GRAVITATIONAL-INSTABILITY IN TURBULENT, NONUNIFORM MEDIA

We present a gravitational instability analysis for a non-uniform medi um, with ''microturbulence'' characterized by a kinetic energy spectru m E(k) = Ak(-alpha), and within which density condensations (''clouds' ') follow a density-size scaling law of the form rho(k) = Bk-beta, whe re k similar to 1/l, and l is the scale size. Model terms are used for the turbulent pressure and for the scale dependence of the gravitatio nal potential. Since the initial state is already non-uniform, this wo rk bypasses the problem of cloud formation, and just focuses on the pr oblem of cloud support against gravitational collapse. We find that a variety of regimes exist depending on the parameters alpha and beta. T he case beta > 2 implies a total inversion of the Jeans criterion, wit h small clouds being unstable and large clouds stabilized by turbulent pressure, regardless of the spectral index alpha. If beta < 2, then t wo possibilities exist: if alpha + beta < 3, then the original Jeans c riterion is recovered, while if alpha + beta > 3 small clouds are stab ilized by thermal pressure, and large clouds are stabilized by turbule nt pressure, with the possible existence of an intermediate range of c loud sizes that are unstable. The special case alpha + beta = 3 is dis cussed. It corresponds to virial balance between gravity and turbulent pressure at all cloud sizes. This case includes the empirical scaling relations rho similar to l(-1) and Delta upsilon similar to l(1/2), a lthough a continuum of other possible combinations exist. More general ly, however, a wide range of stable configurations exist that do not r equire precise balance between gravity and turbulence at all cloud siz es. Finally, we discuss the assumptions necessary to perform a linear instability analysis for this problem, in particular that of microturb ulence. We conclude that this type of calculations can only provide cr ude guidelines for media with large-amplitude fluctuations such as the interstellar medium, a complete understanding of which most likely ne cessitates fully nonlinear calculations.