Inconsistencies in the Notions of Acoustic Stress and Streaming

TL;DR

This paper critically examines the concept of acoustic stress in hydrodynamics, arguing it is inconsistent with pressure-based force analysis and proposing vorticity-driven mechanisms as the true source of acoustic streaming.

Contribution

It challenges the traditional notion of acoustic stress and introduces a vorticity-based explanation for acoustic streaming, emphasizing the role of viscosity and boundary effects.

Findings

Acoustic stress concepts are inconsistent with pressure-based force analysis.

Vorticity generated by viscous forces drives acoustic streaming.

Nonlinear pressure corrections are preferable to acoustic stress calculations.

Abstract

Inviscid hydrodynamics mediates forces through pressure and other, typically irrotational, external forces. Acoustically induced forces must be consistent with arising from such a pressure field. The use of "acoustic stress" is shown to have inconsistencies with such an analysis and generally arise from mathematical expediency but poor overall conceptualization of such systems. This contention is further supported by the poor agreement of experiment in many such approaches. The notion of momentum as being an intrinsic property of sound waves is similarly found to be paradoxical. Through an analysis that includes viscosity and attenuation, we conclude that all acoustic streaming must arise from vorticity introduced by viscous forces at the driver or other solid boundaries and that calculations with acoustic stress should be replaced with ones using a nonlinear correction to the overall pressure field.