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Universality concepts have played a pivotal role in the development of complex systems. This has not been the case in compressible turbulence as no unifying set of parameters has been found to yield universal scaling laws. An analysis supported with DNS databases and studies across the literature shows how universality can indeed be achieved in homogeneous compressible turbulence from specific limiting behavior, paving the way toward a more unified fundamental understanding of compressible turbulence and development of robust compressible turbulence models.

Numerical simulations of isotropic turbulence find that the energy spectrum in the dissipation range cannot be described by a single exponential for R${}_{\ensuremath{\lambda}}$g20, and that this effect is associated with intermittent energy transfer.

We consider transition to strong turbulence in an infinite fluid stirred by a gaussian random force. The transition is {\bf defined} as a first appearance of anomalous scaling of normalized moments of velocity derivatives (dissipation rates) emerging from the low-Reynolds-number Gaussian background. It is shown that due to multi-scaling, strongly intermittent rare events can be quantitatively described in terms of an infinite number of different "Reynolds numbers" reflecting multitude of anomalous scaling exponents. The theoretically predicted transition disappears at $R_{\lambda}\leq 3$. The developed theory, is in a quantitative agreement with the outcome of large-scale numerical simulations., Comment: 5 pages two figures