Stability of acoustic streaming jets confined in cylindrical cavities

We study the stability of a steady Eckart streaming jet flowing in a closed cylindrical cavity. This configuration is a generic representation of industrial processes where driving flows in a cavity by means of acoustic forcing offers a contactless way of stirring or controlling flows. Successfully doing so, however, requires sufficient insight into the topology induced by the acoustic beam. This, in turn, raises the more fundamental question of whether the basic jet topology is stable and, when it is not, of the alternative states that end up being acoustically forced. To answer these questions, we consider a flow forced by an axisymmetric diffracting beam of attenuated sound waves emitted by a plane circular transducer at one cavity end. At the opposite end, the jet impingement drives recirculating structures spanning nearly the entire cavity radius. We rely on linear stability analysis (LSA) together with three-dimensional nonlinear simulations to identify the flow destabilisation mechanisms and to determine the bifurcation criticalities. We show that flow destabilisation is closely related to the impingement-driven recirculating structures, and that the ratio between the cavity and the maximum beam radii plays a key role on the flow stability. In total, we identified four mode types destabilising the flow. For, a non-oscillatory perturbation rooted in the jet impingement triggers a supercritical bifurcation. For, the flow destabilises through a subcritical non-oscillatory bifurcation and we explain the topological change of the unstable perturbation by analysing its critical points. Further reducing increases the shear within the flow and gradually moves the instability origin to the shear layer between impingement-induced vortices: for, an unstable travelling wave grows out of a subcritical bifurcation, which becomes supercritical for. For each geometry, the nonlinear three-dimensional (3-D) simulations confirm both the topology and the growth rate of the unstable perturbation returned by LSA. This study offers fundamental insight into the stability of acoustically driven flows in general, but also opens possible pathways to either induce turbulence acoustically or to avoid it in realistic configurations.