Acoustic amplification and bifurcation in a moving fluid

TL;DR

This paper investigates how acoustic waves in a moving fluid can be amplified and lead to complex bifurcation and chaotic behavior due to nonlinear interactions influenced by flow velocity and Reynolds number.

Contribution

It introduces a novel analysis of acoustic wave amplification and bifurcation in moving fluids using the Lagrange parameter variation method, revealing the conditions for chaos.

Findings

Nonlinear interactions cause period-doubling and bifurcations.

Amplitude of subharmonics depends on Mach and Reynolds numbers.

Flow momentum can amplify acoustic waves leading to chaos.

Abstract

The quasi-accumulation solutions of acoustic wave in a moving fluid are obtained by using the Lagrange parameter variation method to solve the differential equation that describes the interaction between the acoustic waves and the flow. The results show that the nonlinear interaction causes the period-doubling followed by the odd multiple half-period bifurcation and all order subharmonics are generated subsequently, of which the amplitudes depend not only on the acoustic Mach number but also on the Mach number of the flow. The latter result indicates that the acoustic wave has been amplified by the momentum of the flow. The result also shows that the amplitudes of the generated subharmonics are proportional to the (the order number of the approximation) powers of the acoustic Reynolds number (and hence the Reynolds number of the flow). If the kinetic energy gained from momentum amplification is greater than the energy loss due to the acoustic attenuation, which means, the Reynolds number exceeds its critical value, a chain-reaction of the period-doubling followed by the odd multiple half-period bifurcation can continue to proceed so that the number of degrees of freedom in the flow increases infinitely resulting a chaos.