On Devising Boussinesq-type Equations with Bounded Eigenspectra: Two Horizontal Dimensions

Boussinesq-type equations are used to describe the propagation and transformation of free-surface waves in the nearshore region. The nonlinear and dispersive performance of the equations are determined by tunable parameters. Recently the authors presented conditions on the free parameters under which a Nwogu-type equations would yield bounded eigenspectra [5]. This leads to a global conditional CFL time-step restriction which is shown to not be affected by the discretisation method and in this sense the CFL condition is tamed to impose a minimal constraint. In this paper we extend the previous study and provide numerical experimentswhich confirms the theoretical results also is valid in two horizontal dimensions.