The sonic scale revealed by the world's largest supersonic turbulence simulation

TL;DR

This paper presents a high-resolution simulation of interstellar turbulence to precisely locate the sonic scale, revealing a smooth transition from supersonic to subsonic turbulence and providing quantitative data for star formation models.

Contribution

The study offers the first detailed measurement of the sonic scale and cascade properties in interstellar turbulence using a 10048^3 grid simulation, advancing understanding of turbulence transition.

Findings

The sonic scale l_s relates to Mach number via l_s / L = phi_s Mach^(-1/p_sup).

The cascade transitions smoothly over a factor of 3 in scale, not sharply.

Measured phi_s values indicate a gradual transition from supersonic to subsonic turbulence.

Abstract

Understanding the physics of turbulence is crucial for many applications, including weather, industry, and astrophysics. In the interstellar medium (ISM), supersonic turbulence plays a crucial role in controlling the gas density and velocity structure, and ultimately the birth of stars. Here we present a simulation of interstellar turbulence with a grid resolution of 10048^3 cells that allows us to determine the position and width of the sonic scale (l_s) - the transition from supersonic to subsonic turbulence. The simulation simultaneously resolves the supersonic and subsonic cascade, v(l) ~ l^p, where we measure p_sup = 0.49 +/- 0.01 and p_sub = 0.39 +/- 0.02, respectively. We find that l_s agrees with the relation l_s / L = phi_s Mach^(-1/p_sup), where Mach is the three-dimensional Mach number, and L is either the driving scale of turbulence or the diameter of a molecular cloud. If L is the driving scale, we measure phi_s = 0.42 (+0.12) (-0.09), primarily because of the separation between the driving scale and the start of the supersonic cascade. For a supersonic cascade extending beyond the cloud scale, we get phi_s = 0.91 (+0.25) (-0.20). In both cases, phi_s < 1, because we find that the supersonic cascade transitions smoothly to the subsonic cascade over a factor of 3 in scale, instead of a sharp transition. Our measurements provide quantitative input for turbulence-regulated models of filament structure and star formation in molecular clouds.