DNS of compressible turbulent plane Couette flows

Direct numerical simulations of compressible turbulent plane Couette flows are performed at two different wall Mach numbers M_w = 0.8 and 1.5 for wall Reynolds numbers up to Re_w = 10000. Various turbulence statistics are examined and compared with their incompressible counterparts at comparable semilocal Reynolds numbers. With proper scaling transformations, both the mean velocity and turbulent Reynolds stresses profiles collapse well between the compressible and incompressible cases, with the only exception for the inner peak of the streamwise Reynolds stress – found to increase with increasing M_w. The streamwise and spanwise energy spectra reveal that the size of near-wall structures does not vary with the M_w. Consistent with the observations in incompressible flows, the superstructures (i.e., the large-scale streamwise rollers) with a typical spanwise scale of λ_z/h ≈ 1.5π become stronger with increasing Re_w and contribute about 40% of the Reynolds shear stress at the center of the domain for the highest Re_w studied. Interestingly, flow visualization and correlation analysis reveal that the streamwise organization of these structures degrades with increasing M_w.