Volume Scaling of Intense Mixing Regions in Homogeneous Stratified Turbulence

The spontaneous generation of localized turbulent patches or bursts in otherwise homogeneous flow is a widely accepted characteristic of stratified turbulence and can occur through many mechanisms. Here, we address this spacio-temporal variability in homogeneously forced stationary turbulence across a broad Fr-Re parameter space as realized through pseudo-spectral DNS of Boussinesq turbulence. Using a conditional averaging scheme based on local density gradient inversions, a domain is objectively subdivided into `quiescent regions', `intermittent layers' and `turbulent patches'. We observe that these regions may be characterized by an appropriate locally averaged $\mathrm{Gn} \equiv \epsilon / \nu N^2$ in that they exhibit $\mathrm{Gn} \sim O(1)$, $\mathrm{Gn} \sim O(10)$, and $\mathrm{Gn} \sim O(100)$, respectively. We show that even at nominal bulk $\mathrm{Gn}$, the majority of mixing is confined to small and intense turbulence patches. The volume of these patches scales with the bulk $\mathrm{Gn}^{1/2}$.