Abstract
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.
Highlights
The propagation of an incident surface gravity wave disturbance over a fluid layer that is subject to a sudden vertical movement may excite a second disturbance travelling in an opposite direction
The main objective of this paper is to demonstrate an analogy for the evolution of a ‘time-reversed’ wave amplitude from a nonlinear acoustic-gravity triad resonance perspective
To illustrate the analogy to instantaneous time reversal we present a numerical example of an incident gravity wave packet interacting with the long crested
Summary
The propagation of an incident surface gravity wave disturbance over a fluid layer that is subject to a sudden vertical movement (oscillation) may excite a second disturbance travelling in an opposite direction. [1] who modelled the wave celerity by employing a doorstep rectangular function whose limit case, when time tends to zero, is the Dirac delta function Such setting dictates that once the reversed wave is generated the surface is exclusively governed by the two gravity waves; an assumption which is valid in linear wave theory. For a rigid bottom the water should be deep enough, otherwise an elastic boundary needs to be considered which allows propagation of the fundamental mode in the water at any depth [12] Under these settings, the evolution of an ‘instantaneous’ wave amplitude is derived, but the contribution of modulated surface amplitude due to energy transfer in the interior of the fluid is assessed. To illustrate the generality of the interaction mechanism, we discuss two more cases of interaction involving higher propagating modes or when the oscillation is harmonic resulting in the evolution of standing waves of double the frequency, which can arguably describe the evolution of Faraday-type waves
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