_ Vol. 26 (4) (2000) pp. 235-255 _
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Fluid Dynamics Research, Vol. 26 (4) (2000) pp. 235-255
© 2000 The Japan Society of Fluid Mechanics and Elsevier Science B.V. All rights reserved.
PII: S0169-5983(99)00025-8

Long surface wave scattered by a step in a two-layer fluid

E. Barthélemy * eric.barthelemy@hmg.inpg.fr, A. Kabbaj and J.-P. Germain

Laboratoire des Ecoulements Géophysiques et Industriels (LEGI), Lab. de I'UJF et de L'INPG, UMR CNRS, B.P. 53, 38041 Grenoble Cedex 9, France

Received 15 May 1998; received in revised form 25 March 1999; accepted 15 May 1999

Abstract

A WKBJ technique is used to investigate theoretically the scattering of a surface long wave by a step bottom in a two-layer fluid. It enables one to overcome the main inconsistency of the shallow-water theory in the presence of obstacles. In the vicinity of the obstacle, the present theory introduces evanescent modes to take into account the essentially two-dimensional motions close to the abrupt changes in the bottom. The reflection and transmission coefficients for both fast and slow modes are computed. Approximations of oceanographical relevance are derived. The homogeneous fluid case is recovered. Finally, the detailed kinematics in the vicinity of the step break is investigated by means of complex functions and conformal mapping.

*Corresponding author. Fax: +33(0)4-76-82-50-9
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