Quantifying mixing and available potential energy in vertically periodic simulations of stratified flows

Turbulent mixing exerts a significant influence on many physical processes in the ocean. In stably stratified Boussinesq fluid, this irreversible describes conversion of available potential energy (APE) to background (BPE). some settings APE framework is difficult apply and approximate measures are used estimate mixing. For example, numerical simulations turbulence often use triply periodic domains increase computational efficiency. setup however, BPE not uniquely defined method Winters et al. (1995, J. Fluid Mech., 289) cannot be directly applied calculate APE. We propose new technique with mean stratification. By defining control volume bounded by surfaces constant buoyancy, we can construct an appropriate buoyancy profile $b_\ast(z,t)$ accurately quantify diapycnal such systems. This also permits accurate calculation finite amplitude local density domains. The evolution analysed various turbulent flow simulations. show that dissipation rate variance $\chi$ provides good approximation rate, even flows variations When quantifying efficiency transient flows, find variation depending whether laminar diffusion included kinetic rate. discuss how best interpret these results context diffusivity real oceanographic flows.