A Toomre-like stability criterion for the clumpy and turbulent
  interstellar medium
  We explore the gravitational instability of clumpy and turbulent gas discs,
taking into account the Larson-type scaling laws observed in giant molecular
clouds (GMCs) and HI, as well as more general scaling relations. This degree of
freedom is of special interest in view of the coming high-z ISM surveys, and is
thus potentially important for understanding the dynamical effects of
turbulence at all epochs of galaxy evolution. Our analysis shows that
turbulence has a deep impact on the gravitational instability of the disc. It
excites a rich variety of stability regimes, several of which have no classical
counterpart. Among other diagnostics, we provide two useful tools for observers
and simulators: (1) the stability map of turbulence, which illustrates our
stability scenario and relates it to the phenomenology of interstellar
turbulence: GMC/HI observations, simulations and models; (2) a Toomre-like
stability criterion, $Q\geq\bar{Q}$, which applies to a large class of
clumpy/turbulent discs. We make specific predictions about GMC and cold-HI
turbulence, and point out the implications of our analysis for high-z galaxy
surveys.
