Momentum Fluxes in the Bryan–Cox Ocean Circulation Model

Abstract

The velocities used by the original, standard version of the Bryan?Cox model 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 bathymetry. This is shown to be related to the way in which the velocities are divided into baroclinic and barotropic parts when the barotropic flow is represented by a streamfunction. A list of desirable properties for the velocities at the faces of the velocity cells is suggested. Five schemes for calculating them, including Webb?s scheme and two new schemes (which are modified versions of the original scheme), are discussed and their properties derived. Simple estimates are also made of the effect of grid-scale noise in the streamfunction and thermal fields on these horizontal and vertical velocities. The velocities from short integrations of a 1° global model using these schemes are compared. The horizontal velocities produced by the 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 stepped bathymetry Webb?s scheme will be the best one to use.