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