Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-26T23:42:03.574Z Has data issue: false hasContentIssue false
  • English
  • Français

Reflection from a water waves from a vertical vortex sheet in water of finite depth

Published online by Cambridge University Press:  17 February 2009

W. D. McKee  and
F. Tesoriero
W. D. McKee
Affiliation:
School of Mathemactics, University of New South Wales, P. O. Box 1, Kensington, N.S.W. 2033, Australia.
F. Tesoriero
Affiliation:
4 Wackett Street, Maroubra, N.S.W. 2035, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The reflection-transmission properties of water waves obliquely incident upon a vortex sheet in water of finite depth are studied. The problem is reduced to that of solving two integral equation. An accurate Galerkin solution is obtained which supports the use of the “variational method” in water wave problems that has recently been questioned by Kirby and Dalyrmple.

Type
Research Article
Information
The ANZIAM Journal , Volume 29 , Issue 2 , October 1987 , pp. 127 - 141
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Evans, D. V., “The transmission of deep-water waves across a vortex sheet”, J. Fluid Mech. 68 (1975) 389–401.CrossRefGoogle Scholar
[2]Kirby, J. T. and Dalrymple, R. A., “Propagation of obliquely incident water waves across a trench”, J. Fluid Mech. 133 (1983) 47–63.CrossRefGoogle Scholar
[3]Mei, C.-C., The applied dynamics of ocean surface waves (Wiley, New York, 1983).Google Scholar
[4]Miles, J. W., “Surface-wave scattering matrix for a shelf”, J. Fluid Mech. 28 (1967) 755–767.CrossRefGoogle Scholar
[5]Mollo-Christensen, E., “Over-reflection of horizontally propagating gravity waves by a vertical shear layer”, Phys. Fluids 21 (1978) 1908–1911.CrossRefGoogle Scholar
[6]Peregrine, D. H., “Interaction of water waves and currents”, Adv. in Appl. Mech. 16 (1976) 9–129.CrossRefGoogle Scholar
[7]Smith, J., “On surface gravity waves crossing weak current jets”, J. Fluid Mech. 134 (1983) 277–299.CrossRefGoogle Scholar
[8]Tesoriero, F., “The propagation of surface waves across a shear current in water of finite depth”, B. Sc. Thesis, School of Mathematics, University of New South Wales, 1984.Google Scholar