What is the Strouhal number of turbulence driven by supernovae?

Abstract

The Strouhal number, $\mathrm{St}=t_{\mathrm{cor}}/t_{\mathrm{out}}$, measures the temporal coherence of turbulent driving relative to the outer-scale eddy turnover time. In turbulence-box models one commonly sets $\mathrm{St}=1$, 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 $\mathrm{St}$ 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 $\mathrm{St}=0.26_{-0.16}^{+0.30}$ for the Milky Way-like model and $\mathrm{St}=0.25_{-0.12}^{+0.11}$ for the starburst model. These values are consistent with the picture that supernova remnants (SNRs) drive turbulence locally near $R_{\mathrm{cool}}$, where the unstable contact discontinuity in the expanding SNR sets comparable forcing and eddy times, $\mathrm{St}(R_{\mathrm{cool}})\approx 1$. The reconstructed scale-dependent curves reach $\mathrm{St}=1$ at a nearly universal outer-scale fraction, ${\ell }_{\ast }/{\ell }_{\mathrm{out}}\approx 0.12\text{–}0.13$ (${\ell }_{\ast }\approx 25\text{–}32\mathrm{pc}$), so the standard $\mathrm{St}=1$ 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.

10 pages, 3 figures main text. 6 pages, 2 figures appendix. Submitted to ApJL. Comments welcome!