Evidence of experimental three-wave resonant interactions between two dispersion branches

Filip Novkoski (1) , Chi-Tuong Pham (2, 3) , Eric Falcon (1)

1 MSC - Matière et Systèmes Complexes
2 COMET - COuplages Multiphysiques Et Transferts - LISN
3 LISN - Laboratoire Interdisciplinaire des Sciences du Numérique

We report the observation of nonlinear three-wave resonant interactions between two different branches of the dispersion relation of hydrodynamic waves, namely the gravity-capillary and sloshing modes. These atypical interactions are investigated within a torus of fluid for which the sloshing mode can be easily excited. A triadic resonance instability is then observed due to this three-wave two-branch interaction mechanism. An exponential growth of the instability and phase locking are evidenced. The efficiency of this interaction is found to be maximal when the gravity-capillary phase velocity matches the group velocity of the sloshing mode. For a stronger forcing, additional waves are generated by a cascade of three-wave interactions populating the wave spectrum. Such a three-wave two-branch interaction mechanism is probably not restricted to hydrodynamics and could be of interest in other systems involving several propagation modes.

Mots clés: Nonlinear wave resonant interaction; Experiments; Gravity capillary waves; Sloshing; Dispersion relation; Cascade of resonances; Triadic resonance instability

Domaines: Mécanique des fluides [physics.class-ph]; Dynamique Chaotique [nlin.CD]

Filip Novkoski, Chi-Tuong Pham, Eric Falcon. Evidence of experimental three-wave resonant interactions between two dispersion branches. Physical Review E , 2023, 107 (4), pp.045101. ⟨10.1103/PhysRevE.107.045101⟩. ⟨hal-04136586⟩