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Internal waves in a wedge-shaped region

Published online by Cambridge University Press:  29 March 2006

D. G. Hurley
D. G. Hurley
Affiliation:
Department of Mathematics, University of Western Australia
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Abstract

The Green's functions are found for a line source of internal waves in a wedge of stratified fluid of constant Brunt–Väisälä frequency, and are used to discuss the diffraction of internal waves by a wedge in all cases when the vertex angle of the wedge of fluid exceeds the acute angle between a characteristic and the horizontal. Robinson's (1970) results are confirmed and extended.

It is found that the diffracted waves are as important as the incident and reflected ones at all points that lie within a quarter-wavelength or so of either characteristic that passes through the apex. Also, in cases when all the reflected waves are inclined forwards, the diffracted waves lead to a positive backscatter of energy. When the vertex angle of the fluid wedge is less than the characteristic angle, the diffraction problem appears to be ill-posed, and, instead, the motion due to a vibrating body in the wedge of fluid is considered.

A general conclusion is that the so-called ray theory for internal waves, in which the incident and reflected waves alone are considered, has similar limitations to the geometrical theory of optics. Both theories involve the assumption that the typical dimensions in the problem are large compared to the wavelength.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 43 , Issue 1 , 17 August 1970 , pp. 97 - 120
Copyright
© 1970 Cambridge University Press

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References

Ambramowitz, M. & Stegun, I. A. 1967 Handbook of Mathematical Functions. National Bureau of Standards.
Barcilon, V. & Bleistein, N. 1969 Studies Appl. Maths. 48, 91–104.
Bers, L., John, F. & Schechter, M. 1964 Partial Differential Equations. New York: Interscience.
Cox, C. S. & Sandstrom, H. 1962 J. Ocean. Soc. Japan, 20th Anniver. Vol., pp. 499–513.
Fofonoff, N. P. 1967 Proc. IAPO Symposium on Internal Waves, General Assembly of IUGG, Berne, Switzerland.
Greenspan, H. P. 1969 Studies Appl. Maths. 48, 19–28.
Hurley, D. G. 1969 J. Fluid Mech. 36, 657–72.
Hurley, D. G. & Imberger, J. 1969 Bull. Austr. Math. Soc. 1, 29–46.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Larson, L. 1969 Deep Sea Res. 16, 411–419.
Longuet-Higgins, M. S. 1969 J. Fluid Mech. 37, 231–50.
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Robinson, R. M. 1969 Deep Sea Res. 16, 421–9.
Robinson, R. M. 1970 J. Fluid Mech. 42, 257–68.
Sagan, H. 1961 Boundary and Eigenvalue Problems in Mathematical Physics. New York: John Wiley.
Wunsch, C. 1968 Deep Sea Res. 25, 251–8.
Wunsch, C. 1969 J. Fluid Mech. 35, 131–44.