Kolmogorov turbulence across multi-fractal gas in Polaris Flare

Abstract

We reveal a pristine, scale-invariant 3D Kolmogorov velocity cascade ($α_V^{\mathrm{3D}} \sim 2/3$) spanning $0.05$--$20$~pc in the Polaris Flare using \texttt{PPCOS} $^{12}\text{CO}$ data. A transition scale at $\sim 0.5$~pc marks a bifurcation in the structure functions' exponents, below which the degree of intermittency is also saturated. By deriving an analytical mapping relation ($α_V^{\mathrm{3D}}=α_V-\frac{1}{3}α_I$), we obtain the scale-invariant value of $α_V^{\mathrm{3D}}$, proving that the apparent transition stems from geometric projection and a changing density fractal dimension rather than a turbulent mode shift. Kolmogorov turbulence is smoothly inherited from the large-scale cold neutral medium, remaining uninterrupted by compression or gravity below 0.1 pc.