A diapycnal diffusivity model for stratified environmental flows

• The mixing efficiency varies with the turbulence intensity.
• At low turbulence intensity, the mixing efficiency is Prandtl number dependent.
• We compare multi-scale diffusivity estimates from laboratory, numerical and field data.

The vertical diffusivity of density, Kρ, regulates ocean circulation, climate and coastal water quality. Kρ is difficult to measure and model in these stratified turbulent flows, resulting in the need for the development of Kρ parameterizations from more readily measurable flow quantities. Typically, Kρ is parameterized from turbulent temperature fluctuations using the Osborn–Cox model or from the buoyancy frequency, N, kinematic viscosity, ν, and the rate of dissipation of turbulent kinetic energy, ε, using the Osborn model. More recently, Shih et al. (2005, J. Fluid Mech. 525: 193–214) proposed a laboratory scale parameterization for Kρ, at Prandtl number (ratio of the viscosity over the molecular diffusivity) Pr = 0.7, in terms of the turbulence intensity parameter, Reb=ϵ/(νN2), which is the ratio between the destabilizing effect of turbulence to the stabilizing effects of stratification and viscosity. In the present study, we extend the SKIF parameterization, against extensive sets of published data, over 0.7 < Pr < 700 and validate it at field scale. Our results show that the SKIF model must be modified to include a new Buoyancy-controlled mixing regime, between the Molecular and Transitional regimes, where Kρ is captured using the molecular diffusivity and Osborn model, respectively. The Buoyancy-controlled regime occurs over 102/3Pr−1/2