Dynamics of fronts in thermally bistable fluids

Fronts between different thermal phases of a fluid, when the cooling function allows two thermally stable phases around an unstable one (bistability), are investigated. Fluid motion is included (in contrast to an earlier work), in addition to thermal conduction. For a one-dimensional case we investigate the front dynamics by introducing an appropriate Lyapunov functional. It is assumed that the coefficient of thermal conductivity is small, so that the front thickness is very small compared with front separations. Pairs of adjacent fronts define a cloud (or an intercloud region), and their motion gives rise to the growth of the cloud (condensation) or of the intercloud region (evaporation). We discuss the properties of various types of fronts separating the different thermal phases of the fluid. Interaction between fronts and its effect on front motion is found using an approximation method. An ensemble of stationary fronts is then used to model a quasi-stationary cloudy medium. Equations of motion for fronts separating the hot and cold stable phases are derived. We find, for a general (but consistent with bistability) cooling function, that as in our previous work the medium exhibits an inverse cascade, with increasingly larger clouds predominating. The lifetime of a particular stage is exponentially dependent on the size of the structures, and thus large clouds can persist for a very long time. The effects of small pressure variations on the front motions (and thus on cloud condensation and evaporation) are then included in the formalism. An example utilizing a simplistic approximation for the cooling function and a sinusoidal pressure variation is solved in detail, manifesting the possible occurrence of inherent complexity in thermally unstable fluids. Extensions of our approach to more realistic, multidimensional models are discussed briefly, together with possible astrophysical applications.