Momentum fluxes in the Bryan-Cox ocean circulation model

The velocities used by the original, standard version of the Bryan-Cox mode l to advect momentum are shown to be inconsistent with the main velocities over steps in the bathymetry. In particular, the vertical shears of the two sets of horizontal velocities disagree at the top edges of steps in the ba thymetry. This is shown to be related to the way in which the velocities ar e divided into baroclinic and barotropic parts when the barotropic Bow is r epresented by a streamfunction. A list of desirable properties for the velo cities at the faces of the velocity cells is suggested. Five schemes for ca lculating them, including Webb's scheme and two new schemes (which are modi fied versions of the original scheme), are discussed and their properties d erived. Simple estimates are also made of the effect of grid-scale noise in the streamfunction and thermal fields on these horizontal and vertical vel ocities. The velocities from short integrations of a 1 degrees global model using these schemes are compared. The horizontal velocities produced by th e original scheme suffer from gridpoint noise in the streamfunction. One of the new schemes represents these velocities well if the streamfunction is smoothed appropriately. While the vertical velocities with this scheme are less noisy than with the original scheme, they are still inferior to those generated by Webb's scheme. It is argued that in any model with realistic s tepped bathymetry Webb's scheme will be the best one to use.