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

Abstract

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.

References in corpus (5)

• Experiments in Surface Gravity-Capillary Wave Turbulence
• Experimental quasi-1D capillary-wave turbulence
• Wave turbulence in a two-layer fluid: coupling between free surface and interface waves
• Forced three-wave interactions of capillary-gravity surface waves
• Experimental Dispersion Relation of Surface Waves Along a Torus of Fluid