Nonlinear coupling mechanisms in acoustic oscillator systems which can lead to synchronization

Abstract

We present results on the coupling mechanisms in wind-driven, self-sustained acoustic oscillators. Such systems are found in engineering applications, as gas burners, and—more beautiful—in musical instruments. As a result, we find that coupling and oscillators are nonlinear in character, which can lead to synchronization. We demonstrate our ideas using one of the oldest and most complex musical devices: organ pipes. Building up on the questions of preceding works, the elements of the sound generation are identified using detailed experimental and theoretical studies, as well as numerical simulations. From these results, we derive the nonlinear coupling mechanisms of the mutual interaction of organ pipes. This leads to a nonlinear coupled acoustic oscillator model, which is based on the aeroacoustical and fluid dynamical first principles. The model calculations are compared with the experimental results from preceding works. It appears that the sound generation and the coupling mechanisms are properly described by the developed nonlinear coupled model of self-sustained oscillators. In particular, we can explain the unusual nonlinear shape Arnold tongues of the coupled two-pipe system. Finally, we show the power of modern CFD simulations by a 2D simulation of two mutually interacting organ pipes, i.e., the compressible Navier-Stokes equations are numerically solved.