  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. However, 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. This result appears to
be consistent with the physical fact that vortices stretch stronger in a
compressible fluid hence postponing viscous intervention. The consequent
generation of enhanced velocity gradients in a compressible fluid appears to
provide an underlying physical basis for the previous results indicating that
fully-developed compressible turbulence is effectively more dissipative than
its incompressible counterpart.
