Acoustic time-reversal experiments in the nonlinear regime

Abstract

Until now, time-reversal mirrors (TRM) were only used in a low power regime for which nonlinearities can be neglected. Here, their behavior is investigated in a higher power regime compelling nonlinearities to be taken into account. If one considers the acoustic wave equation in a weakly nonlinear medium, the time-reversal invariance holds. Thus, Burger’s equation is invariant when time and direction of propagation are simultaneously reversed. In a nonlinear medium, the shape of a sinusoid changes continuously during propagation as energy is transferred to harmonics. The inverse process would take place after reflection on a TRM. This property holds as long as the shock distance is not reached, otherwise the shock discontinuity implies an irreversible change of the entropy and the time-reversal invariance is broken. These results are confirmed by a finite differences simulation of Burger’s equation. However, experiments are very difficult to carry out because of the limited bandwidth of transducers. Nevertheless, for 1-D problems and an antisymmetric wave packet, a time reversal is equivalent to a reflection on a pressure release interface. This trick has been used to conduct an experiment giving qualitative good agreements with the simulation. a)Also at Lab. de Modélisation en Mécanique, Univ. Paris VI, CNRS UMR 7607, 4 place jussieu, F75252 Paris Cedex 05, France.