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On wave scattering by random inhomogeneities, with application to the theory of weak bores

Published online by Cambridge University Press:  29 March 2006

M. S. Howe
M. S. Howe
Affiliation:
Imperial College, London, S.W. 7
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Abstract

This paper considers the propagation and scattering of waves in dispersive and non-dispersive media containing random inhomogeneities. A detailed discussion of the propagation of the coherent component of the wave field is presented, and a rather general method for obtaining the absorption coefficient and scattering cross-section per unit volume of medium is described. A major objective is to derive macroscopic equations for the propagation of the coherent field in the sense that the damping due to scattering appears in the wave equation as pseudo-viscosity. The paper is concluded by a detailed application of the theory to the problem of the propagation of surface gravity waves over a stretch of shallow water with a ‘rough’ bed. By including finite amplitude effects a balance is achieved between the dispersion of the pseudo-viscous term and the non-linear convective terms, which enables the steady profile of a weak bore to be calculated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 45 , Issue 4 , 26 February 1971 , pp. 785 - 804
Copyright
© 1971 Cambridge University Press

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