Amplitude modulation of acoustic waves in accelerating flows quantified using acoustic black and white hole analogues

We investigate the amplitude modulation of acoustic waves in accelerating flows, a problem that is still not fully understood, but essential to many technical applications, ranging from medical imaging to acoustic remote sensing. The proposed modeling framework is based on a convective form of the Kuznetsov equation, which incorporates the background flow field and is solved numerically by a finite-difference method. Using acoustic black and white hole analogues as model systems, we identify a modulation of the wave amplitude which is shown to be driven by the divergence/convergence of the acoustic wave characteristics in an accelerating/decelerating flow, and which is distinct from the convective amplification accompanying an acoustic emitter moving at a constant velocity. To rationalize the observed amplitude modulation, a leading-order model is derived from first principles, leveraging a similarity of the wave characteristics and the wave amplitude with respect to a modified Helmholtz number. This leading-order model may serve as a basis for the numerical prediction and analysis of the behavior of acoustic waves in accelerating flows, by taking advantage of the notion that any accelerating flow field can be described locally as a virtual acoustic black or white hole.