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Books > Science & Mathematics > Physics > Classical mechanics > Fluid mechanics
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Water Wave Scattering (Paperback)
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Water Wave Scattering (Paperback)
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The theory of water waves is most varied and is 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
configurations that are of interest to ocean engineers.
Unfortunately, even the apparently simple problems appear to be
difficult to tackle mathematically unless some simplified
assumptions are made. Fortunately, one can assume water to be an
incompressible, in viscid and homogeneous fluid. The linearised
theory of water waves is based on the assumption that the amplitude
of the motion is small compared to the wave length. If rotational
motion is assumed, then the linearised theory of water waves is
essentially concerned with solving the Laplace equation in the
water region together with linearised boundary condition. There are
varied classes of problems that have been/are being studied
mathematically in the literature within the framework of linearised
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 laid on the
mathematical and computational techniques required to study these
problems mathematically. The book contains nine chapters. The first
chapter is introductory in nature. It includes the basic equations
of linearised theory for a single layer fluid, a two-layer fluid,
solution of dispersion equations, and a general idea on scattering
problems and the energy identity in water with a free surface.
Chapter 2 is concerned with wave scattering involving thin rigid
plates of various geometrical configurations, namely, plane
vertical barriers or curved barriers, inclined barriers, horizontal
barrier, and also thin elastic vertical plate. For the horizontal
case, the barrier is submerged below an ice-cover modelled as a
thin elastic plate floating on water. Chapter 3 discusses wave
scattering by a rectangular trench by using Galerkin technique.
Chapter 4 involves wave scattering by a dock by using Carleman
singular integral equation followed by reduction to Riemann-Hilbert
problems. Chapter 5 involves several wave scattering problems
involving discontinuities at the upper surface of water by using
the Wiener-Hopf technique, by reduction to Carleman singular
integral equations. Chapter 6 considers scattering by a long
horizontal circular cylinder either half immersed or completely
submerged. In chapter 7, some important energy identities are
derived for scattering problems in a single-layer and also in a
two-layer fluid. Chapter 8 is concerned with wave scattering in a
two-layer fluid by a thin vertical plate and by a long horizontal
circular cylinder submerged in either of the two layers. Chapter 9
is the final chapter which considers a number of wave scattering
problems in a single-layer or a two-layer fluid with variable
bottom topography by using a simplified perturbation analysis It is
hoped that this book will be useful to researchers on water waves.
The several wave scattering problems presented in the book are
mostly based on the research work carried out by the authors and
their associates.
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