Dissipation ratio and eddy diffusivity of turbulent and salt finger mixing derived from microstructure measurements

Abstract

Eddy diffusivity is usually estimated using the Osborn relation assuming a constant dissipation ratio of 0.2. In this study, we examine dissipation ratios and eddy diffusivities of turbulent mixing and salt finger mixing based on microstructure datasets. We find that the dissipation ratio of turbulence, 0T, is highly variable with a median value clearly greater than 0.2, which shows strong seasonal variation and decreases slightly with depth in the western equatorial Pacific but obviously increases with depth in the midlatitude Atlantic. 0T is jointly modulated by the Ozmidov scale to the Thorpe scale ratio ROT and the buoyancy Reynolds number Reb, namely 0T ∝ ROT−4/3 · Reb1/2. The eddy diffusivity based on observed 0T is larger than that estimated with 0.2 and presents a much stronger bottom enhancement. The eddy diffusivities of heat and salt for a salt finger are calculated using two “analogical” Osborn equations, and their corresponding “effective” dissipation ratios 0θF and 0SF are examined. 0θF scatters over 2 orders of magnitude with a median value of 0.47 and is mostly linearly correlated with 0SF as 0SF ≈ 5 0θF. The density flux ratio for a salt finger decreases sharply with a density ratio Rρ smaller than 2.4 but regrows to a larger value with Rρ exceeding 2.4. The salt-finger-induced eddy diffusivities also increase with depth, with some being comparable to even stronger ones than the mean turbulent ones. This study highlights the influences of variable dissipation ratios and different mixing types on eddy diffusivity estimates and should help the improvement of mixing estimate and parameterization.