Sliding or stumbling on the staircase: numerics of ocean circulation
along piecewise-constant coastlines
Abstract
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 modelling.
Pioneering work by Adcroft and Marshall (1998) revealed that artificial
indentation of model coastlines, obtained by rotating the numerical mesh
within an idealized square basin, generates a
\textit{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
\textit{physical} convergence (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 faithfully simulated
with exclusive implementation of impermeability conditions. These
results provide guidance for a better numerical treatment of coastlines
(and isobaths) in ocean general circulation models.