Amplitude degradation of time-reversed pulses in nonlinear absorbing thermoviscous fluids

The linear wave equation in a lossless medium is time reversible, i.e., every solution p(x, t) has a temporal mirror solution p(x, -t). Analysis shows that time reversal also holds for the lossless nonlinear wave equation. In both cases, time-reversal invariance is violated when losses are present. For nonlinear propagation loses cannot normally be ignored; they are necessary to prevent the occurrence of multivalued waveforms. Further analysis of the nonlinear wave equation shows that amplification of a time-reversed pulse at the array elements also leads to a violation of time reversal even for lossless nonlinear acoustics. Numerical simulations are used to illustrate the effect of nonlinearity on the ability of a time-reversal system to effectively focus on a target in an absorbing fluid medium. We consider both the amplitude and arrival time of retrodirected pulses. The numerical results confirm that both shock generation (with the accompanying absorption) and amplification at the array, adversely affect the ability of a time-reversal system to form strong retrodirective sound fields.