Anisotropy of turbulence in stably stratified mixing layers

Abstract

Direct numerical simulations of turbulence resulting from Kelvin–Helmholtz instability in stably stratified shear flow are used to study sources of anisotropy in various spectral ranges. The set of simulations includes various values of the initial Richardson and Reynolds numbers, as well as Prandtl numbers ranging from 1 to 7. We demonstrate that small-scale anisotropy is determined almost entirely by the spectral separation between the small scales and the larger scales on which background shear and stratification act, as quantified by the buoyancy Reynolds number. Extrapolation of our results suggests that the dissipation range becomes isotropic at buoyancy Reynolds numbers of order 105, although we cannot rule out the possibility that small-scale anisotropy persists at arbitrarily high Reynolds numbers, as some investigators have suggested. Correlation-coefficient spectra reveal the existence of anisotropic flux reversals in the dissipation subrange whose magnitude decreases with increasing Reynolds number. The scalar concentration field tends to be more anisotropic than the velocity field. Estimates of the dissipation rates of kinetic energy and scalar variance based on the assumption of isotropy are shown to be accurate for buoyancy Reynolds numbers greater than O(102). Such estimates are therefore reliable for use in the interpretation of most geophysical turbulence data, but may give misleading results when applied to smaller-scale flows.