Is the subharmonic threshold always lower than the fundamental one in plane Poiseuille flow?

Abstract

We revisit the secondary instability of a Tollmein-Schlichting wave in plane Poiseuille flow at Re = 5000 and find that the fundamental threshold can be lower than the subharmonic one in the wavenumber space, in contrast to the prevalent view in the literature that only instability of subharmonic modes occurs at very low disturbance amplitudes and fundamental modes need a higher disturbance amplitude to become unstable. This is because of overlooking the even class of fundamental modes, which happen to produce the lower threshold at those wavenumbers.