On Energy and Turbulent Mixing in the Thermocline

Abstract

AbstractA new method for computing the rate at which turbulent mixing builds potential energy in the ocean is described. The traditional approach has focused on the rate of change of the background potential energy associated with an adiabatically leveled state. We argue that when examining mixing events, so‐called “Thorpe” sorting yields a useful and local measure of diabatically generated potential energy and exhibits some advantages relative to adiabatic leveling. Among these, the open question about the leveling domain is avoided, the fate of kinetic energy during a mixing event is clearly defined, and the computational load associated with the leveling is relieved. The resultant kinetic energy equation leads to a natural definition of mixing efficiency and turbulent diffusivity in terms of sign definite viscous and diffusive contributions. Applications to 2‐D Kelvin Helmholtz instability demonstrate the utility of the procedure. We find an integrated efficiency of ≈ 0.15 for a Prandtl number of 1, and of ≈ 0.08 for a Prandtl number of 10. The larger is comparable to the classical value of 0.2 used frequently by the mixing community and smaller than that found in some recent simulations.