The issue of the physical mechanism(s) that control the efficiency with which the density field in stably stratified fluid is mixed by turbulent processes has remained enigmatic. Similarly enigmatic has been an explanation of the numerical value of ∼0.2, which is observed to characterize this efficiency experimentally. We review recent work on the turbulence transition in stratified parallel flows that demonstrates that this value is not only numerically predictable but also that it is expected to be a nonmonotonic function of the Richardson number that characterizes preturbulent stratification strength. This value of the mixing efficiency appears to be characteristic of the late-time behavior of the turbulent flow that develops after an initially laminar shear flow has undergone the transition to turbulence through an intermediate instability of Kelvin-Helmholtz type.

We investigate the detailed nature of the ‘mixing transition’ through which turbulence may develop in both homogeneous and stratified free shear layers. Our focus is upon the fundamental role in transition, and in particular the associated ‘mixing’ (i.e. small-scale motions which lead to an irreversible increase in the total potential energy of the flow) that is played by streamwise vortex streaks, which develop once the primary and typically two-dimensional Kelvin–Helmholtz (KH) billow saturates at finite amplitude.Saturated KH billows are susceptible to a family of three-dimensional secondary instabilities. In homogeneous fluid, secondary stability analyses predict that the stream-wise vortex streaks originate through a ‘hyperbolic’ instability that is localized in the vorticity braids that develop between billow cores. In sufficiently strongly stratified fluid, the secondary instability mechanism is fundamentally different, and is associated with convective destabilization of the statically unstable sublayers that are created as the KH billows roll up.We test the validity of these theoretical predictions by performing a sequence of three-dimensional direct numerical simulations of shear layer evolution, with the flow Reynolds number (defined on the basis of shear layer half-depth and half the velocity difference) Re = 750, the Prandtl number of the fluid Pr = 1, and the minimum gradient Richardson number Ri(0) varying between 0 and 0.1. These simulations quantitatively verify the predictions of our stability analysis, both as to the spanwise wavelength and the spatial localization of the streamwise vortex streaks. We track the nonlinear amplification of these secondary coherent structures, and investigate the nature of the process which actually triggers mixing. Both in stratified and unstratified shear layers, the subsequent nonlinear amplification of the initially localized streamwise vortex streaks is driven by the vertical shear in the evolving mean flow. The two-dimensional flow associated with the primary KH billow plays an essentially catalytic role. Vortex stretching causes the streamwise vortices to extend beyond their initially localized regions, and leads eventually to a streamwise-aligned collision between the streamwise vortices that are initially associated with adjacent cores.It is through this collision of neighbouring streamwise vortex streaks that a final and violent finite-amplitude subcritical transition occurs in both stratified and unstratified shear layers, which drives the mixing process. In a stratified flow with appropriate initial characteristics, the irreversible small-scale mixing of the density which is triggered by this transition leads to the development of a third layer within the flow of relatively well-mixed fluid that is of an intermediate density, bounded by narrow regions of strong density gradient.

Turbulent mixing produced by breaking of internal waves plays an important role in setting the patterns of downwelling and upwelling of deep dense waters and thereby helps sustain the global deep ocean overturning circulation. A key parameter used to characterize turbulent mixing is its efficiency, defined here as the fraction of the energy available to turbulence that is invested in mixing. Efficiency is conventionally approximated by a constant value near one sixth. Here we show that efficiency varies significantly in the abyssal ocean and can be as large as approximately one third in density stratified regions near topographic features. Our results indicate that variations in efficiency exert a first‐order control over the rate of overturning of the lower branch of the meridional overturning circulation.

Understanding how turbulence leads to the enhanced irreversible transport of heat and other scalars such as salt and pollutants in density-stratified fluids is a fundamental and central problem in geophysical and environmental fluid dynamics. This review discusses recent research activity directed at improving community understanding, modeling, and parameterization of the subtle interplay between energy conversion pathways, instabilities, turbulence, external forcing, and irreversible mixing in density-stratified fluids. The conceptual significance of various length scales is highlighted, and in particular, the importance is stressed of overturning or scouring in the formation and maintenance of layered stratifications, i.e., robust density distributions with relatively deep and well-mixed regions separated by relatively thin interfaces of substantially enhanced density gradient. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 53 is January 7, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.