Unveiling the Burgers-Riccati physics of fast acoustic streaming

Abstract

Inaccurate slow streaming models of acoustically-induced fluid flow remain in use due to the lack of a generalized alternative. The Multiscale Articulated Differentials Method (MADaM; [see co-article]) solves this problem with a complete, scale-sensitive spatiotemporal expansion. Applied to classic axial Eckart streaming, the MADaM produces, in terms of a Burgers equation, a long-sought transient solution able to accommodate frequencies and amplitudes far beyond slow streaming models. Steady streaming is governed by a corresponding Riccati equation that, when solved, produces simple expressions explaining innate features of fast acoustic streaming.