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Free-surface, wave-free gravity flow of an inviscid, incompressible fluid over a topography: an inverse problem. (English) Zbl 1489.76012

Summary: 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.

MSC:

76B07 Free-surface potential flows for incompressible inviscid fluids
76M21 Inverse problems in fluid mechanics
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