  Cloud-wind interactions play an important role in long-lived multiphase flows
in many astrophysical contexts. When this interaction is primarily mediated by
hydrodynamics and radiative cooling, the survival of clouds can be phrased in
terms of the comparison between a timescale that dictates the evolution of the
cloud-wind interaction, (the dynamical time-scale $\tau_{\rm dyn}$) and the
relevant cooling timescale $\tau_{\rm cool}$. Previously proposed survival
criteria, which can disagree by large factors about the size of the smallest
surviving clouds, differ in both their choice of $\tau_{\rm cool}$ and (to a
lesser extent) $\tau_{\rm dyn}$. Here we present a new criterion which agrees
with a previously proposed empirical formulae but is based on simple physical
principles. The key insight is that clouds can grow if they are able to mix and
cool gas from the hot wind faster than it advects by the cloud. Whereas prior
criteria associate $\tau_{\rm dyn}$ with the cloud crushing timescale, our new
criterion links it to the characteristic cloud-crossing timescale of a
hot-phase fluid element, making it more physically consistent with shear-layer
studies. We develop this insight into a predictive expression and validate it
with 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 primarily
emerged due to different choices of simulation conditions and cooling
properties, and discuss how they can be reconciled.
