifi ed assumptions are made. Fortunately for water, one can assume it to be an incompressible, inviscid and homogeneous fluid. The linearized theory of water waves is based on the assumption that the amplitude of the motion is small compared to the wave length. If irrotational motion is assumed, then the linearized theory of water waves is essentially concerned with solving the Laplace equation in the water region together with linearized boundary condition. There are varied classes of problems which have been/are being studied mathematically in the literature within the frame work of linearized theory of water waves for last many years. Scattering by obstacles of various geometrical configurations is one such class of water wave problems. This book is devoted to advanced mathematical work related to water wave scattering. Emphasis is given on the mathematical and computational techniques required to study these problems mathematically.