New layer thickness parameterization of diffusive convection in the ocean

- New parameterization has been proposed to describe the convecting layer thickness in diffusive convection in a wider range of conditions in the oceans and lakes.
- The proposed length scale H0=[qT3/(κTN8)]1/4 can be regarded as the scale of an energy-containing eddy in diffusive convection.
- This parameterization is a generalized representation of the thickness of convecting layer in diffusive convection. It is expected to describe the same phenomena in other various fields like geology, astrophysics, metallurgy.

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.