Non-geostrophic baroclinic instability in coastal buoyancy-driven flow

Baroclinic instabilities are ubiquitous in open oceans but seldom observed in coastal zones, even though lateral density gradients within coastal fronts are often stronger than those of open ocean fronts. This study explores the non-geostrophic baroclinic instability theories adapted to the scenario with sloping bathymetry and demonstrates the suppression of instabilities, through a reduction in growth rate, in the non-geostrophic limit. Both the layered and continuously stratified models reveal that the suppression is related to a new parameter, slope-relative Burger number Sr, which has not been discussed in the literature. Sr represents the gradient of potential vorticity supplemented by topographic effects. The underlying mechanism of Sr is that the growth of baroclinic instabilities is directly related to Rossby wave resonance, and Sr controls the wave resonance by modifying the properties of the Rossby waves, thereby influencing the the growth of instabilities. Instability growth is found to be inhibited with increasing Sr, and coastal fronts are often energetic, characterized by high Sr, which is why baroclinic instabilities may be suppressed in coastal regions where they might otherwise be expected.