INFLUENCE OF COOLING-INDUCED COMPRESSIBILITY ON THE STRUCTURE OF TURBULENT FLOWS AND GRAVITATIONAL COLLAPSE

We investigate the properties of highly compressible turbulence, the c ompressibility arising from a small effective polytropic exponent gamm a(e) due to cooling. In the limit of small gamma(e), the density jump at shocks is shown to be on the order of e(M2), much larger than the M (2) jump associated with high Mach number hows in the isothermal regim e. In the absence of self-gravity, the density structures that arise i n the moderately compressible case consist mostly of patches separated by shocks and behaving like waves while, in the highly compressible c ase, clearly defined, long-lived object-like clouds emerge. The transi tion from wavelike to object-like behavior requires a change in the re lative phase of the density and velocity fields analogous to that in t he development of an instability. When the forcing in the momentum equ ation is purely compressible, the rotational energy decays monotonical ly in time, indicating that the vortex-stretching term is not efficien t in transferring energy to rotational modes. This property may be at the origin of the low amount of rotation found in interstellar clouds. Vorticity production is found to rely heavily on the presence of addi tional terms in the equations, such as the Coriolis force at large sca les and the Lorentz force at small scales in the interstellar medium, or on the presence of local sources of heating. In the presence of sel f-gravity, we suggest that turbulence can produce bound structures for gamma(e) < 2(1 - n(-1)), where n is the typical dimensionality of the turbulent compressions. We support this result by means of numerical simulations in which, for sufficiently small gamma(e), small-scale tur bulent density fluctuations eventually collapse even though the medium is globally stable. This result is preserved in the presence of a mag netic held for supercritical mass-to-flux ratios. At larger polytropic exponents, turbulence alone is not capable of producing bound structu res, and collapse can only occur when the medium is globally unstable. This mechanism is a plausible candidate for the differentiation betwe en primordial and present-day stellar cluster formation and for the lo w efficiency of star formation. Finally, we discuss models of the inte rstellar medium at the kiloparsec scale including rotation, which rest ores a high-gamma(e) behavior.