Symmetric supercritical free surface flow over a polygonal obstacle

Abstract In this paper, we consider steady, supercritical, plane, incompressible and irrotational flow in a channel with an obstacle of polygonal shape placed on the bottom. The solution is based on the combined use of a conformal mapping and the Riemann-Hilbert solution of a mixed boundary-value problem in the upper half plane. Numerical methods are introduced, and numerical solutions for some symmetric examples are presented. Numerical checks are applied showing good agreement. A comparison with the solution of the corresponding linearised problem shows that there are large differences, and contrary behaviour of the shape of the free surface as the Froude number is varied.

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