Study Identifies Two Distinct Pathways to Turbulent Mixing in Strongly Stratified Flows
Researchers have identified two separate mechanisms by which horizontal shear instabilities can generate turbulence and diapycnal mixing in strongly stratified, low-Froude-number flows that initially lack vertical shear. Using linear theory combined with direct numerical simulations, the study shows that vertical shear — and the small-scale Kelvin-Helmholtz instabilities it drives — inevitably emerges from horizontal shear at sufficiently high buoyancy Reynolds numbers. The findings matter because the two pathways produce different vertical scale distributions and distinct peak mixing efficiencies, with implications for ocean and stellar interior mixing models.
A new preprint submitted to the Journal of Fluid Mechanics investigates how turbulence and diapycnal (cross-density-layer) mixing arise in strongly stratified flows — characterized by low Froude numbers and high Reynolds numbers — that have no initial vertical shear. The authors, led by Pascale Garaud, combine linear stability analysis with direct numerical simulations to characterize two distinct pathways. In the first pathway, vertically-modulated eigenmodes of the primary horizontal shear instability directly generate vertical shear, which then becomes unstable to secondary small-scale Kelvin-Helmholtz (KH) instabilities at the buoyancy scale when the buoyancy Reynolds number is sufficiently large. In the second pathway, a vertically-invariant eigenmode initially dominates, driving the background flow into a long-lived, two-dimensional columnar vortical state; these vortices subsequently undergo three-dimensional hyperbolic instabilities that produce vertical shear, which in turn triggers tertiary KH instabilities. A key finding is that the emergence of vertical shear driving small-scale KH instabilities is an inevitable outcome of horizontal shear instabilities at high enough buoyancy Reynolds numbers, regardless of pathway. However, the two routes excite different ranges of vertical scales, leading to meaningfully different peak mixing efficiencies — a distinction relevant to parameterizing mixing in ocean circulation and stellar interior models.
What's missing
The simulations are necessarily limited in the range of Reynolds and Froude numbers they can access, leaving open whether the identified pathways and their mixing efficiency differences persist at geophysically or astrophysically realistic parameter values. The relative prevalence of each pathway under natural oceanic or stellar conditions is not quantified. Additionally, the study does not address how these results translate into practical mixing parameterizations for large-scale models.
What different sources said
- arXiv physicsCenter
Two pathways to diapycnal mixing in strongly stratified flows with no initial vertical shear
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