What is the Strouhal number of turbulence driven by supernovae?

Abstract

The Strouhal number, ${\rm{St}}=t_{\rm cor}/t_{\rm out}$, measures the temporal coherence of turbulent driving relative to the outer-scale eddy turnover time. In turbulence-box models one commonly sets ${\rm{St}}=1$, although recent work by \citet{Grete2025_density_distribution} and \citet{Scannapieco2025_density_distribution} has shown that turbulence statistics, especially the mass-density distribution in compressively driven turbulence, are sensitive to this choice. In this Letter, we compute ${\rm{St}}$ directly from the measured two-time correlation tensor and outer-scale eddy time in stratified multiphase ISM simulations of Milky Way-like and starburst disks. We find isotropic median values ${\rm{St}}=0.26^{+0.30}_{-0.16}$ for the Milky Way-like model and ${\rm{St}}=0.25^{+0.11}_{-0.12}$ for the starburst model. These values are consistent with the picture that supernova remnants (SNRs) drive turbulence locally near $R_{\rm cool}$, where the unstable contact discontinuity in the expanding SNR sets comparable forcing and eddy times, ${\rm{St}}(R_{\rm cool})\approx 1$. The reconstructed scale-dependent curves reach ${\rm{St}}=1$ at a nearly universal outer-scale fraction, $\ell_\ast/\ell_{\rm out}\approx0.12\text{--}0.13$ ($\ell_\ast\approx25\text{--}32\,\rm{pc}$), so the standard ${\rm{St}}=1$ prescription is not an outer-scale model of SN-driven ISM turbulence, but a local-scale approximation tied to injection near the cooling radius of the SNR.