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.

Vertical mixing is often regarded as the Achilles' heel of ocean models. In particular, few models include a comprehensive and energy-constrained parameterization of mixing by internal ocean tides. Here, we present an energy-conserving mixing scheme which accounts for the local breaking of high-mode internal tides and the distant dissipation of low-mode internal tides. The scheme relies on four static two-dimensional maps of internal tide dissipation, constructed using mode-by-mode Lagrangian tracking of energy beams from sources to sinks. Each map is associated with a distinct dissipative process and a corresponding vertical structure. Applied to an observational climatology of stratification, the scheme produces a global three-dimensional map of dissipation which compares well with available microstructure observations and with upper-ocean finestructure mixing estimates. This relative agreement, both in magnitude and spatial structure across ocean basins, suggests that internal tides underpin most of observed dissipation in the ocean interior at the global scale. The proposed parameterization is therefore expected to improve understanding, mapping and modelling of ocean mixing.

Diapycnal mixing shapes the distribution of climatically-important tracers, such as heat and carbon, as these are carried by dense water masses in the ocean interior. Here, we analyze a suite of observation-based estimates of diapycnal mixing to assess its role within the Atlantic Meridional Overturning Circulation. The rate of water mass transformation in the Atlantic Ocean’s interior shows that there is a robust buoyancy increase in the North Atlantic Deep Water (NADW), with a diapycnal circulation of up to 4 Sv between 24N and 32S in the Atlantic Ocean. Moreover, tracers within the southward-flowing NADW may undergo a substantial diapycnal transfer, equivalent to hundreds of metres in the vertical. This result is confirmed with a zonally-averaged numerical model of the AMOC and indicates that tracer mixing can lead to divergent global pathways and ventilation timescales following the upwelling of tracers in the Southern Ocean. These results point to the need for a realistic mixing representation in climate models in order to understand and credibly project the ongoing climate change.