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The effects of a corner on a propagating internal gravity wave

Published online by Cambridge University Press:  29 March 2006

R. M. Robinson
R. M. Robinson
Affiliation:
Department of Mathematics, University of Western Australia
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Abstract

A solution satisfying the usual radiation conditions is found to the problem of an internal wave propagating towards a corner. It is found that, far from the corner, and the characteristic emanating from the corner, the solution is asymptotically equivalent to the solution found by plane wave reflexions from an infinite wall. The present solution shows that, by imposing the radiation condition, a singularity predicted by the ray theory along the corner characteristic is absent. A further singularity in the present solution along the same characteristic is shown to be due to an inability of the usual linear internal wave equations to fully describe the motion. The solution is for restricted corner angles.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 42 , Issue 2 , 22 June 1970 , pp. 257 - 267
Copyright
© 1970 Cambridge University Press

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References

Erdelyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1954 Tables of Integral Transform, vol. 1. Bateman Manuscript Project. New York: McGraw-Hill.
Levey, H. C. & Mahoney, J. J. 1968 Series representations of Fourier integrals. Quart. J. Appl. Math. 26, 101–109.Google Scholar
Mowbray, D. E. & Rarity, B. S. H. 1967 A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified liquid. J. Fluid Mech. 28, 1–16.Google Scholar
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Sandstrom, H. 1966 On the importance of topography in generation and propagation of internal waves. Ph.D. Thesis, University of California, San Diego.
Wunsch, C. 1969 Progressive internal waves on slopes. J. Fluid Mech. 35, 131–144.Google Scholar