Inconsistencies in the Notions of Acoustic Stress and Streaming

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 expedi-ency but poor overall conceptualization of such systems. This contention is further supported by the poor agreement of experiment in many such approaches. The no-tion 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 pres-sure field. This article is meant as the fourth part of an installment on wave motion [3, 4, 2]. One of the major thrusts of 20th century physics has been unification. Through some combination of vanity and poor conceptualization in favor of clever mathematical pre-sentation we have often over reached in this respect. Aspects of different wave systems are attempted to be treated by similar frameworks when, given more careful analysis, no such unified description is justified. One of the greater sins has been in the use of pseu-domomentum [11]. Translational symmetries in systems give conserved quantities that have the units of linear momentum yet have no such meaning in terms of actual forces at boundaries. Often these arise from clever integration by parts constructions where the integration constant is ignored. In the case of fluids, these translational cases often miss essential nonlinear features of packet motion. When using conserved quantities, especially angular momentum, the end-of-packet contributions can be dominant. Since conservation laws give a powerful check on often freewheeling perturbation approaches, getting this right is very important. In the case of dielectric response, the Abraham-Minkowskii debate has lingered over a century. It can be considered as either about the correct momentum of a photon i