Compressible turbulence: Multi-fractal scaling in the transition to the dissipative regime

► Multi-fractal scaling in the transition to the dissipative regime for fully-developed compressible turbulence is considered. ► The multi-fractal power law scaling behavior breaks down for very small length scales thanks to viscous effects. ► The effect of compressibility is found to extend the single-scaling multi-fractal regime further into the dissipative range. ► In the ultimate compressibility limit, thanks to the shock waves which are the appropriate dissipative structures, the single-scaling regime is found to extend indeed all the way into the full viscous regime.