Stationary Simple Waves on a Barotropic Liquid Shear Flow

Abstract

Stationary three‐dimensional flows of a barotropic liquid in a gravity field are considered. In the shallow‐water approximation, the Euler equations are transformed into a system of integrodifferential equations by the Euler‐Lagrange change of coordinates. A system of simple‐wave equations is obtained, for which the theorem of existence of a solution attached to a given shear flow is proved. As an example, a particular solution analogous to the solution of the problem of a gas flow around a convex angle is given.