  In this work, we study the scale characteristics of the log- and outer-region
motions and structures in subsonic and supersonic turbulence. To this end, a
series of direct numerical simulations of the compressible turbulent channel
flow at medium Reynolds numbers are performed. Based on this database, the
streamwise and spanwise length scales of the outer-region motions are
investigated by the two-point correlations and the one-dimensional spectra. The
energy distribution among the multi-scale structures in the outer region is
found to be dominated by the semilocal friction-Reynolds-number effects rather
than the Mach-number effects. This conclusion not only holds for the velocity
fluctuations but also the fluctuations of the thermodynamic variables. Besides,
the streamwise and spanwise length scales of the outer motions do not alter
significantly when the flow passes the sound barrier as reported by a previous
experimental study (Bross et al., J. Fluid Mech., vol. 911, 2021, A2). On the
other hand, the self-similar structures populating the logarithmic region are
investigated by adopting a linear coherence spectrum. The
streamwise/wall-normal aspect ratio of the self-similar wall-attached
structures of the streamwise velocity and temperature fluctuations is
approximately 15.5, and the counterpart of density and pressure fluctuations is
1.8. The present study confirms the existence of self-similar structures in
compressible wall turbulence and assesses their geometrical characteristics.
