Sheared stratified turbulence driven by Kolmogorov flow

TL;DR

This study uses direct numerical simulations to explore how stratification influences turbulence, layering, and flow stability in a sheared Kolmogorov flow, revealing new scaling laws and transition regimes.

Contribution

It provides new insights into stratified turbulence dynamics, including the formation of layered structures, turbulence scaling laws, and the transition to intermittent turbulence regimes.

Findings

Layered density structures with sharp interfaces emerge at higher stratification.

Nusselt number scales with buoyancy Reynolds number as Nu ~ Re_b^{0.8}.

Transition to intermittent turbulence is controlled by buoyancy Reynolds number.

Abstract

We investigate three-dimensional turbulence in a stably stratified fluid driven by a vertically sheared Kolmogorov flow using direct numerical simulations of the Boussinesq equations. As stratification increases, mean profiles evolve toward piecewise-linear shapes while layered density structures emerge, with sharp interfaces separating well-mixed bulk layers. These highly stable interfaces form in the low-shear regions of the mean velocity profile and tend to promote flow relaminarisation, while shear-generated turbulence persists in the bulk layers. We analyse turbulent fluctuations, buoyancy transport and its spatial organisation, and flow stability via profiles of the gradient Richardson number $Ri_g$. The Richardson number in the bulk layers remains of order unity or less, $Ri_g \lesssim 1$, so that efficient turbulent shear production can take place there. Mixing efficiency analysis shows that the Nusselt number scales with the buoyancy Reynolds number $Re_b$ as $Nu = 1 + \Gamma Re_b$ (with $\Gamma = \epsilon_p / \epsilon$), with the data collapsing onto a robust master curve and roughly following a power-law $Nu \sim Re_b^{0.8}$. Further increase of stratification leads to a temporally intermittent turbulent regime, characterised by quasi-periodic bursts. We propose that the transition from stationary turbulence to this temporally intermittent regime is controlled by the buoyancy Reynolds number and highlight the mechanisms disrupting the turbulence and layered structures.