Open Boundary Conditions for Dispersive Waves

Abstract

Approximate outgoing radiation conditions have been widely used at open boundaries in dispersive wave computations. Exact outgoing radiation conditions are constructed here for infinitesimal surface inertia-gravity waves, barotropic Rossby waves, and non-hydrostatic internal gravity waves incident at infinite plane open boundaries. They are also constructed for infinitesimal two-dimensional surface gravity waves incident at a square open boundary, a finite straight open boundary in a channel, and a circular open boundary, The constructions use Laplace transforms, various Fourier transforms, and a wave field splitting technique. The exact outgoing radiation conditions all involve weighted space and time averages. Their numerical implementation would be most complex and would require computer storage approaching that which one is trying to avoid by the introduction of open boundaries. Alternatives are discussed.