Free-surface flow past arbitrary topography and an inverse approach for wave-free solutions

Abstract

[Received on 8 December 2012; revised on 19 March 2013; accepted on 20 March 2013] An efficient numerical method to compute nonlinear solutions for 2D steady free-surface flow over an arbitrary channel bottom topography is presented. The approach is based on a boundary integral equation technique which is similar to that of Vanden-Broeck’s (1996). The typical approach for this problem is to prescribe the shape of the channel bottom topography, with the free surface being provided as part of the solution. Here we take an inverse approach and prescribe the shape of the free surface ap rioriand solve for the corresponding bottom topography. We show how this inverse approach is particularly useful when studying topographies that give rise to wave-free solutions, allowing us to easily classify 11 basic flow types. Finally, the inverse approach is also adapted to calculate a distribution of pressure on the free surface, given the free surface shape itself.