Sliding or Stumbling on the Staircase: Numerics of Ocean Circulation Along Piecewise-Constant Coastlines

Coastlines in most ocean general circulation models are piecewise constant. Accurate representation of boundary currents along staircase-like coastlines is a long-standing issue in ocean modeling. Pioneering work by Adcroft and Marshall (1998, https://doi.org/10.3402/tellusa.v50i1.14514) revealed that artificial indentation of model coastlines, obtained by rotating the numerical mesh within an idealized square basin, generates a spurious form drag that slows down the circulation. Here, we revisit this problem and show how this spurious drag may be eliminated. First, we find that physical convergence to spatial resolution (i.e., the main characteristics of the flow are insensitive to the increase of the mesh resolution) allows simulations to become independent of the mesh orientation. An advection scheme with a wider stencil also reduces sensitivity to mesh orientation from coarser resolution. Second, we show that indented coastlines behave as straight and slippery shores when a true mirror boundary condition on the flow is imposed. This finding applies to both symmetric and rotational-divergence formulations of the stress tensor, and to both flux and vector-invariant forms of the equations. Finally, we demonstrate that the detachment of a vortex flowing past an outgoing corner of the coastline is missed with a free-slip (zero vorticity) condition at the corner. These results provide guidance for a better numerical treatment of coastlines (and isobaths) in ocean general circulation models.