THE INFLUENCE OF SWIRL AND CONFINEMENT ON THE STABILITY OF COUNTERFLOWING STREAMS

A linear stability analysis of laterally confined swirling flow is giv en, of the type described by Long's equation in the inviscid limit or by the von Karman similarity equations in the absence of lateral confi nement. The flow of interest involves identical counterflowing fluid s treams injected with equal velocity W0 through opposing porous disks, rotating with angular velocities OMEGA and +/-OMEGA, respectively, abo ut a common normal axis. By means of mass transfer experiments on an a queous system of this type we have detected an apparent hydrodynamic i nstability having the appearance of an inviscid supercritical bifurcat ion at a certain Absolute value of OMEGA > 0. As an attempt to elucida te this phenomenon, linear stability analyses are performed on several idealized flows, by means of a numerical Galerkin technique. An analy sis of high-Reynolds-number similarity flow predicts oscillatory insta bility for all non-zero OMEGA. The spatial structure of the most unsta ble modes suggests that finite container geometry, as represented by t he confining cylindrical sidewalls, may have a strong influence on flo w stability. This is borne out by an inviscid stability analysis of a confined flow described by Long's equation. This analysis suggests a n ovel bifurcation of the inviscid variety, which serves qualitatively t o explain the results of our mass transfer experiments.