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Vortex scattering by step topography

Published online by Cambridge University Press:  04 January 2007

A. K. HINDS ,
E. R. JOHNSON  and
N. R. MCDONALD
A. K. HINDS
Affiliation:
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK
E. R. JOHNSON
Affiliation:
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK
N. R. MCDONALD
Affiliation:
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK
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Abstract

The scattering at a rectilinear step change in depth of a shallow-water vortex pair consisting of two patches of equal but opposite-signed vorticity is studied. Using the constants of motion, an explicit relationship is derived relating the angle of incidence to the refracted angle after crossing. A pair colliding with a step from deep water crosses the escarpment and subsequently propagates in shallow water refracted towards the normal to the escarpment. A pair colliding with a step from shallow water either crosses and propagates in deep water refracted away from the normal or, does not cross the step and is instead totally internally reflected by the escarpment. For large depth changes, numerical computations show that the coherence of the vortex pair is lost on encountering the escarpment.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 571 , 25 January 2007 , pp. 495 - 505
Copyright
Copyright © Cambridge University Press 2007

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References

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