Stability of time-periodic flows in a circular pipe

The stability of time-periodic flows in a circular pipe is investigated. The disturbance is assumed to be axially symmetric and to have a small amplitude, so that the governing differential equation is linear. Calculations are carried out for the first ten modes for a range of values of the frequency of the primary motion, of the wavenumber of the disturbance, and of the Reynolds number of the primary flow. In the ranges of the parameters for which the calculations have been carried out, the flows are found to be stable and, as for Stokes flows (von Kerczek & Davis 1974), it is conjectured that the flows under study here are stable for all frequencies and all Reynolds numbers.