Classical scaling and intermittency in strongly stratified Boussinesq turbulence

Abstract

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$8192\times 8192\times 4096$grid points with buoyancy Reynolds numbers of$\mathit{Re}_{b}=13$, 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$\mathit{Re}_{b}=220$; the$4/5$law is not observed. At lower$\mathit{Re}_{b}$, 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$\mathit{Re}_{b}=48$and 220 as it does for the unstratified case. For lower$\mathit{Re}_{b}$, 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$\mathit{Re}_{b}$. There is no broad scaling range, but the intermittency exponents at length scales near the Taylor length are in the range of$0.25\pm 0.05$and$0.35\pm 0.1$for the velocity and scalar respectively.