Turbulence and Mixing in the Intracluster Medium
  The intracluster medium (ICM) is stably stratified in the hydrodynamic sense
with the entropy $s$ increasing outwards. However, thermal conduction along
magnetic field lines fundamentally changes the stability of the ICM, leading to
the "heat-flux buoyancy instability" when $dT/dr>0$ and the "magnetothermal
instability" when $dT/dr<0$. The ICM is thus buoyantly unstable regardless of
the signs of $dT/dr$ and $ds/dr$. On the other hand, these
temperature-gradient-driven instabilities saturate by reorienting the magnetic
field (perpendicular to $\hat{\bf r}$ when $dT/dr>0$ and parallel to $\hat{\bf
r}$ when $dT/dr<0$), without generating sustained convection. We show that
after an anisotropically conducting plasma reaches this nonlinearly stable
magnetic configuration, it experiences a buoyant restoring force that resists
further distortions of the magnetic field. This restoring force is analogous to
the buoyant restoring force experienced by a stably stratified adiabatic
plasma. We argue that in order for a driving mechanism (e.g, galaxy motions or
cosmic-ray buoyancy) to overcome this restoring force and generate turbulence
in the ICM, the strength of the driving must exceed a threshold, corresponding
to turbulent velocities $\gtrsim 10 -100 {km/s}$. For weaker driving, the ICM
remains in its nonlinearly stable magnetic configuration, and turbulent mixing
is effectively absent. We discuss the implications of these findings for the
turbulent diffusion of metals and heat in the ICM.
