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.
Highlights
Stratified turbulence facilitates the upwelling of deep, dense waters in the abyssal polar oceans, thereby enabling the closure of the meriodional overturning circulation (Wunsch &Ferrari 2004)
Become turbulent and the properties of the subsequent mixing has been the subject of multiple recent studies that invoke high-resolution direct numerical simulations (DNS) at increasingly large Reynolds number Re and Prandtl number Pr
We have analysed the data from four simulations of turbulence produced by Kelvin–Helmholtz instability (KHI) in a stratified shear layer, two with a hyperbolic tangent background density profile and two with a linear profile, classed as T and L, respectively
Summary
Stratified turbulence facilitates the upwelling of deep, dense waters in the abyssal polar oceans, thereby enabling the closure of the meriodional overturning circulation (Wunsch &Ferrari 2004). It is thought that this turbulence, at least far from boundaries, predominantly arises during discrete mixing events caused by the breaking of internal gravity waves generated by the flow of tidal currents over rough bottom topography (MacKinnon et al.2017). Attempts to model these wave-breaking processes frequently use the destabilisation of a parallel shear flow as the paradigm by which turbulence is generated, a physically plausible approach if we assume that the primary instabilities occur on a scale that is small compared with the internal waves. An appropriately defined mixing efficiency may be used to compute a diapycnal eddy diffusivity Kρ from measurements of dissipation ε and buoyancy frequency N in the ocean via an equation of the form
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