Non-monotonic drag instability induced by rough bathymetry in non-zonal flows

Topographic roughness, defined as irregular variability of ocean depth on lateral scales of 1–10 km, has recently been shown to substantially impact the dynamics of large-scale and mesoscale ocean flows, including eddies, Rossby waves and baroclinic instability. This suggests that accurate modelling of roughness-induced forcing is critical for representing large-scale ocean behaviour. A recent multi-scale analysis of flows affected by small-scale bathymetry has produced the ‘sandpaper theory’, an explicit parametrisation of the roughness-induced bottom drag. This model accurately captures the impact of small-scale topography on large-scale flows without the need to resolve it in general circulation models. A peculiar facet of the sandpaper theory is that the drag is a non-monotonic function of the flow speed above the bottom boundary layer, which results in an instability. We characterise this non-monotonic drag instability for a series of barotropic and baroclinic systems, and explore a dynamically rich variety of scenarios that can produce stable jets, overstable Rossby waves, mesoscale eddy streets and self-amplifying hetons. We describe and quantify the properties of each flow type as they pertain to this non-monotonic drag regime.