AbstractBaroclinic instabilities are important processes that enhance mixing and dispersion in the ocean. The presence of sloping bathymetry and the nongeostrophic effect influence the formation and evolution of baroclinic instabilities in oceanic bottom boundary layers and in coastal waters. This study explores two nongeostrophic baroclinic instability theories adapted to the scenario with sloping bathymetry and investigates the mechanism of the instability suppression (reduction in growth rate) in the buoyant flow regime. Both the two-layer and continuously stratified models reveal that the suppression is related to a new parameter, slope-relative Burger number Sr ≡ (M2/f2)(α + αp), where M2 is the horizontal buoyancy gradient, α is the bathymetry slope, and αp is the isopycnal slope. In the layer model, the instability growth rate linearly decreases with increasing Sr {the bulk form Sr = [U0/(H0f)](α + αp)}. In the continuously stratified model, the instability suppression intensifies with increasing Sr when the regime shifts from quasigeostrophic to nongeostrophic. The adapted theories are intrinsically applicable to deep ocean bottom boundary layers and could be conditionally applied to coastal buoyancy-driven flow. The slope-relative Burger number is related to the Richardson number by Sr = δrRi−1, where the slope-relative parameter is δr = (α + αp)/αp. Since energetic fronts in coastal zones are often characterized by low Ri, that implies potentially higher values of Sr, which is why baroclinic instabilities may be suppressed in the energetic regions where they would otherwise be expected to be ubiquitous according to the quasigeostrophic theory.
Slippery bottom boundary layers: the loss of energy from the general circulation by bottom drag
