  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.
