Anisotropy of emergent large-scale dynamics in forced stratified shear flows

TL;DR

This study uses direct numerical simulations to investigate the steady-state dynamics of forced stratified shear flows, revealing finite shear layer depths, emergent large-scale structures, and a tendency towards a critical Richardson number in turbulent regimes.

Contribution

It provides new insights into the large-scale structure and stability properties of forced stratified shear flows through detailed numerical analysis.

Findings

Shear layer half-depth converges to approximately 8 units.

Large-scale flow structures with spanwise length scale around 50 emerge.

Flow tends to a gradient Richardson number below 0.2.

Abstract

Although stably stratified shear flows, where the base velocity shear is quasi-continuously forced externally, arise in many geophysically and environmentally relevant circumstances, the emergent dynamics of their ensuing statistically steady stratified turbulence is still an open question. We address this phenomenon in a series of three-dimensional direct numerical simulations using spectral element methods. We consider a forced, stably stratified shear flow with an initial bulk Reynolds number $\ReO = 50$, an initial bulk Richardson number $\RiO = 1/80$ (also corresponding to the initial minimum gradient Richardson number $\Rig$), and a fluid of Prandtl number $\Pr = 1$ in horizontally extended domains. Although the initial configuration is unstable to a primary Kelvin-Helmholtz instability, the ensuing turbulence is sustained by continuously relaxing the resulting flow back towards the initial profiles of streamwise velocity and buoyancy. We study statistical as well as structural aspects of the final statistically steady flows, including the flux coefficient $\Gchi$ and dynamically emergent length scales $\Lambda$ associated with the large-scale dynamics, respectively. Despite the ongoing stirring and mixing, we find that the shear layer half-depth converges to a finite value of $d \approx 8$ (i.e., $\Lambda_{z} \approx 16$) once the horizontal extent of the domain $\Gh \gtrsim 96$. While this implies a final $\Re \approx 400$ and $\Ri \approx 0.1$, we hypothesise that such forced flows \enquote{tune} themselves eventually to a state of a gradient Richardson number $\Rig \lesssim 0.2$, consistently with several previous studies. Moreover, provided sufficiently extended domains, we observe the emergence of large-scale flow structures with spanwise $\Lambda_{y} \approx 50$ and streamwise $\Lambda_{x} \lesssim 115$. ...