Simulation of Internal Waves in the Strait of Gibraltar Using a Two-layer Shallow-water Model

This paper is concerned with the simulation of the flow of a stratified fluid through a channel with irregular geometry. The channel is supposed to have a straight axis and to be symmetric with regard to a vertical plane passing through its axis. The cross-sections are supposed to be of arbitrary shape. The fluid is assumed to be composed of two shallow layers of immiscible fluids of constant density. Moreover, we assume that the flow is one dimensional, i.e., at every layer the velocities are uniform over the cross-section and the thickness only depend on the coordinate related to the axis and on the time. Therefore, the equations to be solved are a system of two coupled Shallow Water equations with source terms involving depth and breadth functions. Extensions of the Q-schemes of van Leer and Roe are proposed where the coupling and source terms are treated by adapting the techniques developed in [9], [5] and [2]. Finally we apply the numerical scheme to the simulation of the flow through the Strait of Gibraltar, performing simulations of tidal effects and comparing the results with observed data.