  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,
$L_O=\sqrt{\epsilon/N^3}$, and the Kolmogorov length scale,
$L_K=(\nu^3/\epsilon)^{1/4}$, up to $\mathrm{Re_b}\equiv
(L_O/L_K)^{4/3}=\epsilon/(\nu N^2) \sim O(1000)$, where $\epsilon$ is the mean
turbulent kinetic energy dissipation rate, $\nu$ 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 $\Gamma=\chi/\epsilon$, where $\chi$ is the dissipation rate of
buoyancy variance, but, for this flow, there is no evidence of the commonly
suggested $\Gamma \propto \mathrm{Re_b}^{-1/2}$ dependence when $100 \leq
\mathrm{Re_b} \leq 1000$.
