Saturation Level of Turbulence in Collapsing Gas Clouds

We investigate the physical mechanism that decides saturation level of turbulence in collapsing gas clouds. perform a suite high-resolution numerical simulations following collapse turbulent clouds with various effective polytropic exponents $\gamma_{\rm eff}$, initial Mach numbers $\mathcal{M}_0$, and seeds. Equating energy injection rate by gravitational contraction dissipation turbulence, we obtain an analytic expression compare it results. Consequently, results are well described model, given driving scale is one-third Jeans length core. These indicate strength at first core formation early universe/present-day star-formation process can be estimated solely eff}$.