Mechanisms of jet instability: role of deceleration

Abstract

This paper shows that decrease of velocity magnitude downstream enhances the shear-layer instability in jetlike single- and two-fluid flows. This feature has not been recognized in stability studies, performed in the parallel and quasi-parallel flow approximations, because the deceleration effect is strongly non-parallel. It was first revealed in conical similarity flows. The similarity allows for reducing the base-flow and stability problems to ordinary differential equations exactly conserving the acceleration terms. This helps reveal the deceleration effect. The development of numerical technique for stability studies of two-dimensional flows helped understand the instability nature of swirling flows in sealed containers. It was found for an elongated cylinder with one rotating end disk and stationary other walls that the instability develops in the counterflow near the rotating disk, where the backflow decelerates and the shear-layer and deceleration effects cooperate. An interesting stabilizing effect of acceleration is observed in a model heat exchanger. The thermal convection develops in a rotating cylindrical container whose sidewall is adiabatic and the end disks have different temperatures. The centrifugal acceleration suppresses, while the temperature difference stimulates, the shear-layer instability of this flow. Next, the review discusses two-fluid flows in a sealed vertical container, driven by either bottom (whirlpool model) or lid (waterspout model) rotation. As the rotation speeds up, the shear-layer instability develops in a jet-like boundary layer in the air–water flows. The jet forms near a rotating disk, goes to the interface near the sidewall, and converges to the axis near the interface. New circulatory cells emerge in both fluids and the interface significantly bends. The instability develops after such flow pattern becomes well formed. The instability focuses near the interface where the jet-like motion approaches a new cell, decelerates, and diverges—hence the deceleration and shear-layer effects work together. In oil–water flows, the instability develops in the lower fluid, either in its depth or near the interface depending on the water volume fraction. Thus, the review shows that deceleration enhanced the shear-layer instability in a wide group of flows.