Acoustic black hole analogy to analyze nonlinear acoustic wave dynamics in accelerating flow fields

We present a physical model and numerical method based on space- time-dependent Galilean-type coordinate transformation to simulate acoustic waves in the presence of an accelerating background flow field with sonic transition. Kinematically, is designed so as maintain well-posedness transformed wave equation, which solved fixed computational domain using standard finite differences. Considering black hole analogy, we analyze nonlinear dynamics stationary but non-uniformly under assumption spherical symmetry. The choice analogy motivated by fact that steady-state horizon allows us parameterize wave-flow configuration terms Helmholtz number [Formula: see text], expressed function speed sound c, emitted wavelength acceleration at horizon, is, surface gravity text]. results simulations show He describes geometrically similar sets characteristics for different combinations text] However, also observe variations amplitude along characteristics, are attributed Doppler modulations. It appears these modulations depend can, therefore, differ characteristics.