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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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Longuet-Higgins, M. S.1953Mass-transport in water waves. Phil. Trans. A, 245, 53581.

Unna, P. J.1941White horses. Nature, Lond., 148, 2267.

Unna, P. J.1942Waves and tidal streams. Nature, Lond., 149, 21920.

Unna, P. J.1947Sea 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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