The propagation speed Vc of the streamwise velocity fluctuations u' in turbulent channel flows is calculated using direct numerical simulation (DNS) data at four Mach numbers (M=0, 0.8, 2.0, and 3.0). The profiles of Vc are shown to display remarkable similarity at different M. Quantitative models are developed based on a statistical structure called Velocity-Vorticity Correlation Structure (VVCS), defined as the vorticity region most correlated to velocity fluctuations at a fixed location. Good agreement with DNS-measured propagation velocities is obtained throughout the channel and for all M. The result confirms earlier speculation that the near-wall propagation is due to an advection by coherent vortex structures, and validates the concept of the VVCS.