Turbulent Heating in a Stratified Medium
  There is considerable evidence for widespread subsonic turbulence in galaxy
clusters, most notably from {\it Hitomi}. Turbulence is often invoked to offset
radiative losses in cluster cores, both by direct dissipation and by enabling
turbulent heat diffusion. However, in a stratified medium, buoyancy forces
oppose radial motions, making turbulence anisotropic. This can be quantified
via the Froude number ${\rm Fr}$, which decreases inward in clusters as
stratification increases. We exploit analogies with MHD turbulence to show that
wave-turbulence interactions increase cascade times and reduces dissipation
rates $\epsilon \propto {\rm Fr}$. Equivalently, for a given energy
injection/dissipation rate $\epsilon$, turbulent velocities $u$ must be higher
compared to Kolmogorov scalings. High resolution hydrodynamic simulations show
excellent agreement with the $\epsilon \propto {\rm Fr}$ scaling, which sets in
for ${\rm Fr} < 0.1$. We also compare previously predicted scalings for the
turbulent diffusion coefficient $D \propto {\rm Fr}^2$ and find excellent
agreement, for ${\rm Fr} < 1$. However, we find a different normalization,
corresponding to stronger diffusive suppression by more than an order of
magnitude. Our results imply that turbulent diffusion is more heavily
suppressed by stratification, over a much wider radial range, than turbulent
dissipation. Thus, the latter potentially dominates. Furthermore, this shift
implies significantly higher turbulent velocities required to offset cooling,
compared to previous models. These results are potentially relevant to
turbulent metal diffusion (which is likewise suppressed), and to planetary
atmospheres.
