Free-surface, wave-free gravity flow of an inviscid, incompressible fluid over a topography: an inverse problem

A simple semi-analytical approach relying on Fourier-type finite expansions and boundary collocation is proposed to solve an inverse problem for the fully nonlinear two-dimensional, steady, free-surface, wave-free gravity fluid flow in an infinite channel with topography of finite extent. The fluid is of constant density, and the flow is assumed irrotational. The coefficients involved in the series representation for the streamfunction are determined from a linear system of algebraic equations. Results are plotted for four cases belonging to two main classes of the flow.