Direct numerical simulation of compressible isotropic turbulence

Direct numerical simulation (DNS) of decaying compressible isotropic turbulence at turbulence Mach numbers of M-r = 0.2-0.7 and Taylor Reynolds numbers of 72 and 153 is performed by using the 7th order upwind-biased difference and 8th order center difference schemes. Results show that proper upwind-biased difference schemes can release the limit of "start-up" problem to Mach numbers. Compressibility effects on the statistics of turbulent flow as well as the mechanics of shocklets in compressible turbulence are also studied, and the conclusion is drawn that high Mach number leads to more dissipation. Scaling laws in compressible turbulence are also analyzed. Evidence is obtained that scaling laws and extended self similarity (ESS) hold in the compressible turbulent flow in spite of the presence of shocklets, and compressibility has little effect on scaling exponents.