Abstract
We apply the gas-kinetic scheme (GKS) for direct numerical simulation (DNS) of compressible decaying homogeneous isotropic turbulence. We compute dynamics of the kinetic energy K(t), the dissipation rate (t), the probability density functions (PDFs) of the twopoint longitudinal velocity dierence u (r ) with a separation distance r , the shocklet strength , and the local Mach number Mat. Our results show that, (a) With initial Taylor microscale Reynolds number Re fixed, the maximum dissipation rate attained at the initial stage increases as the initial turbulent Mach number Mat increases; (b) The initial turbulence Mach number Mat has no observable eect on kinetic energy K(t) and the asymptotic behavior of the dissipation rate (t); (c) At the lower Mat (=0.1), the PDF of u (r ) for some r remain non-Gaussian for a long time, indicating persisting intermittency, while at higher Mat (= 0.5), the PDF of u (r ) quickly becomes Gaussian regardless r . And (d) The PDF’s of both shock strength and the local Mach number all obey a scaling law.
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