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Changes in the form of short gravity waves on long waves and tidal currents

  • M. S. Longuet-Higgins (a1) and R. W. Stewart (a2)

Short gravity waves, when superposed on much longer waves of the same type, have a tendency to become both shorter and steeper at the crests of the longer waves, and correspondingly longer and lower in the troughs. In the present paper, by taking into account the non-linear interactions between the two wave trains, the changes in wavelength and amplitude of the shorter wave train are rigorously calculated. The results differ in some essentials from previous estimates by Unna. The variation in energy of the short waves is shown to correspond to work done by the longer waves against the radiation stress of the short waves, which has previously been overlooked. The concept of the radiation stress is likely to be valuable in other problems.

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Lamb, H.1932 Hydrodynamics, 6th ed. Cambridge University Press.
Longuet-Higgins, M. S.1953 Mass-transport in water waves. Phil. Trans. A, 245, 53581.
Stokes, G. G.1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc., 8, 44155. (Reprinted in Math. and Phys. Papers, 1, 314-26.)
Unna, P. J.1941 White horses. Nature, Lond., 148, 2267.
Unna, P. J.1942 Waves and tidal streams. Nature, Lond., 149, 21920.
Unna, P. J.1947 Sea waves. Nature, Lond., 159, 23942.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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