Mixing Efficiency in the Presence of Stratification: When Is It Constant?

The efficiency of the conversion of mechanical to potential energy, often expressed as the flux Richardson number, Ri f , is an important determinant of vertical mixing in the ocean. To examine the dependence of Ri f on the buoyancy Reynolds number, Re B , we analyze three sets of data: microstructure profiler data for which mixing is inferred from rates of dissipation of turbulent kinetic energy ( ε ) and temperature variance ( χ ) measured in the open ocean, time series of spectrally fit values of ε and covariance‐derived buoyancy fluxes measured in nearshore internal waves, and time series of spectrally fit values of ε and χ measured in an energetic estuarine flow. While profiler data are well represented by Ri f ≈ 0.2 for 1 < Re B < 1,000, the covariance data have much larger values of Re B and, consistent with direct numerical simulation results, show that Ri f ~ Re B −0.5 . The estuarine data have values of Re B that fall between those of the other two data sets but also shows Ri f ≈ 0.2 for Re B < 5000. Overall, these data suggest that Ri f is in general not constant and may be substantially less than 0.2 when Re B is large, although the value at which the transition from constant to Re B ‐dependent mixing may depend on additional parameters that are yet to be determined. Nonetheless, for much of the ocean, Re B < 100 and so Ri f is constant there.