A two-layer finite volume model for flows through channels with irregular geometry: Computation of maximal exchange solutions. Application to the Strait of Gibraltar

Abstract The aim of this paper is to present a numerical model for solving the two layer exchange problem through channels with irregular geometry both in breadth and depth and the obtaining of maximal exchange solutions as defined by Armi and Farmer [J. Fluid Mech. 164 (1986) 27]. First, the equations are presented for each of the two layers of fluid. For numerically approximate the solution of the two layer system, we have considered the first-order upwind scheme presented by M.J. Castro, J. Macias, C. Pares, M.A. Vazquez-Cendon (in preparation). Then, the model is used to compute a maximal exchange solution for a channel with rectangular cross-sections and a single bump. This solution is compared against the approximate analytical solutions provided by Armi and Farmer [J. Fluid Mech. 164 (1986) 53]. Finally, the model is used to obtain a maximal two-layer exchange flow through the Strait of Gibraltar for which a realistic geometry has been considered.