Wave focusing on the surface of a fluid

Jules Fillette

Wave focusing is a common process in optics and acoustic but has not been much studied un hydrodynamics despite its interest in understanding strong nonlinear waves, formation of rogue waves and amplification of tsunami energy.

We study experimentally the focusing of circular converging waves generated by the vertical oscillation of a ring on the surface of water. We measure the wave profile as function of space and time. As the ring oscillates with a weak amplitude, the stationnary wave profile coincide with the bessel function, which is the linear prediction for this problem. When the forcing frequency and amplitude satisfy certain conditions, focusing leads to a main divergence at the center of the ring which can itself evolve towards ejection of a drop. We report on the phase diagram of the system and the three regimes we observed. Then we present the departures between linear theory and experiments.

We thank French ANR Dysturb ANR17CE300004 and the Simons Foundation MPS651463.