Study of compressible turbulent plane Couette flows via direct numerical simulation

Compressible turbulent plane Couette flows are studied via direct numerical simulation for wall Reynolds numbers up to and wall Mach numbers up to. Various turbulence statistics are compared with their incompressible counterparts at comparable semilocal Reynolds numbers. The skin friction coefficient, which decreases with, only weakly depends on. On the other hand, the thermodynamic properties (mean temperature, density and others) strongly vary with. Under proper scaling transformations, the mean velocity profiles for the compressible and incompressible cases collapse well and show a logarithmic region with the Kárman constant. Compared with wall units, the semilocal units yield a better collapse for the profiles of the Reynolds stresses. While the wall-normal and spanwise Reynolds stress components slightly decrease in the near-wall region, the inner peak of the streamwise component notably increases with increasing - indicating that flow becomes more anisotropic when compressible. In addition, the near-wall turbulence production decreases as increases - due to rapid wall-normal changes of viscosity caused by viscous heating. The streamwise and spanwise energy spectra show that the length scale of near-wall coherent structures does not vary with in semilocal units. Consistent with those in incompressible flows, the superstructures (the large-scale streamwise rollers) with a typical spanwise scale of become stronger with increasing. For the highest studied, they contribute about of the Reynolds shear stress at the channel centre. Interestingly, flow visualization and correlation analysis show that the streamwise coherence of these structures degrades with increasing. In addition, at comparable, the amplitude modulation of these structures on the near-wall small scales is quite similar between incompressible and compressible cases - but much stronger than that in plane Poiseuille flows.