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Author Kuznet︠s︡ov, N. G. (Nikolaĭ Germanovich), author
Title Linear water waves : a mathematical approach / N. Kuznetsov, V. Mazʹya, B. Vainberg
Imprint Cambridge : Cambridge University Press, 2002
book jacket
Descript 1 online resource (xvii, 513 pages) : digital, PDF file(s)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Note Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Introduction: Basic Theory of Surface Waves -- Mathematical Formulation -- Linearized Unsteady Problem -- Linear Time-Harmonic Waves (the Water-Wave Problem) -- Linear Ship Waves on Calm Water (the Neumann-Kelvin Problem) -- Time-Harmonic Waves -- Green's Functions -- Three-Dimensional Problems of Point Sources -- Two-Dimensional and Ring Green's Functions -- Green's Representation of a Velocity Potential -- Submerged Obstacles -- Method of Integral Equations and Kochin's Theorem -- Conditions of Uniqueness for All Frequencies -- Unique Solvability Theorems -- Semisubmerged Bodies -- Integral Equations for Surface-Piercing Bodies -- John's Theorem on the Unique Solvability and Other Related Theorems -- Trapped Waves -- Uniqueness Theorems -- Horizontally Periodic Trapped Waves -- Two Types of Trapped Modes -- Edge Waves -- Trapped Modes Above Submerged Obstacles -- Waves in the Presence of Surface-Piercing Structures -- Vertical Cylinders in Channels -- Ship Waves on Calm Water -- Green's Functions -- Three-Dimensional Problem of a Point Source in Deep Water -- Far-Field Behavior of the Three-Dimensional Green's Function -- Two-Dimensional Problems of Line Sources -- The Neumann-Kelvin Problem for a Submerged Body -- Cylinder in Deep Water -- Cylinder in Shallow Water -- Wave Resistance -- Three-Dimensional Body in Deep Water -- Two-Dimensional Problem for a Surface-Piercing Body -- General Linear Supplementary Conditions at the Bow and Stern Points -- Total Resistance to the Forward Motion -- Other Supplementary Conditions
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
TAEBDC; 2009
Link Print version: 9780521808538
Subject Wave-motion, Theory of
Water waves -- Mathematics
Alt Author Mazʹi︠a︡, V. G., author
Vaĭnberg, B. R. (Boris Rufimovich), author
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