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Linear Water Waves

Linear Water Waves
A Mathematical Approach

  • Date Published: August 2002
  • availability: Available
  • format: Hardback
  • isbn: 9780521808538

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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 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.'

    • Suitable both as a textbook for graduate students and as a reference book with a complete and up-to-date bibliography
    • Covers all modern trends in the mathematical theory of water waves
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    Reviews & endorsements

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

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    Product details

    • Date Published: August 2002
    • format: Hardback
    • isbn: 9780521808538
    • length: 532 pages
    • dimensions: 229 x 152 x 29 mm
    • weight: 0.88kg
    • contains: 42 b/w illus.
    • availability: Available
  • Table of Contents

    Preface
    Part I. Time-Harmonic Waves:
    1. Green's functions
    2. Submerged obstacles
    3. Semisubmerged bodies, I
    4. Semisubmerged bodies, II
    5. Horizontally-periodic trapped waves
    Part II. Ship Waves on Calm Water:
    6. Green's functions
    7. The Neumann-Kelvin problem
    8. Two-dimensional problem
    Part III. Unsteady Waves:
    9. Submerged obstacles: existence
    10. Waves due to rapidly stabilizing and high-frequency disturbances
    Bibliography
    Name index
    Subject index.

  • Authors

    N. Kuznetsov, Russian Academy of Sciences

    V. Maz'ya, Linköpings Universitet, Sweden

    B. Vainberg, University of North Carolina, Charlotte

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