Fluxes through diffusive staircases: A new formulation

This paper deals with two aspects of the flux law for diffusive convection: (1) the dependence on density ratio, and (2) the dependence on Δ T . Empirical formulations of the dependence of temperature and salinity fluxes on density ratio are developed using published measurements. At high density ratios ( R ρ > 4) our temperature fluxes agree with those given by Marmorino and Caldwell's (1976) formulation, but at low density ratios ( R ρ < 2.5) our temperature fluxes are smaller by half. However, it is suggested that any formulation of the 4/3 flux law should be used with caution. A simple convection theory implies that fluxes are not proportional to Δ T 4/3 , as the 4/3 law states, but rather are proportional to Δ T raised to an power closer to 5/4. The theory accurately matches measurements of velocity and heat flux in thermal convection. There are insufficient data to test (or even fully formulate) the theory for diffusive convection, but if the thermal convection results carry over to the diffusive case, then the 4/3 flux law overestimates oceanic fluxes by up to about 30%.