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Time-Reversal Analogy by Nonlinear Acoustic–Gravity Wave Triad Resonance

School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK
Department of Mathematics, Massachusetts Institute of Technology, 77 Mass Ave, Cambridge, MA 02139, USA
Fluids 2019, 4(2), 91;
Received: 13 April 2019 / Revised: 30 April 2019 / Accepted: 13 May 2019 / Published: 17 May 2019
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics)
PDF [1255 KB, uploaded 20 May 2019]


Time reversal of free-surface water (gravity) waves due to a sudden change in the effective gravity has been extensively studied in recent years. Here, we show that an analogy to time-reversal can be obtained using nonlinear acoustic-gravity wave theory. More specifically, we present a mathematical model for the evolution of a time-reversed gravity wave packet from a nonlinear resonant triad perspective. We show that the sudden appearance of an acoustic mode in analogy to a sudden vertical oscillation of the liquid film, can resonate effectively with the original gravity wave packet causing energy pumping into an oppositely propagating (time-reversed) surface gravity wave of an almost identical shape. View Full-Text
Keywords: nonlinear triads; acoustic-gravity waves; triad resonance; time reversal nonlinear triads; acoustic-gravity waves; triad resonance; time reversal

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Kadri, U. Time-Reversal Analogy by Nonlinear Acoustic–Gravity Wave Triad Resonance. Fluids 2019, 4, 91.

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