Stability of flow in a channel with vibrating walls

The effects of small wall vibrations in the form of traveling waves on the asymptotic stability of a channel flow are analyzed. It is shown that vibrations may affect flow instability only if they consist of modes with wavelength and frequency close to those of the neutral Tollmien–Schlichting (TS) waves. Vibrations in resonance with the neutral TS waves produce instability that amplifies linearly in time. It is shown that vibrations detuned with the neutral TS waves may lead to an initial transient growth linear in time. It is further demonstrated that this growth may lead to flow destabilization through nonlinear effects, resulting in a significant reduction in the critical Reynolds number. The wealth of possible flow responses for various forms of detuning, including modulated wall vibrations, is also discussed.