Compressibility effects on turbulence production

Turbulence in compressible flows plays a major role in a variety of applications such as air/fuel mixing strategies for scramjet combustors. Therefore, the ability of controlling its production is of particular interest. However, compressible turbulence is more challenging than its incompressible counterpart due to the fact that thermodynamic quantities also fluctuate. In particular, the compressible turbulent kinetic energy production is a function of both velocities and density fluctuations. The so-called Morkovin's hypothesis has been often used in the literature to express the density fluctuations as a function of the velocity ones and the local Mach number. In this work, we discuss the validity of this hypothesis, and we use its expression to reformulate the turbulence production as a function of velocity only. The resulting expression shows that the planar component of turbulence production is substantially unaffected by compressibility effects. This result validates a previous work aimed at the sustainment of turbulence production using streamwise vortices. On the other hand, the turbulence production terms aligned with the convective velocity are affected by compressibility, even at relatively low Mach numbers.