The Stability of Oscillatory Hagen-Poiseuille Flow

Abstract

The linear stability theory of the nonzero mean, sinusoidally oscillating flow in a tube of circular cross section is examined. It is found that the relevant axisymmetric disturbances in the oscillatory flow are more stable (i.e., have larger decay rates) than the axisymmetric disturbances of the mean flow alone. This result holds for values of the cross-sectional average oscillation velocity amplitude at least as large as seven-tenths the average mean-flow velocity amplitude. Although the instantaneous velocity profile contains generalized inflection rings for a substantial portion of the oscillation period, the disturbances do not become instantaneously unstable at any time, even for very low frequency oscillations.