Acoustic Streaming due to Attenuated Plane Waves

TLDR

The paper reviews theories for calculating steady acoustic streaming, comparing methods and approximations from various authors. The study works out two illustrative problems of rectilinear flow induced by irrotational sound fields. The authors solve a single attenuated plane wave in a tube and a pair of crossed plane waves, incorporating boundary conditions and static pressure gradients to derive rectilinear streaming solutions. Streaming speeds depend critically on the attenuation constant α (from heat conduction, scattering, thermal relaxation, etc.), measurements cannot distinguish absorption mechanisms, and numerical results indicate high flow speeds may occur in bubbly media.

Abstract

Theories for calculating steady streaming associated with sound fields are reviewed, comparing the methods and approximations of various authors. Two illustrative problems are worked out, both for rectilinear flow due to irrotational sound fields. The first deals with a single attenuated plane wave traveling down a tube, as in Cady's quartz wind experiments. In the second, a pair of crossed plane waves is treated, giving rise to a quite different kind of streaming. In obtaining solutions, attention is given to boundary conditions; here, gradients of She excess static pressure, another second-order quantity, come into consideration. Significantly, streaming speeds depend critically upon α, the attenuation constant, where α may be due to any common cause, such as heat conduction, scattering, thermal relaxation, etc. From these results it appears that streaming measurements cannot be used to distinguish between absorption mechanisms. Numerical values are given for a few cases; high flow speeds may be expected in a bubbly medium.