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

Abstract

The efficiency of the conversion of mechanical to potential energy, often expressed as the flux Richardson number, Rif, is an important determinant of vertical mixing in the ocean. To examine the dependence of Rif on the buoyancy Reynolds number, ReB, 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 Rif ≈ 0.2 for 1 < ReB < 1,000, the covariance data have much larger values of ReB and, consistent with direct numerical simulation results, show that Rif ~ ReB−0.5. The estuarine data have values of ReB that fall between those of the other two data sets but also shows Rif ≈ 0.2 for ReB < 5000. Overall, these data suggest that Rif is in general not constant and may be substantially less than 0.2 when ReB is large, although the value at which the transition from constant to ReB-dependent mixing may depend on additional parameters that are yet to be determined. Nonetheless, for much of the ocean, ReB < 100 and so Rif is constant there.