Transient unidirectional acoustic streaming in annular resonators

Theoretical description of the transient process of the acoustic streaming excitation in a toroidal waveguide with driven walls is developed. Particular attention is paid to the analysis of the closed-loop (unidirectional) streaming excitation by purely propagating acoustic mode. This mode might be excited by proper phasing of the two localized acoustic sources. It is demonstrated that the evolution of the local streaming velocity can be non-monotonous in some points of the resonator cross-section. A numerical evaluation of the analytical solutions highlights the influence of the ratio of the acoustic boundary layer thickness to the waveguide width on the acoustic-streaming stabilization time. The results obtained for the acoustic streaming in the annular resonator can be useful for the analysis of the annular thermoacoustic engines and refrigerators. They might be also applied in microfluidics where there is a growing interest to different possible physical mechanisms of fluid pumping in microscale channels.