  Turbulent flows, ubiquitous in nature and engineering, comprise fluctuations
over a wide range of spatial and temporal scales. While flows with fluctuations
in thermodynamic variables are much more common, much less is known about these
flows than their incompressible counterparts in which thermodynamics is
decoupled from hydrodynamics. A critical element in the study of the latter has
been the concept of universal scaling laws which provides fundamental as well
as practical information about the spatio-temporal behavior of these complex
systems. Part of this success is due to the dependence on a single
non-dimensional parameter, that is the Reynolds number. Universality in
compressible flows, on the other hand, have proven to be more elusive as no
unifying set of parameters were found to yield universal scaling laws. This
severely limits our understanding of these flows and the successful development
of theoretically sound models. Using results in specific asymptotic limits of
the governing equations we show that universal scaling is indeed observed when
the set of governing parameters is expanded to include internally generated
dilatational scales which are the result of the driving mechanisms that produce
the turbulence. The analysis demonstrate why previous scaling laws fail in the
general case, and opens up new venues to identify physical processes of
interest and create turbulence models needed for simulations of turbulent flows
at realistic conditions. We support our results with a new massive database of
highly-resolved direct numerical simulations along with all data available in
the literature. In search of universal features, we suggest classes which
bundle the evolution of flows in the new parameter space. An ultimate
asymptotic regime predicted independently by renormalization group theories and
statistical mechanics is also assssed with available data.
