Three-wave resonant interactions between two dispersion branches*

We report the experimental 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 [1]. 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, with a mother wave on the sloshing branch generating two gravity-capillary daughter waves. The waves are shown to be phase-locked and 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, both at large and small scales. 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

[1]. F. Novkoski, C.-T. Pham and E. Falcon, Evidence of experimental three-wave resonant interactions between two dispersion branches, Phys. Rev. E, 107, 045101 (2023).