A Simple Model for Mixing and Cooling in Cloud-Wind Interactions

We introduce a simple entropy-based formalism to characterize the role of mixing in pressure-balanced multiphase clouds and demonstrate example applications using enzo-e (magneto)hydrodynamic simulations. Under this formalism, the high-dimensional description of the system's state at a given time is simplified to the joint distribution of mass over pressure (P) and entropy (K = P rho (-gamma )). As a result, this approach provides a way to (empirically and analytically) quantify the impact of different initial conditions and sets of physics on the system evolution. We find that mixing predominantly alters the distribution along the K direction and illustrate how the formalism can be used to model mixing and cooling for fluid elements originating in the cloud. We further confirm and generalize a previously suggested criterion for cloud growth in the presence of radiative cooling and demonstrate that the shape of the cooling curve, particularly at the low-temperature end, can play an important role in controlling condensation. Moreover, we discuss the capacity of our approach to generalize such a criterion to apply to additional sets of physics and to build intuition for the impact of subtle higher-order effects not directly addressed by the criterion.