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ABSTRACT  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 H  i , as well as more general scaling relations. This degree of freedom is of special interest in view of the coming high‐ z  interstellar medium 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/H  i  observations, simulations and models; (2) a Toomre‐like stability criterion, , which applies to a large class of clumpy/turbulent discs. We make specific predictions about GMC and cold‐H  i  turbulence and point out the implications of our analysis for high‐ z  galaxy surveys.

A Toomre‐like stability criterion for the clumpy and turbulent interstellar medium