A newly developed statistical correlation structure is used to analyze compressible channel flows up to M=3.0. Using velocity-vorticity correlation structure (VVCS), the Mach number dependence of the characteristic scales of near wall structure are analyzed. The detailed results show that the length scale and the spanwise spacing of VVCS exponentially increase with Mach number in the near wall region. For example, for VVCSuωx, the length scale of the statistical streamwise structure is Lx uωx=e6.5+M/2.8+(M/4.1)2, and spacing between the structure is Dxuωx=60eM/2.2+13.3, where the parameters 2.8, 4.1 and 2.2 are characteristic Mach numbers to be explained further. The geometrical features of the statistical structure are consistent with the observations of Coleman et al., and it is also argued that the quantitative relationship between the characteristic scales of VVCS and Mach number is important to consider in performing numerical computation of compressible flows. This study also suggests that a set of geometrical structures should be invoked for modeling inhomogeneous compressible shear flows.