Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Patterns of ship waves

Authors: Chia-Shun Yih and Songping Zhu
Journal: Quart. Appl. Math. 47 (1989), 17-33
MSC: Primary 76B20; Secondary 76C10
DOI: https://doi.org/10.1090/qam/987892
MathSciNet review: 987892
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Abstract: Patterns of water waves created by a moving disturbance representing a moving body, floating or submerged, can be found by applying (1) the principle of stationary phase, (2) the principle that the phase lines are normal to the wave-number vector, and (3) the perception that the local phase velocity of the waves must be equal to the component of the velocity of the disturbance normal to the phase line. The three equations thus obtained are solved, and formulas for the phase lines are derived, which depend explicitly on the dispersion equation, and on that equation only. These formulas are applied to deep-water surface waves, surface waves in water of finite depth, internal waves, and capillary waves in thin sheets to obtain the wave patterns sufficiently far from the moving disturbance.

References [Enhancements On Off] (What's this?)

  • [1] G. F. Carrier and P. Bakshi, Internal wave generation by a moving object, Harvard Report, 1963
  • [2] Albert A. Hudimac, Ship waves in a stratified ocean, J. Fluid Mech. 11 (1961), 229–243. MR 0136202, https://doi.org/10.1017/S0022112061000482
  • [3] D. T. Havelock, The propagation of groups of waves in dispersive media, with application to waves on water produced by a travelling disturbance, Proc. Roy. Soc. A 81, 398-430 (1908)
  • [4] H. Lamb, Hydrodynamics, Dover Edition, Dover Publishing Co., New York, 1945
  • [5] Lord Kelvin (Sir W. Thomson), On ship waves, Proc. Inst. Mech. Eng., Aug. 3, 1887
  • [6] F. Ursell, On Kelvin’s ship-wave pattern, J. Fluid Mech. 8 (1960), 418–431. MR 0114441, https://doi.org/10.1017/S0022112060000700
  • [7] G. B. Whitham, Linear and nonlinear waves, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. Pure and Applied Mathematics. MR 0483954
  • [8] Chia-Shun Yih, Gravity waves in a stratified fluid, J. Fluid Mech. 8 (1960), 481–508. MR 0115461, https://doi.org/10.1017/S002211206000075X
  • [9] Chia Shun Yih, Stratified flows, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London-Toronto, Ont., 1980. Second edition of Dynamics of nonhomogeneous fluids. MR 569474
  • [10] C.-S. Yih, Patterns of gravity waves created by a body moving in a stratified ocean, Tech. Rep. to the Office of Naval Research, 1985

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DOI: https://doi.org/10.1090/qam/987892
Article copyright: © Copyright 1989 American Mathematical Society

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