Preprint A290/2004
The eddy viscosity for time reversing waves in an irreversible environment
Andre Nachbin | Garnier, Josselin
Keywords: waves in random media | time reversal | eddy viscosity
We present new results for the time-reversal of weakly nonlinear pulses traveling in a random irreversible environment. We consider long water waves propagating in the presence of a spatially random depth. A viscous shallow water model is considered. We demonstrate that weakly nonlinear waves can still be time-reversed under weak dissipation. Incoherently scattered signals are recompressed, both, for time-reversal in transmission as well as in reflection. Under the weakly nonlinear, weakly dissipative regime dissipation only affects the refocused pulse profile regarding its amplitude, but not its shape. Numerical experiments are presented. Moreover we also describe a new theory for calculating the eddy viscosity for weakly nonlinear waves propagating over a random surface.