Efficiency of high order numerical schemes for momentum advection

The usefulness of high order numerical schemes for treating the advection of momentum in the primitive equations is examined. It is shown that the use of high order advection schemes for the momentum advection can improve the dynamics of potential vorticity for length scales similar to the deformation radius. This is illustrated using numerical experiments in academic and realistic configurations. In particular, a model of the North Sea is used to evaluate the effect of a high order momentum advection scheme. It is found that a fourth order scheme at 4 km resolution gives results close to a second order scheme at 2 km resolution, as far as mean and eddy kinetic energy, position of currents, size eddies are concerned. It is concluded that computing the advection of momentum with a fourth order scheme is more cost effective than doubling their resolution.