How slippery are piecewise-constant coastlines in numerical ocean models?

Coastlines in numerical ocean models are oriented at various finite angles to the model grid. The true coastline is usually replaced by a piecewise-constant approximation in which the model coastline is everywhere aligned with the model grid. Here we study the consequences of the piecewise-constant approximation in an idealised shallow-water ocean model. By rotating the numerical grid at various finite angles to the physical coastlines, we are able to isolate the impact of piecewise-linear boundaries on the model circulation. We demonstrate that piecewise-constant coastlines exert a spurious form stress on model boundary currents, dependent on both the implementation of the slip boundary condition and the form of the viscous stress tensor. In particular, when free-slip boundary conditions are applied, the character of the circulation can be reduced to no-slip in the presence of a piecewise-constant boundary. The spurious form stress can be avoided in a free-slip limit if the viscous stress tensor is written in terms of vorticity and divergence.