Flutter and long-wave instabilities in compliant channels conveying developing flows

A partially collapsed lung airway or other flexible tube is modelled as a two-dimensional channel of infinite length. We consider the linear stability of this system conveying a developing flow, analysing the full Orr–Sommerfeld system analytically for long waves and numerically for arbitrary wavelengths. We find a long-wave instability which has not been observed in previous channel studies. This long-wave instability is stabilized by increasing the elastance of the wall, but other wall properties do not affect it except in correction terms. In addition to the long-wave instability, there is the finite wavelength (flutter) instability, which, depending on the parameter values chosen, may be critical at a higher or lower flow speed than the long-wave instability. For special parameter values the long-wave and flutter instabilities are critical at the same flow speed. Comparisons with experiments show that theoretical predictions are in agreement with experimental observations.