Universality and scaling in homogeneous compressible turbulence

Abstract

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.