Uncertainty Quantification of Bathymetric Effects in a Two-Layer Shallow Water Model: Case of the Gibraltar Strait

Abstract

The flow occurring in the strait of Gibraltar raises an interface as a result of different water temperatures and salinities in the Atlantic Ocean and the Mediterranean Sea. These differences yield to the well-established exchange flow problem in hydraulics. Many numerical models have been designed for solving this particular problem including the shallow water equations. In the current study, we consider a two-layer shallow water problem accounting for friction terms in the topography. We present a class of numerical techniques to examine effects of the bathymetric parameters on the water free-surface and the interface between the two layers. Special attention is given to a coupled algorithm of polynomial chaos expansions and proper orthogonal decomposition and its performance to accurately assess the uncertainty in two-layer shallow water flows. In addition, using the Karhuen-Loeve decomposition, high dimensions in stochastic input and physical output are also dealt with in our simulations. Numerical results are presented for the problem of exchange flow in the strait of Gibraltar.