A series-solution method for free-boundary problems arising from flow over topography

Abstract

An analytical series method is presented for steady, two-dimensional, irrotational flow of a single layer of constant-density fluid over topography. This problem is formulated as a Laplacian free-boundary problem with fully nonlinear boundary conditions. The method is an iterative scheme that allows the calculation of analytical series solutions for supercritical, transcritical and subcritical flow regimes over arbitrary topography. By an appropriate choice of the free-boundary representation, exponential convergence of the series solution is achieved. With this accuracy, the issue of apparent dual transcritical/subcritical solutions previously obtained by boundary-integral-equation methods (BIEM) is resolved. Results are compared with solutions previously obtained using BIEM, and solutions are presented for flow over asymmetric and arbitrarily shaped obstacles.