Eddy shocklets in decaying compressible turbulence

Abstract

The existence of eddy shocklets in three‐dimensional compressible turbulence is controversial. To investigate the occurrence of eddy shocklets, numerical simulations of temporally decaying isotropic turbulence are conducted. Dilatation statistics from simulations with different initial fluctuation Mach numbers, M_t, show that dilatation is more intermittent and more negatively skewed for higher M_t. By studying instantaneous flow fields, shocklets are found and verified to have all the characteristics of a typical shock wave, such as proper jumps in pressure and density along with a local entropy peak inside the high‐compression zone. Although overall compressible dissipation contributes to less than one‐tenth of the total dissipation, compressible dissipation around shocklets is about an order of magnitude larger than typical values of incompressible dissipation. In the zones of eddy shocklets, pressure is highly correlated with dilatation to convert kinetic energy into internal energy. These mechanisms near shocklets should be accounted for in phenomenological modeling for highly compressible turbulence. Three‐dimensional turbulence is found to be less sensitive to the initial compressibility, and requires higher initial M_t for eddy shocklets to form than for two‐dimensional turbulence. Higher M_t and higher Reynolds number are found to increase the probability of shocklet occurrence.