Is it Always True that the Mixing Efficiency Decreases for Large (>400) Values of the Buoyancy Reynolds Number?

Traditionally, oceanographers have assumed that turbulent processes in the stratified ocean interior achieve a constant mixing efficiency γ≈1/6, where the efficiency is defined as the ratio of turbulent buoyancy flux to total production (i.e. dissipation ε plus buoyancy flux). This value is currently used in ocean models to parameterize the eddy diffusivity when the dissipation is known. Numerical simulations and some observations appear to paint a different picture: 1/6 represents a peak efficiency that is attained within a narrow range of values of the buoyancy Reynolds number Re_b = ε⁄νN² . In particular, the efficiency is reported to decay as C Re_b ^-1/2 when the buoyancy Reynolds number is large. However, the value reported for C ranges from 0.7 (DNS simulations, Shih et al., 2005) to 50 (observations in the Atmospheric Boundary Layer, Lozovatsky and Fernando, 2013). Recently, de Lavergne et al. (2015) have shown that replacing a constant efficiency with a decaying efficiency with C=4 profoundly affects, inter alia,the upwelling of AABW in the Southern Ocean. It is therefore extremely important to ascertain to what extent the Reynolds buoyancy number can be considered a good predictor of the efficiency in the energetic regime. In this talk, we show that a one-to-one relationship between the buoyancy Reynolds number and the mixing efficiency cannot exist in shear-driven turbulent mixing. We do this combining theoretical analysis with simulations. Our results indicate that the constant value assumed by oceanographers represents a reasonable compromise for the type of turbulent processes that are expected to dominate energetic mixing in the ocean. If anything, 1/6 should perhaps be revised upward.

This work was supported by NSF, under grant OCE-1155558,
and ONR under grant N00014-09-1-0288. Computer time was provided by UNC ITS.