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We performed direct numerical simulations of a stratified turbulent flows in a periodic
domain, using a forcing mechanism designed to excite internal gravity waves. We added
fourth order hyper-viscosity and hyper-diffusivity for most simulations to stabilize
simulations. However, the resolution was increased sufficiently such that it has a
negligible effect on the measures of considered quantities and spectra in the inertial
range, except for some simulations at high $F_h$ and $\R$. We obtained a dataset of
more than $40$ simulations spanning the $(F_h, \R)$ parameters space, which allows for
parametric studies of stratified flows. We showed that regimes already predicted in the
literature \cite{Brethouwer-Billant-Lindborg-Chomaz2007, Maffioli2016mixing,
Garanaik-Venayagamoorthy2019mixing} can be classified using a large-scale isotropy
coefficient, a small-scale isotropy coefficient, and the mixing coefficient. These
turbulent regimes are: passive scalar, weakly stratified, Layered Anisotropic
Stratified Turbulence (LAST), and viscosity affected.
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When the buoyancy Reynolds number is large ($\R \geq 10$), the optimal mixing occurs
between the weakly stratified and the LAST regimes. This optimal mixing happens for a
maximal potential energy ratio \cite{Maffioli2016mixing}, which is also a minimum of
toroidal (i.e. vertical vorticity modes) energy ratio in our simulations. The
dependency of the mixing ratio are consistent with the scaling predictions of
\cite{Maffioli2016mixing, Garanaik-Venayagamoorthy2019mixing}. However, we observed a
different limit $\lim\limits_{F_h \rightarrow 0} \Gamma \simeq 0.42$ which is different
from the value measured in \cite{Maffioli2016mixing} with a vertical vorticity,
uncorrelated forcing. Also the position of the optimal mixing appeared to be slightly
different ($F_h \simeq 0.13$ in our simulations vs $F_h \simeq 0.3$ in
\cite{Maffioli2016mixing}). This enforced the idea that the forcing mechanism is
important in the precise evaluation of the mixing in stratified flows
\cite{Howland2020mixing}.
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Following \cite{Yokoyama-Takaoka2019}, we performed a spectral analysis of each regime
in the $(k_h, k_z)$ plane for a simulation in the LAST regime. In addition to the
potential, poloidal, and toroidal energy ratios, we also looked at the energy transfer,
buoyancy, and dissipation rate ratios. We observe that conversion to potential energy
becomes negligible when the parameter $\gamma_{\kk}$ (\ref{eq:gamma}) becomes greater
than one. Dissipation is important when $\gamma_{\kk}$ is large mostly ar small
vertical scales, or when eddie turnover times is comparable to the linear wave
frequency $\chi_{\kk} \simeq 1$ (\ref{eq:chi}) and $k\geq k_{\rm b}$. This suggests two
mechanisms for dissipation in stratified turbulence, occurring at different scales:
dissipation by vertical shears at small vertical scales and wave-breaking at small
horizontal scales.
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To use the data do hg clone https://foss.heptapod.net/fluiddyn/fluidsim.