PATTERN EVOLUTION IN THERMALLY BISTABLE MEDIA

We investigate numerically the time evolution of two-dimensional inter faces between the stable phases in a thermally bistable medium under t he assumption of a uniform pressure. A model equation, including a gen eric bistable cooling function and a spatial coupling diffusion term, is studied with different initial conditions and perturbative forcing terms. We find, similarly to the previously studied one-dimensional ca se, that without any forcing the medium exhibits an inverse cascade on the way to phase separation, with increasingly larger structures pred ominating, but ultimately the phase imposed on the boundary wins over. Subjecting the medium to short pressure variations (as if the system passes through the pressure wave) may alter this evolution only tempor arily. The introduction of spatiotemporal forcing on small scales, how ever, may give rise to persisting complex patterns with ''clouds'' hav ing fractal boundaries in an appropriate scale range. In this model fl uid motions are allowed only in the perpendicular direction, and sever al physical processes are ignored. Thus, the direct application of the model to a particular astrophysical system may be premature. However, we demonstrate here that thermal instability and heat diffusion alone (together with some random spatial excitation) are able to produce mu ltidimensional cloudy complex structures, not unlike those observed in some astrophysical settings, notably the interstellar medium.