Abstract

Water waves propagating over non-smooth, large amplitude, disordered topography leads to novel asymptotic theory both at the level of equations (i.e. reduced models) as well as at the level of solutions (i.e. effective behavior). In the reduced modeling of two-dimensional flows, conformal mapping plays an important role. This lecture will introduce the use of conformal mapping together with nonlinear potential theory. The Schwarz-Christoffel Toolbox (by T. Driscoll) will also be introduced showing how to extract quantitative information from the conformal mapping in a specific flow domain. This is useful for computational applications. As time permits recent research examples will be presented such as pulse shaped waves over a disordered (random) topography or in branching channels