The influence of far field stratification on shear-induced turbulent mixing

Abstract

We compare the properties of the turbulence induced by the breakdown of Kelvin–Helmholtz instability (KHI) at high Reynolds number in two classes of stratified shear flows where the background density profile is given by either a linear function or a hyperbolic tangent function, at different values of the minimum initial gradient Richardson number ${{Ri}}_0$ . Considering global and local measures of mixing defined in terms of either the irreversible mixing rate $\mathscr {M}$ associated with the time evolution of the background potential energy, or an appropriately defined density variance dissipation rate $\chi$ , we find that the proliferation of secondary instabilities strongly affects the efficiency of mixing early in the flow evolution, and also that these secondary instabilities are highly sensitive to flow perturbations that are added at the point of maximal (two-dimensional) billow amplitude. Nevertheless, mixing efficiency does not appear to depend strongly on the far field density structure, a feature supported by the evolution of local horizontally averaged values of the buoyancy Reynolds number ${Re}_b$ and gradient Richardson number ${Ri}_g$ . We investigate the applicability of various proposed scaling laws for flux coefficients $\varGamma$ in terms of characteristic length scales, in particular discussing the relevance of the overturning ‘Thorpe scale’ in stratified turbulent flows. Finally, we compare a variety of empirical model parameterizations used to compute diapycnal diffusivity in an oceanographic context, arguing that for transient flows such as KHI-induced turbulence, simple models that relate the ‘age’ of a turbulent event to its mixing efficiency can produce reasonably robust mixing estimates.

Stratified turbulent mixing in oscillating shear flows

“…For these flows, there are coherent wave-like structures corresponding to larger at the top and bottom of the mixing layer which emerge as the shear decelerates. Similar structures were also observed for KHI billows forming in a linear background stratification in Lewin & Caulfield (2021), caused by anisotropic turbulence rotating around the laminar billow core. Once the shear starts to accelerate again, values of in these regions decrease, in particular leading to distinct patches of in flows WN72D, WN62D and WN52D which leads to the development of a secondary turbulence phase.…”

“…Secondly, the energetic pathways leading to mixing are profoundly modified in the absence of shear such that turbulent fluctuations have a characteristically different structure whilst remaining just as energetic as flows with a constant background shear. This latter effect becomes more important as Re increases, and it reinforces the idea that a purely two-phase description of turbulence produced by shear instability consisting of a coherent preturbulent phase of highly efficient mixing followed by an energetic phase of constant mixing efficiency of η ≈ 0.2 does not appropriately characterise the mixing , even when the final decaying phase of flow evolution does not play a significant role (Lewin & Caulfield 2021). Mashayek et al (2021b) point out that mixing by KHI might be more appropriately characterised as primarily convective once the primary billow has rolled up.…”

“…The dependence of key mixing properties in this flow on a range of parameters has been the subject of a number of recent studies (e.g. as reviewed in Caulfield 2021) though it is becoming increasingly apparent that mixing also depends on the precise structure of the environment in which instabilities develop (Kaminski & Smyth 2019; VanDine, Pham & Sarkar 2021), as well as transient flow dynamics (Mashayek & Peltier 2013; Mashayek, Caulfield & Peltier 2017; Lewin & Caulfield 2021).…”

A comparative study of turbulent stratified shear layers: effect of density gradient distribution

“…The wavelength is approximately 17% longer in the R = 0 case when compared to the R = 1 case. Previous studies have shown that the wavelength becomes shorter when the Ri b,0 (and Ri min ) increases for either the R = 0 or R = 1 density profiles [10,28]. In the present study, we keep Ri b,0 to be the same among the cases with different R values and the wavelength becomes shorter with increasing R. Thus, the wavelength of the FGM is correlated better with Ri min rather than Ri b,0 .…”

“…5b, c. The stratification in the R = 0 case is enhanced at the edges of the shear layer when compared to the unstratified ambient; however, unlike Lewin and Caulfield [10], the local N 2 is not larger than the values inside the shear layer. Thus, a distinctive transition layer does not form in the two-layer stratification.…”