Modeling near-bottom advective acceleration in surface water models

Abstract

This paper describes problems related to the evaluation of near-bottom horizontal velocity gradients in cartesian coordinates. An analytical model and simple scaling arguments show that computing advective accelerations in cartesian coordinates may require extremely fine horizontal grids. Numerical tests are used to confirm this conclusion and to exemplify the unrealistic velocity profiles that can be obtained due to large errors in the evaluation of the advective acceleration. It is therefore recommended that horizontal gradients of velocity be evaluated in sigma coordinates. This conclusion is in stark contrast with similar studies for the baroclinic pressure gradient, and is due to the rapid variation of the vertical gradient of horizontal velocities in the bottom boundary layer.