On the Surface Waves in a Shallow Channel with an Uneven Bottom

Abstract

This paper examines surface gravity waves in a shallow channel with periodic or random bottom irregularities. Three types of bottom topography are distinguished, allowing a simplification of the basic shallow‐water‐wave equations. For two of them, asymptotic equations of the Korteveg‐de Vries type are derived (the third type has been considered earlier by other authors).