Determine the influence of large-scale turbulence on multi-point VDFs

Determine how large-scale turbulent motions influence the velocity dispersion functions and clarify the coupling between large- and small-scale turbulence in observational molecular-cloud velocity fields.

Background

The paper explains that multi-point velocity dispersion functions (VDFs) are designed to suppress ordered velocity components, but observational velocity fields may contain both small-scale ordered motions and large-scale turbulent motions. Although higher-order VDFs can better remove small-scale ordered structures, the behavior of large-scale turbulent contributions is not established. In particular, the renewed increase of the VDF beyond its plateau cannot be unambiguously interpreted because it may reflect large-scale turbulence as well as large-scale ordered motions. Resolving this issue would require observations spanning a broader and more complete kinematic range.

References

On the other hand, the role of large-scale turbulent motions in shaping the VDF remains poorly constrained. As a result, the increase in the VDF beyond the plateau cannot be uniquely attributed to large-scale ordered motions, and the coupling between large- and small-scale turbulence remains unclear.

— Turbulence Cascade in Cygnus X Revealed by Multi-point VDF Method  (2609.08894 - Huang et al., 8 Sep 2026) in Section 3.2, Multi-point Velocity Centroid Dispersion Functions