Instability of channel flow with oscillatory wall suction/blowing

The stability of channel flow modulated by oscillatory wall suction/blowing is investigated using linear stability analysis together with Floquet theory based on numerical calculation and asymptotic expansion. Two typical flows with either the driven pressure gradient or the flow rate constant are considered. The basic flows subject to the oscillatory wall suction/blowing are time periodic with multiple frequency components. The stability problem is formulated into a time-dependent eigenvalue problem, and the Floquet exponents are obtained using a spectral collocation method. It is revealed that the periodic wall suction/blowing induces the Stokes layer, which interacts with the disturbance shear wave and eventually affects the disturbance growth. Results show that the modulations of the oscillatory wall suction/blowing to the channel flows have a destabilizing effect and the similar stability characteristics of both the typical flows occur. Critical Reynolds numbers and wave numbers are predicted for a wide range of parameters. Asymptotic expansions of the growth rate at small amplitude $Δ$ of the oscillatory wall suction/blowing are developed. The correction terms for the growth rate occur in $O(Δ2)$ and are positive, indicating that the flow is destabilized. It is found that the destabilizing effect is mainly connected to the steady corrections of the mean flow profile in the $O(Δ2)$ terms.