Utility of Thorpe and Ozmidov length scales to infer the state of turbulence and mixing in geophysical flows

Accurate parameterization of the mixing coefficient Γ is essential to estimate mixing in geophysical flows. Direct measurement of Γ is not feasible and hence it must be parameterized. However, a universal parameterization of Γ remains elusive. Using dominate time scales that govern stratified turbulent flows, scaling arguments are used to provide functional relations between Γ and the turbulent Froude number Fr across a broad spectrum ranging from weak to strongly stratified turbulence. Validation with different direct numerical simulation data confirms the universality of the proposed parameterization. Considering that Fr is not measurable in the field, scaling analysis is used to infer Fr from two measurable length scales namely: the Thorpe Length scale L_T and the Ozmidov length scale L_O. It is shown that L_T/L_O is not only an indicator of age of turbulence but more importantly, also as an indicator of strength of stratification in a turbulent flow. These findings will be helpful in field oceanography to infer Fr using a microstructure profiler, and hence determine the dynamic state of ocean turbulence in order to use the most appropriate parameterization of Γ for estimating diapycnal (irreversible) mixing.