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Cloud-wind interactions play an important role in long-lived multiphase flowsin many astrophysical contexts. When this interaction is primarily mediated byhydrodynamics and radiative cooling, the survival of clouds can be phrased interms of the comparison between a timescale that dictates the evolution of thecloud-wind interaction, (the dynamical time-scale $\tau_{\rm dyn}$) and therelevant cooling timescale $\tau_{\rm cool}$. Previously proposed survivalcriteria, which can disagree by large factors about the size of the smallestsurviving clouds, differ in both their choice of $\tau_{\rm cool}$ and (to alesser extent) $\tau_{\rm dyn}$. Here we present a new criterion which agreeswith a previously proposed empirical formulae but is based on simple physicalprinciples. The key insight is that clouds can grow if they are able to mix andcool gas from the hot wind faster than it advects by the cloud. Whereas priorcriteria associate $\tau_{\rm dyn}$ with the cloud crushing timescale, our newcriterion links it to the characteristic cloud-crossing timescale of ahot-phase fluid element, making it more physically consistent with shear-layerstudies. We develop this insight into a predictive expression and validate itwith hydrodynamic ENZO-E simulations of ${\sim}10^4\, {\rm K}$,pressure-confined clouds in hot supersonic winds, exploring, in particular,high wind/cloud density contrasts, where disagreements are most pronounced.Finally, we illustrate how discrepancies among previous criteria primarilyemerged due to different choices of simulation conditions and coolingproperties, and discuss how they can be reconciled.

TuRMoiL of Survival: A Unified Survival Criterion for Cloud-Wind Interactions