New layer thickness parameterization of diffusive convection in the ocean

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) m(2) s(-3). We construct an intrinsic thickness scale, H-0 = [q(T)(3)/(KTN8)](1/4), here k(T), is the thermal diffusivity. H-0 is suggested to be the scale of an energy -containing eddy and it can be alternatively represented as H-0 = eta RebPr1/4, here eta is the dissipation length scale, Re-b 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 R-rho and H-0 with the form of H similar to(R-rho-1)H-2(0). 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. (C) 2016 Elsevier B.V. All rights reserved.