Numerical Simulation of Surface and Internal Waves using a Set of Nonlinear Equations with Vorticity

Abstract

A functional for variational problems of multilayer-fluid systems with vorticity was presented, after which a set of nonlinear equations were derived to simulate surface and internal waves considering both strong nonlinearity and strong dispersivity of waves. The linear dispersion relations for surface and internal waves were shown also for deep-wave conditions. Stable results of surface waves propagating over a submerged breakwater, as well as internal waves reciprocating inside a closed tank, were obtained using the numerical model, where two-layer stratification was treated below a fixed horizontal plate. The internal waves resulted by the present model had a different period from that through a Boussinesq-type model. The surface waves over a slope steepened further due to the assumed vorticity effect.