Linear Water Waves: A Mathematical Approach

From Book News, Inc.
An advanced textbook for graduate students of engineering and mathematics who have completed a course in mathematical analysis and are familiar with Bessel functions the Fourier transform. It might also be useful to practitioners in ocean engineering and to mathematicians specializing in partial differential equations and spectral operator theory.Book News, Inc.®, Portland, OR


Review
"This work provides a self-contained and up-to-date...reference for those working in fluid mechanics and engineering." Mechanical Engineering


Book Description
This book gives a self-contained and up-to-date account of mathematical results in the linear theory of water waves. The study of waves has many applications, including the prediction of behavior of floating bodies (ships, submarines, tension-leg platforms etc.), the calculation of wave-making resistance in naval architecture, and the description of wave patterns over bottom topography in geophysical hydrodynamics. The first section deals with time-harmonic waves. Three linear boundary value problems serve as the approximate mathematical models for these types of water waves. The next section uses a plethora of mathematical techniques in the investigation of these three problems. The techniques used in the book include integral equations based on Green's functions, various inequalities between the kinetic and potential energy and integral identities which are indispensable for proving the uniqueness theorems. The so-called inverse procedure is applied to constructing examples of non-uniqueness, usually referred to as 'trapped nodes.'


Download Description
This book gives a self-contained and up-to-date account of mathematical results in the linear theory of water waves. The study of waves has many applications, including the prediction of behavior of floating bodies (ships, submarines, tension-leg platforms etc.), the calculation of wave-making resistance in naval architecture, and the description of wave patterns over bottom topography in geophysical hydrodynamics. The first section deals with time-harmonic waves. Three linear boundary value problems serve as the approximate mathematical models for these types of water waves. The next section, in turn, uses a plethora of mathematical techniques in the investigation of these three problems. Among the techniques used in the book the reader will find integral equations based on Green's functions, various inequalities between the kinetic and potential energy, and integral identities which are indispensable for proving the uniqueness theorems. For constructing examples of non-uniqueness usually referred to as 'trapped modes' the so-called inverse procedure is applied. Linear Water Waves will serve as an ideal reference for those working in fluid mechanics, applied mathematics, and engineering.


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An advanced textbook for graduate students of engineering and mathematics who have completed a course in mathematical analysis and are familiar with Bessel functions the Fourier transform. It might also be useful to practitioners in ocean engineering and to mathematicians specializing in partial differential equations and spectral operator theory. Annotation c. Book News, Inc., Portland, OR


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