The effect of surface tension on the stability of unconfined and confined planar jets and wakes

Abstract

In this theoretical study, a linear spatio-temporal analysis is performed on unconfined and confined inviscid jet/wake flows with surface tension in order to determine convective/absolute instability criteria. There is a single mode that is due to surface tension and many modes that are due to the jet/wake column. In the unconfined case, the full impulse response is considered in the entire outer flow. On the one hand, the surface tension mode propagates slowly in the cross-stream direction but dominates at the front and back of the wavepacket. On the other hand, the jet/wake column modes propagate more quickly in the cross-stream direction and therefore define the boundaries of the central region of the wavepacket. The flow is particularly unstable when these modes interact. For unconfined flows, it is found that at low and intermediate surface tensions the flow can be more absolutely unstable than that without surface tension but at high surface tensions the flow is stabilized. The effect of confinement has previously been studied but not with the inclusion of surface tension. Confinement and surface tension combined cause the transition from convective to absolute instability to occur even with significant coflow. This effect is examined over an infinite domain of density ratios and confinement.