Fluid motion between parallel planes. Dynamical stability

Abstract

If U is the velocity of the mean motion the following main results are obtained: 1. The region where U = c , c being the wave velocity, is the source where vibrations are generated; i.e. the slowly varying vibrations give rise to large rapidly varying vibrations in passing through the critical point. 2. Curved profiles admit a periodic motion at sufficiently high Reynolds numbers. 3. Parabolic flow is unstable at high Reynolds numbers; i.e. an infinitely small disturbance is sufficient to break up such flow. The critical Reynolds number is equal to R = U 0 h/v =6700, and the corresponding wavelength is about three times the width of the channel ( U 0 is the mean velocity at the axis, and h is the half-width of the channel).