Reynolds and Mach Number Scaling in Stationary Compressible Turbulence Using Massively Parallel High Resolution Direct Numerical Simulations

Turbulence is the most common state of fluid motion in both natural and engineering systems. Many real world applications depend on our ability to predict and control turbulent processes. Due to the presence of both hydrodynamic and thermodynamic fluctuations, simulations of compressible flows are more expensive than incompressible flows. A highly scalable code is presented which is used to perform direct numerical simulations (DNS) aimed at understanding fundamental turbulent processes. The code is parallelized using both distributed and shared memory paradigms and is shown to scale well up to 264144 cores. The code is used to generate a large database of stationary compressible turbulence at world-record resolutions and a range of Reynolds and Mach numbers, and different forcing schemes to investigate the effect of compressibility on classical scaling relations, to study the role of thermodynamic fluctuations and energy exchanges between the internal and kinetic modes of energy, and to investigate the plausibility of a universal behavior in compressible flows. We find that pressure has a qualitatively different behavior at low and high levels of compressibility. The observed change in the likelihood of positive or negative fluctuations of pressure impacts the direction of energy transfer between internal and kinetic energy. We generalize scaling relations to different production mechanisms, and discover a plausible universal behavior for compressible flows, which could provide a path to successful modeling of turbulence in compressible flows. Our results, unprecedented in size, accuracy and range of parameters will be helpful in addressing a number of additional open issues in turbulence research.