Unveiling the Burgers-Riccati physics of fast acoustic streaming

TL;DR

This paper introduces a new multiscale method that models fast acoustic streaming using Burgers and Riccati equations, providing accurate transient and steady solutions beyond traditional slow models.

Contribution

The paper develops the MADaM approach, offering a scale-sensitive expansion that captures fast acoustic streaming phenomena with novel Burgers-Riccati physics.

Findings

Transient solutions for axial Eckart streaming derived from Burgers equation.

Steady streaming characterized by Riccati equation solutions.

Enhanced modeling accuracy for high-frequency, high-amplitude acoustic flows.

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.