The generation of the second harmonic wave is studied
through a weakly non linear inviscid theory based on Thorpe (1987)
and extended to finite width plane waves. It turns out that, contrary to
what is claimed in TH87, a resonance for the second harmonic wave generation
is impossible. Results are confronted to numerical experiments which validate
the theory. Perspective: 3D Laboratory experiments at the CORIOLIS platform
show that the main dynamical feature is the set up of a strong horizontal mean current.
