Kolmogorov\'s 1941 theory (K41) of similarity hypotheses and the -5/3 law for energy spectrum are considered as the most important theoretical achievement in turbulence research and the success of the modern turbulence theory. The assumptions of sufficient high Reynolds number and isotropy of turbulence that K41 based upon, however, cannot generally be met in practice, and thus discrepancy is often observed between the-5/3κ law and direct numerical simulation (DNS) results of boundary layers in wall bounded turbulence, especially for moderate to low Reynolds number flows. Liutex vector is a recently defined new physical quantity which is extracted from turbulent flow to represent the rigid rotation part of fluid motion. Actually, Liutex is free from viscous dissipation and thus independent of Reynolds number, relaxing the very high Reynold number assumption of K41. Liutex similarity has been solidly demonstrated by DNS for a moderate Reynolds number turbulent boundary layer(Reθ≈1000), both the frequency and wavenumber spectrum of Liutex accurately matches the-5/3 law, which is obviously much better than the turbulence energy spectrum, while vorticity and other popular vortex identification methods,Q criterion for example, do not possess such a distinguished feature due to stretching and shearing contamination.