An Observational Method to Measure the Relative Fractions of Solenoidal and Compressible Modes in Interstellar Clouds

We introduce a new method for observationally estimating the fraction of momentum density ($\rho \mathbf{v}$) power contained in solenoidal modes (for which $\mathrm{\nabla }\cdot \rho \mathbf{v}=0$) in molecular clouds. The method is successfully tested with numerical simulations of supersonic turbulence that produce the full range of possible solenoidal/compressible fractions. At present the method assumes statistical isotropy, and does not account for anisotropies caused by (e.g.) magnetic fields. We also introduce a framework for statistically describing density–velocity correlations in turbulent clouds.