The draining bathtub flow, a cornerstone in the theory of acoustic black holes, is here extended to thecase of exact solutions for compressible nonviscous flows characterized by a polytropic equation of state.Investigating the analytical configurations obtained for selected values of the polytropic index, it is foundthat each of them becomes nonphysical at the so called limiting circle. By studying the null geodesicsstructure of the corresponding acoustic line elements, it is shown that such a geometrical locus coincideswith the acoustic event horizon. This region is characterized also by an infinite value of space-timecurvature, so the acoustic analogy breaks down there. Possible applications for artificial and naturalvortices are finally discussed.
Acoustic Metric of the Compressible Draining Bathtub
CHERUBINI C;FILIPPI S
2011-01-01
Abstract
The draining bathtub flow, a cornerstone in the theory of acoustic black holes, is here extended to thecase of exact solutions for compressible nonviscous flows characterized by a polytropic equation of state.Investigating the analytical configurations obtained for selected values of the polytropic index, it is foundthat each of them becomes nonphysical at the so called limiting circle. By studying the null geodesicsstructure of the corresponding acoustic line elements, it is shown that such a geometrical locus coincideswith the acoustic event horizon. This region is characterized also by an infinite value of space-timecurvature, so the acoustic analogy breaks down there. Possible applications for artificial and naturalvortices are finally discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
