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On surface waves crossing a step with horizontal shear

Published online by Cambridge University Press:  21 April 2006

Jerome Smith
Jerome Smith
Affiliation:
Marine Physical Laboratory of the Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093, USA
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Abstract

When surface waves encounter a step in bottom topography and/or a change in velocity parallel to the step, refraction and partial reflection occur. Comparison of several approximate solutions indicates that no single approximation works well for all cases. The pattern of success among models suggests that the velocity profile at the boundary favours the free wave with smaller vertical scale. For current changes over a flat bottom, a two-term Galerkin expansion (cf. Evans 1975) is employed for comparison with the other more general models. For small currents (|ΔV| < ½c), an ‘action-based approximation’ (cf. Smith 1983) is favoured, although all models perform adequately. With a strong current, one one-term (one-sided) model performs best, another worst among models; the favoured model includes ephemeral modes on the side with larger-scale free waves. For changes in depth only, the one-sided model with ephemeral modes on the deep side was shown by Miles (1967) to perform well. The two-term expansion (cf. Evans 1975) is not easily extended to this case, and none of the other approximations perform adequately. In the unusual case of a step combined with a strong current, such that much shorter waves occur in the deeper region, it is inferred that none of the models are accurate. Reflection from a submerged wall provides a severe test of the models. Without the ephemeral modes, no net reflection occurs. The Miles-like model overpredicts reflection slightly.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 175 , February 1987 , pp. 395 - 412
Copyright
© 1987 Cambridge University Press

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