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Linear Water Waves : A Mathematical Approach - N. Kuznetsov

Linear Water Waves

A Mathematical Approach

Hardcover Published: 19th August 2002
ISBN: 9780521808538
Number Of Pages: 532

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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.

Industry Reviews

'The style of writing is clear throughout, and the extensive bibliography is one of the most extensive and useful I have seen. This book can be recommended to all whose work involves the study of linear water waves.' Zentralblatt fur Mathematik und ihre Grenzgebiete Mathematics Abstracts
"This work provides a self-contained and up-to-date...reference for those working in fluid mechanics and engineering." Mechanical Engineering

Prefacep. xi
Introduction: Basic Theory of Surface Wavesp. 1
Mathematical Formulationp. 1
Linearized Unsteady Problemp. 5
Linear Time-Harmonic Waves (the Water-Wave Problem)p. 10
Linear Ship Waves on Calm Water (the Neumann-Kelvin Problem)p. 15
Time-Harmonic Wavesp. 19
Green's Functionsp. 21
Three-Dimensional Problems of Point Sourcesp. 21
Two-Dimensional and Ring Green's Functionsp. 37
Green's Representation of a Velocity Potentialp. 42
Bibliographical Notesp. 48
Submerged Obstaclesp. 50
Method of Integral Equations and Kochin's Theoremp. 50
Conditions of Uniqueness for All Frequenciesp. 67
Unique Solvability Theoremsp. 87
Bibliographical Notesp. 96
Semisubmerged Bodiesp. 99
Integral Equations for Surface-Piercing Bodiesp. 99
John's Theorem on the Unique Solvability and Other Related Theoremsp. 116
Bibliographical Notesp. 140
Semisubmerged Bodies, IIp. 142
Trapped Wavesp. 143
Uniqueness Theoremsp. 164
Bibliographical Notesp. 212
Horizontally Periodic Trapped Wavesp. 214
Two Types of Trapped Modesp. 215
Edge Wavesp. 219
Trapped Modes Above Submerged Obstaclesp. 229
Waves in the Presence of Surface-Piercing Structuresp. 237
Vertical Cylinders in Channelsp. 254
Ship Waves on Calm Waterp. 263
Green's Functionsp. 265
Three-Dimensional Problem of a Point Source in Deep Waterp. 265
Far-Field Behavior of the Three-Dimensional Green's Functionp. 283
Two-Dimensional Problems of Line Sourcesp. 305
Bibliographical Notesp. 315
The Neumann-Kelvin Problem for a Submerged Bodyp. 318
Cylinder in Deep Waterp. 319
Cylinder in Shallow Waterp. 341
Wave Resistancep. 349
Three-Dimensional Body in Deep Waterp. 353
Bibliographical Notesp. 359
Two-Dimensional Problem for a Surface-Piercing Bodyp. 361
General Linear Supplementary Conditions at the Bow and Stern Pointsp. 362
Total Resistance to the Forward Motionp. 393
Other Supplementary Conditionsp. 396
Trapped Modesp. 405
Cylinder in the Supercritical Streamp. 411
Bibliographical Notesp. 415
Unsteady Wavesp. 419
Submerged Obstacles: Existence and Properties of Velocity Potentialsp. 421
The Initial-Boundary Value Problem and an Auxiliary Steady-State Problemp. 421
Operator Equation for the Unsteady Problemp. 425
Main Resultsp. 427
Bibliographical Notesp. 432
Waves Caused by Rapidly Stabilizing and High-Frequency Disturbancesp. 435
Rapidly Stabilizing Surface Disturbancesp. 435
Rapidly Stabilizing Underwater Disturbancesp. 453
High-Frequency Surface Pressurep. 460
High-Frequency Underwater Disturbancesp. 474
Bibliographical Notesp. 484
Bibliographyp. 485
Name Indexp. 505
Subject Indexp. 509
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521808538
ISBN-10: 0521808537
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 532
Published: 19th August 2002
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.9 x 15.2  x 2.9
Weight (kg): 0.88