Acoustic horizons for axially and spherically symmetric fluid flow

Details Acoustic horizons for axially and spherically symmetric fluid flow Acoustic horizons for axially and spherically symmetric fluid flow

2005-10-18

arxiv.org/abs/physics/0510164v1

Class.Quant.Grav. 23 (2006) 2427-2434

Physics

Fluid Dynamics

6 pages, 3 figures

Scientific paper

We investigate the formation of acoustic horizons for an inviscid fluid moving in a pipe in the case of stationary and axi-symmetric flow. We show that, differently from what is generally believed, the acoustic horizon forms in correspondence of either a local minimum or maximum of the flux tube cross-section. Similarly, the external potential is required to have either a maximum or a minimum at the horizon, so that the external force has to vanish there. Choosing a power-law equation of state for the fluid, $P\propto \rho^{n}$, we solve the equations of the fluid dynamics and show that the two possibilities are realized respectively for $n>-1$ and $n<-1$. These results are extended also to the case of spherically symmetric flow.

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