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

Published online by Cambridge University Press:  28 March 2006

M. S. Longuet-Higgins  and
R. W. Stewart
M. S. Longuet-Higgins
Affiliation:
National Institute of Oceanography, Surrey
R. W. Stewart
Affiliation:
University of British Columbia
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Abstract

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 8 , Issue 4 , August 1960 , pp. 565 - 583
Copyright
© 1960 Cambridge University Press

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References

Lamb, H. 1932 Hydrodynamics, 6th ed. Cambridge University Press.
Longuet-Higgins, M. S. 1953 Mass-transport in water waves. Phil. Trans. A, 245, 535–81.Google Scholar
Stokes, G. G. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc., 8, 441–55. (Reprinted in Math. and Phys. Papers, 1, 314-26.)Google Scholar
Unna, P. J. 1941 White horses. Nature, Lond., 148, 226–7.Google Scholar
Unna, P. J. 1942 Waves and tidal streams. Nature, Lond., 149, 219–20.Google Scholar
Unna, P. J. 1947 Sea waves. Nature, Lond., 159, 239–42.Google Scholar