TRANSCRITICAL, SHALLOW-WATER FLOW OVER COMPACT TOPOGRAPHY

The flow of a shallow layer of fluid over isolated topography is considered when the velocity is near the critical, long-wave speed. The response of the free surface is obtained when the length-scale of the topographic variation is comparable to the fluid depth (compact topography). The weakly nonlinear response is described by a forced Korteweg de Vries equation. When the topography is compact, an inner and outer matching is required to obtain a uniform description of the free-surface deformation for all streamwise positions. The important classes of compact forcing are defined and general results for the shape of the free surface directly over the topographic forcing are obtained. A variety of stationary, outer solutions are presented including solitary and lee-wave responses.