Pseudospectral methods for Boussinesq-type equations in an annular domain with applications to mid-sized lakes

Abstract

We present a numerical solution procedure for a two-dimensional Boussinesq-type shallow water model on annular domains using pseudospectral discretization methods, including practical implementation details such as spectral filtering to prevent aliasing-driven instabilities and efficient numerical linear algebra techniques. The numerical model's potential for predicting and simulating wave motions in mid-sized lakes is illustrated with three test cases: (1) wave diffraction around an island and near-shore focusing; (2) the formation, propagation and destruction of wave trains and solitary-like waves in rotating basins; and (3) the influence of bottom bathymetry on wave formation and propagation from a Kelvin-seiche.