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On the attenuation of long gravity waves by short breaking waves

Published online by Cambridge University Press:  28 March 2006

O. M. Phillips
O. M. Phillips
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

It is shown that when short wind-generated gravity waves lose energy by breaking (or other dissipative processes) near the crests of longer waves, the loss is supplied partly by the longer wave because of the second-order radiation-stress interaction. This process is discussed in detail analytically and also from energy considerations with use of the concept of radiation stress. The results are applied to the attenuation of swell by a local wind-generated wave field, and it is shown that the rate of decrease of the amplitude a" of the swell is constant and given by $\frac {da^{\prime\prime}}{dt} =- \frac {3\rho_a u_*^2 c }{2\rho _w c^{\prime\prime 2}},$ where ρa,ρw are the air and water densities, u* is the friction velocity of the wind in the interaction zone, and c", c are the phase velocities of the swell and the component of the locally generated field at the spectral maximum.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 16 , Issue 3 , July 1963 , pp. 321 - 332
Copyright
© 1963 Cambridge University Press

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References

Benjamin, T. Brooke 1959 J. Fluid Mech. 6, 161–205.
Hasselmann, K. 1962 J. Fluid Mech. 12, 481–500.
Hasselmann, K. 1963 J. Fluid Mech. 15, 385–98.
Lighthill, M. J. 1962 J. Fluid Mech. 14, 385–98.
Longuet-Higgins, M. S. 1953 Phil. Trans. A, 245, 535–81.
Longuet-Higgins, M. S. 1963 J. Fluid Mech. (in the Press).
Longuet-Higgins, M. S. & Stewart, R. W. 1960 J. Fluid Mech. 8, 565–83.
Miles, J. W. 1957 J. Fluid Mech. 3, 185–204.
Miles, J. W. 1960 J. Fluid Mech. 7, 469–78.
Munk, W. H., Miller, G., Snodgrass, F. & Barber, N. 1963 Phil. Trans. A, (in the Press).
Phillips, O. M. 1960 J. Fluid Mech. 9, 193–217.
Phillips, O. M. & Katz, E. J. 1961 J. Mar. Res. 19, 57–69.
Stewart, R. W. 1961 J. Fluid Mech. 10, 189–94.