Amplitude modulation of acoustic waves in accelerating flows

We investigate the amplitude modulation of acoustic waves in accelerating flows using 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, that 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, we present a leading-order model derived from first principles, leveraging a similarity of the wave characteristics and the wave amplitude, that reproduces this amplitude modulation for sufficiently small time intervals. This leading-order model may serve as a basis for the numerical prediction and analysis of the behavior of acoustic waves in accelerating flows.