Fluid surface oscillations in a shallow two-dimensional basin

Abstract

The two-dimensional oscillation of a free liquid surface in a shallow basin of arbitrary cross-section is considered It is assumed that the fluid motion is not influenced by the earth rotation and that the fluid is ideal, Since the linearized equations are not valid in the region of the shoreline, they are used only in the center region of the basin. In the proximity of the shoreline the method of characteristics is used as applied to the nonlinear shallow water equations. The bottom of the basin in this region is approximated by a straight line. Since it is implicitly assumed that the center region drives the shallow wedge at the shoreline, but conversely the shore region does not affect the center region, the usefulness of the solution is confined to the first few cycles only. The analytical solution was checked by applying a numerical method of solution for the entire basin. The agreement was satisfactory over the first two cycles.