Introduction

To date, there have been few studies focusing on the issue of coastline representation in finite difference models. Schwab and Belestky schwab98 studied the influence of steps on inviscid Kelvin waves. Adcroft and Marshall (1998, hereafter referred as AM) addressed the problem in the context of the single gyre nonlinear Munk problem using a C-grid shallow water (SW) model. They showed (as did Cox, 1979) that the horizontal circulation under no-slip boundary condition is not very sensitive to the presence of steps along the coastline. This can be explained by the fact that the core of the boundary current under no-slip is located a few grid points inside the interior of the basin.

For free-slip, however, they compared results from non-rotated and rotated square basin experiments and showed the circulation to be highly sensitive to the presence of steps along the walls. In rotated basin experiments, the basin was rotated relative to the grid axes (see Fig. 2.1), but the wind forcing and north-south axis were kept constant relative to the basin, so that the only differences between the experiments are due to the discretization. The presence of steps along the boundary tends to reduce the strength of the circulation to the extent that results obtained using free-slip boundary conditions with step-like boundaries more closely resembles those with no-slip boundary conditions than free-slip solutions without steps. Moreover, they showed that, at least for small rotation angles, sensitivity to steps under free-slip conditions could be greatly reduced by using a vorticity-divergence formulation of the viscous stress tensor [Madec et al. , 1991], hereafter referred as the $\delta$-$\zeta$

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