  While interstellar gas is known to be supersonically turbulent, the injection
processes of this turbulence are still unclear. Many studies suggest a dominant
role of gravitational instabilities. However, their effect on galaxy morphology
and large-scale dynamics vary across cosmic times, in particular due to the
evolution of the gas fraction of galaxies. In this paper, we propose numerical
simulations to follow the isothermal turbulent cascade of purely
gravitationally-driven turbulence from its injection scale down to 0.095 pc for
a gas-poor spiral disk and a gas-rich clumpy disk. To this purpose, and to lift
the memory-footprint technical lock of sufficiently resolving the interstellar
medium of a galaxy, we developed an encapsulated zoom method that allows us to
probe self-consistently the self-generated turbulence cascade over three orders
of magnitude on spatial scales. We follow this cascade for 10 Myrs. We find
that the turbulent cascade follows the same scaling laws in both setups.
Namely, in both cases the turbulence is close to equipartition between its
compressive and solenoidal modes, the velocity power spectrum follows the
Burgers' scaling and the density power spectrum is rather shallow, with a
power-law slope of -0.7. Last, gravitationally-bound substructures follow a
mass distribution with a -1.8 slope, similar to that of CO clumps. These
simulations thus suggest a universality of gravity-driven isothermal turbulent
cascade in disk galaxies across cosmic time.
