Dear @Jiantao.Liu,
Yes, by “velocity spectra”, the TurbSim User’s Guide means PSD of the velocity time series.
I have not used the MATLAB function periodogram myself, but you could see if a simpler PSD function produces different results, e.g., you can use my script that calculates the PSD directly via FFT without windowing (but with optional binning to smooth the PSD). This script, Jason_PSD.m can be found in the following forum post: User defined spectrum from routine UserWaveSpctrm in HydroDYn - #7 by Jason.Jonkman.
Best regards,