Layered anisotropic stratified turbulence in columnar Taylor–Green vortices

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

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 ℓ v ∝ U h / N $\ell _v\propto U_h/N$

: LAST and a layered anisotropic viscously affected flow (LAVAF) regime, where

script l Subscript v ℓ v $\ell _v$

is the vertical integral scale,

upper U Subscript h U h $U_h$

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 ℓ b = 2 π U h / N $\ell _b=2\pi U_h/N$

to

script l Subscript v ℓ v $\ell _v$

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 Re b $\textit {Re}_b$

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 Fr h = U h / ( N ℓ h ) $\textit {Fr}_h=U_h/(N\ell _h)$

at peak dissipation is of order

0.01 0.01 $0.01$

, where

script l Subscript h ℓ h $\ell _h$

is the horizontal integral scale. In terms of turbulence-based parameters, LAST is bounded by

italic Fr Subscript h Baseline less than 0.031 Fr h < 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 Re b ≳ 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 Re Fr 5 / 3 ≳ 110 $\textit {Re}\,\textit {Fr}^{5/3}\gtrsim 110$

.