6. Unsteady Motions

  1. J. J. Stoker

Published Online: 22 AUG 2011

DOI: 10.1002/9781118033159.ch6

Water Waves: The Mathematical Theory with Applications

Water Waves: The Mathematical Theory with Applications

How to Cite

Stoker, J. J. (1992) Unsteady Motions, in Water Waves: The Mathematical Theory with Applications, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118033159.ch6

Publication History

  1. Published Online: 22 AUG 2011
  2. Published Print: 10 JAN 1992

ISBN Information

Print ISBN: 9780471570349

Online ISBN: 9781118033159

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Keywords:

  • unsteady motions;
  • Fourier transform technique;
  • Kelvin's method;
  • stationary phase;
  • Green's function

Summary

This chapter contains sections titled:

  • General formulation of the problem of unsteady motions

  • Uniqueness of the unsteady motions in bounded domains

  • Outline of the Fourier transform technique

  • Motions due to disturbances originating at the surface

  • Application of Kelvin's method of stationary phase

  • Discussion of the motion of the free surface due to disturbances initiated when the water is at rest

  • Waves due to a periodic impulse applied to the water when initially at rest. Derivation of the radiation condition for purely periodic waves

  • Justification of the method of stationary phase

  • A time-dependent Green's function. Uniqueness of unsteady motions in unbounded domains when obstacles are present