We present a new robust method for identifying three dynamically distinct regions in a stratified turbulent flow, which we characterise as quiescent flow, intermittent layers, and turbulent patches. The method uses the cumulative filtered distribution function of the local density gradient to identify each region. We apply it to data from direct numerical simulations of homogeneous stratified turbulence, with unity Prandtl number, resolved on up to 8192×8192×4096 grid points. In addition to classifying regions consistently with contour plots of potential enstrophy, our method identifies quiescent regions as regions where /νN 2 ∼ O(1), layers as regions where /νN 2 ∼ O(10), and patches as regions where /νN 2 ∼ O(100). Here is the dissipation rate of turbulence kinetic energy, ν is the kinematic viscosity, and N is the (overall) buoyancy frequency. By far the highest local dissipation and mixing rates, and the majority of dissipation and mixing, occur in patch regions, even when patch regions occupy only 5% of the flow volume. We conjecture that treating stratified turbulence as an instantaneous assemblage of these different regions in varying proportions may explain some of the apparently highly scattered flow dynamics and statistics previously reported in the literature.

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We report on direct numerical simulations of the decay of initially isotropic, homogeneous turbulence subject to the application of stable density stratification. Flows were simulated for three different initial Reynolds numbers, but for the same initial Froude number. We find that the flows pass through three different dynamical regimes as they decay, depending on the local values of the Froude number and activity parameter. These regimes are analogous to those seen in the experimental study of Spedding (J. Fluid Mech., vol. 337, 1997, pp. 283–301) for the wake of a sphere. The flows initially decay with little influence of stratification, up to approximately one buoyancy period, when the local Froude number has dropped below 1. At this point the flows have adjusted to the density stratification, and, if the activity parameter is large enough, begin to decay at a slower rate and spread horizontally at a faster rate, consistent with the predictions of Davidson (J. Fluid Mech., vol. 663, 2010, pp. 268–292) and the scaling arguments of Billant & Chomaz (Phys. Fluids, vol. 13, 2001, pp. 1645–1651). We refer to this second regime as the stratified turbulence regime. As the flows continue to decay, ultimately the activity parameter drops below approximately 1 as viscous effects begin to dominate. In this regime, the flows have become quasi-horizontal, and approximately obey the scaling arguments of Godoy-Diana et al. (J. Fluid Mech., vol. 504, 2004, pp. 229–238).

Classical scaling arguments of Kolmogorov, Oboukhov and Corrsin (KOC) are evaluated for turbulence strongly influenced by stable stratification. The simulations are of forced homogeneous stratified turbulence resolved on up to 8192 × 8192 × 4096 grid points with buoyancy Reynolds numbers of Re b = 13, 48 and 220. A simulation of isotropic homogeneous turbulence with a mean scalar gradient resolved on 8192 3 grid points is used as a benchmark. The Prandtl number is unity. The stratified flows exhibit KOC scaling only for second-order statistics when Re b = 220; the 4/5 law is not observed. At lower Re b , the −5/3 slope in the spectra occurs at wavenumbers where the bottleneck effect occurs in unstratified cases, and KOC scaling is not observed in any of the structure functions. For the probability density functions (p.d.f.s) of the scalar and kinetic energy dissipation rates, the lognormal model works as well for the stratified cases with Re b = 48 and 220 as it does for the unstratified case. For lower Re b , the dominance of the vertical derivatives results in the p.d.f.s of the dissipation rates tending towards bimodal. The p.d.f.s of the dissipation rates locally averaged over spheres with radius in the inertial range tend towards bimodal regardless of Re b . There is no broad scaling range, but the intermittency exponents at length scales near the Taylor length are in the range of 0.25 ± 0.05 and 0.35 ± 0.1 for the velocity and scalar respectively.

Massively parallel computers are now large enough to support accurate direct numerical simulations ͑DNSs͒ of laboratory experiments on isotropic turbulence, providing researchers with a full description of the flow field as a function of space and time. The high accuracy of the simulations is demonstrated by their agreement with the underlying laboratory experiment and on checks of numerical accuracy. In order to simulate the experiments, requirements for the largest and smallest length scales computed must be met. Furthermore, an iterative technique is developed in order to initialize the larger length scales in the flow. Using these methods, DNS is shown to accurately simulate isotropic turbulence decay experiments such as those of Comte-Bellot and Corrsin ͓J. Fluid Mech. 48, 273 ͑1971͔͒.