  Turbulent radiative mixing layers (TRMLs) play an important role in many
astrophysical contexts where cool ($\lesssim 10^4$ K) clouds interact with hot
flows (e.g., galactic winds, high velocity clouds, infalling satellites in
halos and clusters). The fate of these clouds (as well as many of their
observable properties) is dictated by the competition between turbulence and
radiative cooling; however, turbulence in these multiphase flows remains poorly
understood. We have investigated the emergent turbulence arising in the
interaction between clouds and supersonic winds in hydrodynamic ENZO-E
simulations. In order to obtain robust results, we employed multiple metrics to
characterize the turbulent velocity, $v_{\rm turb}$. We find four primary
results, when cooling is sufficient for cloud survival. First, $v_{\rm turb}$
manifests clear temperature dependence. Initially, $v_{\rm turb}$ roughly
matches the scaling of sound speed on temperature. In gas hotter than the
temperature where cooling peaks, this dependence weakens with time until
$v_{\rm turb}$ is constant. Second, the relative velocity between the cloud and
wind initially drives rapid growth of $v_{\rm turb}$. As it drops (from
entrainment), $v_{\rm turb}$ starts to decay before it stabilizes at roughly
half its maximum. At late times cooling flows appear to support turbulence.
Third, the magnitude of $v_{\rm turb}$ scales with the ratio between the hot
phase sound crossing time and the minimum cooling time. Finally, we find
tentative evidence for a length-scale associated with resolving turbulence.
Under-resolving this scale may cause violent shattering and affect the cloud's
large-scale morphological properties.
