Asymptotic dynamics of high dynamic range stratified turbulence

Abstract

Direct numerical simulations of homogeneous sheared and stably stratified turbulence are considered to probe the asymptotic high-dynamic range regime suggested by Gargett et al. 1984 and Shih et al. 2005. We consider statistically stationary configurations of the flow that span three decades in dynamic range defined by the separation between the Ozmidov length scale, $L_O=\sqrt{ε/N^3}$, and the Kolmogorov length scale, $L_K=(ν^3/ε)^{1/4}$, up to $\mathrm{Re_b}\equiv (L_O/L_K)^{4/3}=ε/(νN^2) \sim O(1000)$, where $ε$ is the mean turbulent kinetic energy dissipation rate, $ν$ is the kinematic viscosity, and $N$ is the buoyancy frequency. We isolate the effects of $\mathrm{Re_b}$, particularly on irreversible mixing, from the effects of other flow parameters of stratified and sheared turbulence. Specifically, we evaluate the influence of dynamic range independent of initial conditions. We present evidence that the flow approaches an asymptotic state for $\mathrm{Re_b}\gtrapprox 300$, characterized both by an asymptotic partitioning between the potential and kinetic energies and by the approach of components of the dissipation rate to their expected values under the assumption of isotropy. As $\mathrm{Re_b}$ increases above 100, there is a slight decrease in the turbulent flux coefficient $Γ=χ/ε$, where $χ$ is the dissipation rate of buoyancy variance, but, for this flow, there is no evidence of the commonly suggested $Γ\propto \mathrm{Re_b}^{-1/2}$ dependence when $100 \leq \mathrm{Re_b} \leq 1000$.