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Over-reflection and shear instability in a shallow-water model

Published online by Cambridge University Press:  26 April 2006

Shin-Ichi Takehiro  and
Yoshi-Yuki Hayashi
Shin-Ichi Takehiro
Affiliation:
Department of Earth and Planetary Physics, University of Tokyo, Bunkyo, Tokyo 113, Japan
Yoshi-Yuki Hayashi
Affiliation:
Department of Earth and Planetary Physics, University of Tokyo, Bunkyo, Tokyo 113, Japan
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Abstract

The characteristics of shallow-water waves in a linear shear flow are studied, and the relationship between waves and unstable modes is examined. Numerical integration of the linear shallow-water equations shows that over-reflection occurs when a wave packet is incident at the turning surface. This phenomenon can be explained by the conservation of momentum as discussed by Acheson (1976). The unstable modes of linear shear flow in a shallow water found by Satomura (1981) are described in terms of the properties of wave propagation as proposed by Lindzen and others. Ripas's (1983) theorem, which is the sufficient condition for stability of flows in shallow water, is also related to the wave geometry. The Orr mechanism, which is proposed by Lindzen (1988) as the primary mechanism of wave amplification, cannot explain the over-reflection of shallow-water waves. The amplification of these waves occurs in the opposite sense to that of Orr's solution.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 236 , March 1992 , pp. 259 - 279
Copyright
© 1992 Cambridge University Press

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