Small-scale turbulence alongside large-scale turbulence in a z=1.87 star-forming galaxy with an outflowing wind, revealed by multi-point structure functions

Recently, Goldman (2024) used observations by Vasan et al. (2025) and obtained evidence for a large scale compressible, Burgers turbulence in the ISM of CSWA13, a gravitationally lensed, star-forming galaxy at $ z = 1.87$, with an outflowing wind, Goldman (2024) analyzed the residual line of sight velocity field of the nebular gas, derived from by the C|||] emission line, and the residual, line of sight velocity field of the outflowing wind obtained by observations of the Si∗|| florescent emission line. The two velocity fields are functions of the position along the major galactic axis, The turbulence timescale on the largest spatial scale has been found to be ∼ 500 Myr . This together with the large spatial scale of ∼6.43 kpc suggest a large scale generating mechanism (such as tidal interaction or merger) that lasted for a time ∼500 Myr . On the other hand, the outflowing wind is much younger and is probably the result of the intense star formation. Therefore, could it be that the star formation drives also turbulence on small scales? In the present paper we utilize multi-point second order structure functions (Cho 2019; Seta et al. 2023; Seta & Federrath 2024; Lee et al. 2025) to find whether there exists also a small scale turbulence in this galaxy, and if so, try to identify its drivers. We obtained evidence for small scale turbulence whose largest spatial scale is ls ∼240 pc for the nebular gas velocity field and ls ∼290 pc for the outflowing wind velocity field. These values suggest that stellar sub clumps or large star clusters with an high concentration of young massive stars could be responsible for both the outflow and for the small scale turbulence. In the case of the wind velocity there is an additional, larger small scale turbulence, with ls ∼1.5 kpc. This is about the size of the large clumps of that galaxy, suggesting these large clumps as the drivers of the turbulence on this scale.