TEMPORAL STABILITY OF JEFFERY-HAMEL FLOW

In this study of the temporal stability of Jeffery-Hamel flow, the cri tical Reynolds number based on the volume flux, R(c), and that based o n the axial velocity, Re(c), are computed. It is found that both criti cal Reynolds numbers decrease very rapidly when the half-angle of the channel, alpha, increases, such that the quantity alphaR(c) remains ve ry nearly constant and alphaRe(c) is a nearly linear function of alpha . For a short channel there can be more than one value of the critical Reynolds number. A fully nonlinear analysis, for Re close to the crit ical value, indicates that the loss of stability is supercritical. The resulting asymmetric oscillatory solutions show staggered arrays of v ortices positioned along the channel.