New layer thickness parameterization of diffusive convection in the ocean

Abstract

In the present study, a new parameterization is proposed to describe the convecting layer thickness in diffusive convection. By using in situ observational data of diffusive convection in the lakes and oceans, a wide range of stratification and buoyancy flux is obtained, where the buoyancy frequency N varies between 10−4 and 0.1 s−1 and the heat-related buoyancy flux qT varies between 10−12 and 10−7 m2 s−3. We construct an intrinsic thickness scale, H0=[qT3/(κTN8)]1/4, here κT is the thermal diffusivity. H0 is suggested to be the scale of an energy-containing eddy and it can be alternatively represented as H0 = ηRebPr1/4, here η is the dissipation length scale, Reb is the buoyant Reynolds number, and Pr is the Prandtl number. It is found that the convective layer thickness H is directly linked to the stability ratio Rρ and H0 with the form of H ∼ (Rρ − 1)2H0. The layer thickness can be explained by the convective instability mechanism. To each convective layer, its thickness H reaches a stable value when its thermal boundary layer develops to be a new convecting layer.