Strong evidence for universality in homogeneous compressible turbulence

Quantifying the degree of universality in compressible turbulence is challenging due to the existence of different modes and their complex interactions. For a restricted family of flows, Donzis and John [Phys. Rev. Fluids 5, 084609 (2020)] showed that universal behavior is indeed observed in compressible turbulence if the ratio of dilatational to solenoidal root mean square (rms) velocities (δ=u′d/u′s) is incorporated as a scaling parameter along with the traditional turbulent Mach number (Mt=u′/〈c〉, where u′ is the rms velocity and 〈c〉 is the mean speed of sound). In this paper, we argue for the generality of those results by analyzing a wide range of compressible turbulent flows spanning a variety of flow configurations and setups to assess the degree of universal behavior. These include, among others, reacting flows, flows with solenoidal, thermal, and dilatational forcing, and flows with mean shear and bulk viscosity. We also performed new direct numerical simulations, which include turbulence in situations where vibrational modes of constitutive molecules are not in thermal equilibrium. Collectively, we offer the largest comparison across studies in the literature to date. We find that despite the wide range of forcing conditions and physical processes, universality holds across all these turbulent flows to a very satisfactory degree when both δ and Mt are considered as intrinsic compressibility parameters. The statistics investigated here—single-point statistics up to order four—are chosen such that they represent different ranges across the spectrum of dynamically relevant turbulence scales. We discuss the applicability of the purposed universal behavior for other key statistics in these turbulent flows, including two-point statistics and inhomogeneity effects, and the perspective it opens for modeling them.