Author(s)

J.P. Pascal & S.J.D. D'Alessio

Abstract

Considered in this study is the gravity driven flow of a two-fluid model consisting of one layer floating on top of a slightly denser layer of fluid. The top layer is also subjected to a wind stress. The mathematical model is based on shallow-water theory in connection with a two-layer Boussinesq fluid. The governing equations constitute a hyperbolic system of four equations for the velocities and thicknesses of the two fluid layers. The scaling of the problem suggests that for small density differences the governing equations can be reduced to a system of two equations which are referred to as the weak stratification model. Solutions to the reduced equations have been obtained both numerically and analytically. Analytical solutions involve a wavefront expansion in order to determine the conditions necessary for a continuous waveform moving into a

Keywords