Secondary instability in rotating-disk flow

Abstract

Primary instability of the three-dimensional boundary layer on a rotating disk introduces periodic modulation of the mean flow in the form of stationary crossflow vortices. Here we study the stability of this modulated mean flow with respect to secondary disturbances. These secondary disturbances are found to have quite large growth rates compared to primary disturbances. Both fundamental and subharmonic resonance cases are considered and their corresponding results indicate that the growth rate and the frequency of the secondary instability are insensitive to the exact nature of the resonance condition. The threshold primary stationary crossflow vortex amplitude for secondary instability found in this three-dimensional incompressible boundary layer is significantly larger than that for a two-dimensional boundary layer which is subjected to Tollmien–Schlichting instability. The secondary instability results in a pair of travelling counter-rotating vortices, tilted up and oriented at an angle to the primary stationary crossflow vortices. The computed velocity signals and flow visualization, evaluated based on this secondary disturbance structure, are compared with experimental results.