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The reflexion of internal/inertial waves from bumpy surfaces

Published online by Cambridge University Press:  29 March 2006

P. G. Baines
P. G. Baines
Affiliation:
Department of Meteorology, Massachusetts Institute of Technology, Cambridge, Massachusetts, U.S.A.
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Abstract

When internal and/or inertial waves reflect from a smooth surface which is not plane, there is in general some energy flux which is ‘back-reflected’ in the opposite direction to that of the incident energy flux (in addition to that ‘transmitted’ in the direction of the reflected rays), provided only that the incident wavelength is sufficiently large in comparison with the length scales of the reflecting surface. The reflected wave motion due to an incident plane wave is governed by a Fredholm integral equation whose kernel depends on the form of the reflecting surface. Some specific examples are discussed, and the special case of the ‘linearized boundary’ is considered in detail. For an incoming plane wave incident on a sinusoidally varying surface of sufficiently small amplitude, in addition to the main reflected wave two new waves are generated whose wave-numbers are the sum and difference respectively of those of the surface perturbations and the incident wave. If the incident wave-number is the smaller, the difference wave is back-reflected.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 46 , Issue 2 , 29 March 1971 , pp. 273 - 291
Copyright
© 1971 Cambridge University Press

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