Taming the TuRMoiL: The Temperature Dependence of Turbulence in Cloud-Wind Interactions

Abstract: Turbulent radiative mixing layers (TRMLs) play an important role in many astrophysical contexts where cool ($\lesssim 10<sup>4$ 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.