We studied decaying Incompressible Homogeneous Isotropic Turbulence (IHIT). May be, you can use the same (or similar) initial velocity field what we used for this study. You can check out our paper: Article Freely decaying turbulence in a finite domain at finite Reyn...
This paper (and the references inside it) may help you to find an appropriate initial velocity filed for compressible HIT.