Cloud-wind interactions play an important role in long-lived multiphase flows in various galaxy-related contexts (e.g., galactic fountains and winds, cosmological cold-mode accretion, or multiphase tails of satellites). These interactions occur when a volume-filling hot phase, the wind, moves relative to a cool pressure-confined body of gas, the cloud. The conditions necessary for clouds to survive the destructive effects of mixing and become entrained within the wind (i.e. for the relative velocity to be removed), has been a long-standing problem. This problem has received particular attention in the context of galactic winds: cloud entrainment is expected to play a critical role in explaining observed multiphase structure in these outflows. This thesis investigates a mechanism for facilitating cloud survival in the context of rapid cooling, which we hereafter term TRML (turbulent radiative mixing layer) entrainment. Our investigation leverages numerical (magneto)hydrodynamic ENZO-E simulations of a cool (≲10⁴𝐊) clouds that encounter a hot (≳10⁶𝐊), supersonic winds. We begin by introducing a simple entropy-based formalism to characterize the role of mixing in cloud-wind interactions, and demonstrate example applications using simulations. Under this formalism, the high-dimensional description of the interaction's state at a given time is simplified to the joint distribution of mass over pressure (𝑃 ) and entropy (𝐾=𝑃𝞀^-𝜸). As a result, this approach provides a way for (empirically and analytically) quantifying the impact of different initial conditions and sets of physics on the interaction's 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 survival criterion for clouds undergoing TRML entrainment, 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. Despite the fact that the competition the between turbulent mixing and radiative cooling dictate the outcome of the cloud-wind interaction (as well as many observable properties), turbulence in these interactions remains poorly understood. Thus, we next investigate the turbulence that arises for clouds undergoing TRML entrainment. To obtain robust results, we employ multiple metrics to characterize the turbulent velocity, 𝝂_turb. We find four primary results. First, 𝝂_turb manifests clear temperature dependence. Initially, 𝝂_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 𝝂_turb is constant. Second, the relative velocity between the cloud and wind initially drives rapid growth of 𝝂_turb. As it drops (from entrainment), 𝝂_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 𝝂_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. Finally, we propose a new criterion for clouds to survive interactions with the wind in the via TRML entrainment, and validate it with simulations. Properties of TRML entrainment are generally understood to be controlled by ratio between the relevant dynamical and cooling timescales 𝝉_dyn / 𝝉_cool. Previously proposed survival criteria disagree about the size of the smallest surviving cloud by factors of up to ∼100. These criteria primarily differ in their choice of 𝝉_{\rm cool}$; perplexingly, the choices most consistent with the well-modeled micro-scale physics observed in shear-layer studies are associated with less-accurate criteria. We present a new criterion which agrees with previous fitting formulae but is based on a set of simple physical principles. Whereas prior criteria link 𝝉_dyn with the cloud destruction timescale, our new criterion links it to the characteristic cloud-crossing timescale of a hot-phase fluid element. This choice leads to scaling relations that are more physically consistent with shear-layer studies. Additionally, we illustrate that discrepancies among previous criteria primarily emerged due to the choices of simulation conditions, rather than commonly-cited differences in the definition of cloud destruction.