Compressible Turbulence: Multi-fractal Scaling in the Transition to the Dissipative Regime

TL;DR

This paper explores how compressibility affects multi-fractal scaling in turbulence, showing that compressibility extends the inertial range and influences dissipation, with shock waves playing a key role in the transition.

Contribution

It demonstrates that compressibility extends the multi-fractal scaling regime into the dissipative range and highlights the role of shock waves in this process.

Findings

Compressibility extends the multi-fractal regime into the dissipative range.

Shock waves act as dissipative structures in compressible turbulence.

Compressible turbulence is more dissipative than incompressible turbulence.

Abstract

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.