DNS results (Nusselt number) for: The effect of rotation on double diffusive convection: Perspectives from linear stability analysis

Diffusive convection can occur when two constituents of a stratified fluid
have opposing effects on its stratification and different molecular
diffusivities. This form of convection arises for the particular
temperature and salinity stratification in the Arctic Ocean and is
relevant to heat fluxes. Previous studies have suggested that planetary
rotation may influence diffusive-convective heat fluxes, although the
precise physical mechanisms and regime of rotational influence are not
well understood. A linear stability analysis of a temperature and salinity
interface bounded by two mixed layers is performed here to understand the
stability properties of a diffusive-convective system, and in particular
the transition from non-rotating to rotationally-controlled heat transfer.
Rotation is shown to stabilize diffusive convection by increasing the
critical Rayleigh number to initiate instability. In the
rotationally-controlled regime, a -4/3 power law is found between
the critical Rayleigh number and the Ekman number, similar to the scaling
for rotating thermal convection. The transition from non-rotating to
rotationally-controlled convection, and associated drop in heat fluxes, is
predicted to occur when the thermal interfacial thickness exceeds about 4
times the Ekman layer thickness. A vorticity budget analysis indicates how
baroclinic vorticity production is counteracted by the tilting of
planetary vorticity by vertical shear, which accounts for the
stabilization effect of rotation. Finally, direct numerical simulations
yield generally good agreement with the linear stability analysis. This
study, therefore, provides a theoretical framework for classifying regimes
of rotationally-controlled diffusive-convective heat fluxes, such as may
arise in some regions of the Arctic Ocean.