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In this paper we compare a classical finite-difference and a high orderfinite- volume scheme for barotropic ocean flows. We compare the schemes withrespect to their accuracy, stability, and study various outflow and inflowboundary conditions. We apply the schemes to the problem of eddy formation inshelf slope jets along the Ormen Lange section of the Norwegian shelf. Ourresults strongly confirm the development of mesoscale eddies caused byinstability of the flows.

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