Water waves in time-varying media : from frequency conversion to topological transition
In this talk, I will discuss several examples of water waves manipulation by the mean of an external forcing. In a first part, I will show how high voltage and electrostriction can be used to control the dispersion relation at the surface of a fluid. As a consequence, classical devices such as lenses or wave guiders could be implemented experimentally for water wave control in a contactless way. When the high voltage is varied along time, unusual features such as frequency conversion have been observed. In particular, we show how one can perform up to one octave up or down frequency conversion using properly triggered high voltage signals. In a second part, I will focus on the case where a water tank is vibrated at typically twice the frequency of a specific mode of the liquid interface. In this case, parametric instability occurs and large waves oscillating at half the excitation frequency appear at the surface of the fluid (Faraday instability). The phase of those waves can take two distinct values depending on the initial condition. I will discuss how one can switch on demand from one phase state to the other by introducing a temporal defect in the excitation and discuss a topological interpretation of such transition.
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