[Paper Review] Inconsistencies in the Notions of Acoustic Stress and Streaming

Clifford Chafin|arXiv (Cornell University)|Sep 9, 2014

Scientific Research and Discoveries10 references5 citations

TL;DR

This paper challenges the conventional use of 'acoustic stress' and pseudomomentum in fluid dynamics, arguing they are conceptually inconsistent and poorly validated by experiment. It proposes that acoustic streaming arises not from fictitious stresses but from viscous vorticity at boundaries, with accurate modeling requiring a nonlinear correction to the pressure field, which better captures long-range forces and boundary effects than traditional approaches.

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.

Motivation & Objective

• To critique the conceptual and experimental inconsistencies in the use of 'acoustic stress' and pseudomomentum in hydrodynamics.
• To demonstrate that acoustic streaming originates from viscous vorticity at boundaries, not from pressure or stress fields.
• To argue that traditional acoustic stress models fail to account for boundary effects and long-range pressure variations.
• To advocate for replacing acoustic stress with a nonlinear correction to the pressure field as a more physically consistent approach.
• To highlight the limitations of wave-stress and wave-action models in predicting real-world fluid behavior, especially in non-ideal or asymmetric systems.

Proposed method

• Analyzes inviscid and viscous hydrodynamics to show that acoustic forces must arise from a pressure field consistent with momentum conservation.
• Uses a nonlinear correction to the pressure field, derived from time-averaged kinetic energy terms, to model long-range forces.
• Applies Green’s functions to compute initial pressure variations in a two-liquid strip system under acoustic excitation.
• Imposes mass conservation and density redistribution to determine interface displacement due to pressure changes.
• Compares results with traditional wave-stress models, showing that distinct stresses like Syy ≠ Sxx are invalid; instead, a continuous global pressure field governs transverse forces.
• Uses a simplified dielectric model to show that conserved quantities like momentum and angular momentum can have non-local, end-of-packet contributions that invalidate local approximations.

Experimental results

Research questions

• RQ1 Why do traditional acoustic stress models fail to predict experimental results in acoustic streaming?
• RQ2 What is the true physical origin of acoustic streaming in viscous fluids?
• RQ3 How do boundary conditions and viscous forces at interfaces affect the validity of pseudomomentum and wave-stress concepts?
• RQ4 Can a nonlinear correction to the pressure field replace the concept of acoustic stress in a more consistent and experimentally verifiable way?
• RQ5 Why do wave-stress and wave-action models fail to accurately describe forces on submerged or floating objects in real wave environments?

Key findings

• Acoustic stress is conceptually inconsistent with inviscid hydrodynamics and does not arise from a physically valid pressure field; it is a mathematical expedient with poor physical grounding.
• Acoustic streaming results from vorticity generated by viscous forces at solid boundaries, not from acoustic stress or pseudomomentum.
• The nonlinear correction to the pressure field, ρP, provides a more accurate and physically consistent description of long-range forces than wave-stress models.
• Transverse forces cannot be modeled by distinct normal stresses (e.g., Syy ≠ Sxx); instead, a continuous global pressure field must be used.
• End-of-packet contributions dominate angular momentum and momentum-like quantities in wave systems, invalidating local conservation assumptions.
• The model predicts a net leftward displacement of a fluid interface in a two-liquid strip due to pressure-induced density redistribution, consistent with mass conservation and viscous effects.