Kinetic energy spectrum and transfer within the near-dissipation range of compressible isotropic turbulence

The analysis of kinetic energy spectrum and dissipation mechanisms plays a crucial role in both theoretical examination and real-world implementations within compressible turbulent flows. The previous works within the near-dissipation range are conducted within the framework of incompressible turbulent flow dynamics. We investigate the kinetic energy spectrum and transfer within the near-dissipation range of compressible isotropic turbulent flows via highly resolved direct numerical simulations with different turbulent Mach numbers (Mt). We found that in compressible turbulent flows, the kinetic energy spectrum model is significantly influenced by the turbulent Mach number, with a more pronounced tail as the turbulent Mach number increases. Within the near-dissipation range, there exist strong local spatial fluctuations of the kinetic energy flux with the increase in grid resolution. The viscous dissipation can be decomposed into solenoidal and dilatational components, and its dilatational component leads to stronger intermittency within the near-dissipation range. Besides, the high turbulent Mach number also leads to a stronger dissipation, which serves as an alternative factor for the high intermittency within the near-dissipation range in compressible turbulent flows. The uncovered high intermittency provides a theoretical foundation for the prediction of intense events and the development of turbulent modelings.