Time reversal invariance of nonlinear acoustic wave propagation in weakly viscous media

Time Reversal Mirrors (TRM) are usually used in a low power regime. However, their potential applications in such various fields as hyperthermia or lithotripsy implies to investigate their behavior in a higher power regime. In such high power configurations, nonlinearities have to be taken into account. If one considers the acoustic wave equation in a non viscous medium [for example, Westerfeld's equation], the time reversal invariance holds. In a non linear regime, the shape of a sinusoid emitted by an acoustic source changes continuously during propagation as energy is transferred to harmonics. If this distorted signal is time reversed after some propagation distance and remitted in the opposite direction, it will suffer an inverse shape distortion during the propagation and finally recover a perfect sinusoidal shape. 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. The experimental evidence of such phenomenon is here presented. The experimental results are compared with 1D numerical simulations of Burgers equation.