Scale-dependent Energy Transfer Rate as a Tracer for Star Formation in   Cosmological N-Body Simulations
  We investigate the energy release due to the large-scale structure formation and the subsequent transfer of energy from larger to smaller scales. We calculate the power spectra for the large-scale velocity field and show that the coupling of modes results in a transfer of power predominately from larger to smaller scales. We use the concept of cumulative energy for calculating which energy amount is deposited into the small scales during the cosmological structure evolution. To estimate the contribution due to the gravitational interaction only we perform our investigations by means of dark matter simulations. The global mean of the energy transfer increases with redshift $\sim (z+1)^{3}$; this can be traced back to the similar evolution of the merging rates of dark matter halos.   The global mean energy transfer can be decomposed into its local contributions, which allows to determine the energy injection per mass into a local volume. The obtained energy injection rates are at least comparable with other energy sources driving the interstellar turbulence as, e.g. by the supernova kinetic feedback. On that basis we make the crude assumption that processes causing this energy transfer from large to small scales, e.g. the merging of halos, may contribute substantially to drive the ISM turbulence which may eventually result in star formation on much smaller scales. We propose that the ratio of the local energy injection rate to the energy already stored within small-scale motions is a rough measure for the probability of the local star formation efficiency applicable within cosmological large-scale n-body simulations. 
M. Hoeft, J.P. Muecket, and P. Heide