Acoustic streaming: insights across Reynolds numbers

Abstract

When a fluid system is subjected to an acoustic wave (or another periodic actuation), the response of the fluid is not purely periodic, but is rather characterized by the combination of a periodic flow and a steady Stokes drift component, where the former is, in many cases, an acoustic wave and the latter is commonly referred to as acoustic streaming. Classical theories of acoustic streaming have focused on slow acoustic streaming, where the periodic flow is the leading-order flow, and is insensitive to the steady flow component which appears as a small correction and is characterized by a small hydrodynamic Reynolds number. In contrast, Dubrovski et al. (J. Fluid Mech. vol. 975, 2023, A4) tackle the fast acoustic streaming regime - conceived by Zarembo (Acoustic streaming. In High-Intensity Ultrasonic Fields, 1971, pp. 135-199. Springer) approximately fifty years ago - where both the periodic and steady flow components are of a similar order of magnitude such that the periodic flow both supports and is simultaneously impacted by the steady flow. They present a novel theoretical framework that accounts for the convection of momentum both within and between the periodic and steady flow to extend slow-streaming equations to the case of steady flow with arbitrary hydrodynamic Reynolds number. They leverage a scaling analysis of the resulting system of equations and a case study to demonstrate the compatibility of their equations with slow streaming theories and highlight the distinctive features of fast streaming.