Layered anisotropic stratified turbulence in columnar Taylor–Green vortices

Abstract

Abstract Content of image described in text. We use direct numerical simulations (DNSs) of columnar Taylor–Green vortex arrays under stable density stratification to characterise the route to, and the properties of, layered anisotropic stratified turbulence (LAST). Building on the linear stability analysis of Guo et al. (2024 J. Fluid Mech., vol. 997, A34) and the convection-driven turbulence transition reported by the same authors (2025 J. Fluid Mech., vol. 1016, A44), we extend the DNS database to Froude numbers italic Fr less than or slanted equals 0.25 Fr⩽0.25 $\textit {Fr}\leqslant 0.25$ and Reynolds numbers italic Re Re $\textit {Re}$ up to 3200 3200 $3200$ . In this strongly stratified regime, the vortex array breaks down through a shear-driven path: vertical shear layers that form spontaneously in the zigzag-deformed base flow destabilise locally and transition to LAST, in contrast with the convection-driven path identified at italic Fr greater than or slanted equals 0.5 Fr⩾0.5 $\textit {Fr}\geqslant 0.5$ . Four flow regimes are charted, two of which follow the buoyancy-driven scaling script l Subscript v Baseline proportional to upper U Subscript h Baseline divided by upper N ℓv∝Uh/N $\ell _v\propto U_h/N$ : LAST and a layered anisotropic viscously affected flow (LAVAF) regime, where script l Subscript v ℓv $\ell _v$ is the vertical integral scale, upper U Subscript h Uh $U_h$ the horizontal velocity and upper N N $N$ the buoyancy frequency. In both regimes, the ratio of buoyancy scale script l Subscript b Baseline equals 2 pi upper U Subscript h Baseline divided by upper N ℓb=2πUh/N $\ell _b=2\pi U_h/N$ to script l Subscript v ℓv $\ell _v$ plateaus near 0.74 0.74 $0.74$ at peak dissipation. Layered anisotropic stratified turbulence is distinguished from LAVAF by the buoyancy Reynolds number italic Re Subscript b Reb $\textit {Re}_b$ exceeding unity, so that the Ozmidov and Thorpe scales both rise above the Kolmogorov scale and small-scale overturns develop under weaker viscous damping. Across LAST, the cumulative mixing efficiency is upper Gamma element of left bracket 0.24 comma 0.49 right bracket Γ∈[0.24,0.49] $\varGamma \in [0.24,0.49]$ and the horizontal Froude number italic Fr Subscript h Baseline equals upper U Subscript h Baseline divided by left parenthesis upper N script l Subscript h Baseline right parenthesis Frh=Uh/(Nℓh) $\textit {Fr}_h=U_h/(N\ell _h)$ at peak dissipation is of order 0.01 0.01 $0.01$ , where script l Subscript h ℓh $\ell _h$ is the horizontal integral scale. In terms of turbulence-based parameters, LAST is bounded by italic Fr Subscript h Baseline less than 0.031 Frh<0.031 $\textit {Fr}_h\lt 0.031$ – 0.044 0.044 $0.044$ and italic Re Subscript b Baseline greater than or equivalent to 1 Reb≳1 $\textit {Re}_b\gtrsim 1$ ; via empirical fits, these map to base-flow cutoffs italic Fr less than 0.26 Fr<0.26 $\textit {Fr}\lt 0.26$ – 0.37 0.37 $0.37$ and italic Re italic Fr Superscript 5 divided by 3 Baseline greater than or equivalent to 110 ReFr5/3≳110 $\textit {Re}\,\textit {Fr}^{5/3}\gtrsim 110$ .