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

A WKBJ technique is used to investigate theoretically the scattering of a s urface long wave by a step bottom in a two-layer fluid. It enables one to o vercome the main inconsistency of the shallow-water theory in the presence of obstacles. In the vicinity of the obstacle, the present theory introduce s evanescent modes to take into account the essentially two-dimensional mot ions close to the abrupt changes in the bottom. The reflection and transmis sion coefficients for both fast and slow modes are computed. Approximations of oceanographical relevance are derived. The homogeneous fluid case is re covered. Finally, the detailed kinematics in the vicinity of the step break is investigated by means of complex functions and conformal mapping. (C) 2 000 Published by The Japan Society of Fluid Mechanics and Elsevier Science B.V. All rights reserved.