Time splitting and linear stability of the slow part of the barotropic component

In this paper, the authors analyse the stability of particular numerical schemes used in oceanic general circulation models to deal with the barotropic momentum advection term. It is shown that, when this term is integrated using time splitting, its stability properties can be drastically reduced in configurations where there exists shallow areas, where velocities become comparable to the propagation speed of external gravity waves. A simple alternative scheme with improved stability is proposed and discussed.