Quasinormal ringing of acoustic black holes in Laval nozzles: Numerical simulations

TL;DR

This paper investigates the quasinormal ringing of acoustic black holes in Laval nozzles through numerical simulations, revealing how these modes are excited and how they can be detected experimentally despite boundary reflections.

Contribution

It introduces a semi-analytical calculation of quasinormal frequencies in transonic flows and discusses experimental detection methods considering boundary effects.

Findings

Quasinormal modes are excited during flow formation or perturbation.

Late-time ringing persists longer than ordinary quasinormal ringing.

Detection of quasinormal ringing can be optimized despite wave reflections.

Abstract

Quasinormal ringing of acoustic black holes in Laval nozzles is discussed. The equation for sounds in a transonic flow is written into a Schr\"{o}dinger-type equation with a potential barrier, and the quasinormal frequencies are calculated semianalytically. From the results of numerical simulations, it is shown that the quasinormal modes are actually excited when the transonic flow is formed or slightly perturbed, as well as in the real black hole case. In an actual experiment, however, the purely-outgoing boundary condition will not be satisfied at late times due to the wave reflection at the end of the apparatus, and a late-time ringing will be expressed as a superposition of "boxed" quasinormal modes. It is shown that the late-time ringing damps more slowly than the ordinary quasinormal ringing, while its central frequency is not greatly different from that of the ordinary one. Using this fact, an efficient way for experimentally detecting the quasinormal ringing of an acoustic black hole is discussed.