High-order well-balanced finite-volume schemes for barotropic flows. Development and numerical comparisons

In this paper, we compare a classical finite-difference and a high order finite-volume scheme for barotropic ocean flows. We compare the schemes with respect to their accuracy, stability, and study various outflow and inflow boundary conditions. We apply the schemes to the problem of eddy formation in shelf slope jets along the Ormen Lange section of the Norwegian shelf. Our results strongly confirm the development of mesoscale eddies caused by instability of the flows.