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.

The land-sea breeze is resonant with the inertial response of the ocean at the critical latitude of 30°N/S. 1D-vertical numerical experiments were undertaken to study the key drivers of enhanced diapycnal mixing in coastal upwelling systems driven by diurnal-inertial resonance near the critical latitude. The effect of the land boundary was implicitly included in the model through the ‘Craig approximation’ for first order cross-shore surface elevation gradient response. The model indicates that for shallow water depths (<~100m), bottom shear stresses must be accounted for in the formulation of the ‘Craig approximation’, as they serve to enhance the cross-shore surface elevation gradient response, while reducing shear and mixing at the thermocline. The model was able to predict the observed temperature and current features during an upwelling/mixing event in 60m water depth in St Helena Bay (~32.5°S, southern Benguela), indicating that the locally forced response to the land-sea breeze is a key driver of diapycnal mixing over the event. Alignment of the sub-inertial Ekman transport with the surface inertial oscillation produces shear spikes at the diurnal-inertial frequency, however their impact on mixing is secondary when compared with the diurnal-inertial resonance phenomenon. The amplitude of the diurnal anticlockwise rotary component of the wind stress represents a good diagnostic for the prediction of diapycnal mixing due to diurnal-inertial resonance. The local enhancement of this quantity over St Helena Bay provides strong evidence for the importance of the land-sea breeze in contributing to primary production in this region through nutrient enrichment of the surface layer.