Kolmogorov turbulence across multi-fractal gas in Polaris Flare

We reveal a pristine, scale-invariant 3D Kolmogorov velocity cascade ($\alpha_V^{\mathrm{3D}} \sim 2/3$) 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 ($\alpha_V^{\mathrm{3D}}=\alpha_V-\frac{1}{3}\alpha_I$), we obtain the scale-invariant value of $\alpha_V^{\mathrm{3D}}$, 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.