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

The linear wave equation in a lossless medium is time reversible, i.e., eve ry 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 necess ary to prevent the occurrence of multivalued waveforms. Further analysis of the nonlinear wave equation shows that amplification of a time-reversed pu lse at the array elements also leads to a violation of time reversal even f or lossless nonlinear acoustics. Numerical simulations are used to illustra te the effect of nonlinearity on the ability of a time-reversal system to e ffectively focus on a target in an absorbing fluid medium. We consider both the amplitude and arrival time of retrodirected pulses. The numerical resu lts confirm that both shock generation (with the accompanying absorption) a nd amplification at the array, adversely affect the ability of a time-rever sal system to form strong retrodirective sound fields. (C) 2000 Elsevier Sc ience B.V. All rights reserved.