Abstract:
In propagating wave
systems, three or four-wave resonant interactions constitute a
classical non-linear mechanism exchanging energy between the
different scales. Here we investigate three-wave interactions
for gravitycapillary surface waves in a closed laboratory tank.
We generate two crossing wave-trains and we study their
interaction. Using two optical methods, a local one (Laser
Doppler Vibrometry) and a spatio-temporal one (Diffusive Light
Photography), a third wave of smaller amplitude is detected,
verifying the three-wave resonance conditions in frequency and
in wavenumber. Furthermore, by focusing on the stationary regime
and by taking into account viscous dissipation, we directly
estimate the growth rate of the resonant mode. The latter is
then compared to the predictions of the weakly non-linear
triadic resonance interaction theory. The obtained results
confirm qualitatively and extend previous experimental results
obtained only for collinear wave-trains. Finally, we discuss the
relevance of three-wave interaction mechanisms in recent
experiments studying gravity-capillary turbulence.