modulational instabilities long wave-short waves Fermi-Pasta-Ulam recurrence dynamics
The resonance of two envelopes of short (capillary) waves with a common long (gravity)
wave component is considered. A mismatch in group velocity is incorporated and the
resonance conditions need not be satisfied exactly. This slight detuning permits a wider
choice of modes and consequently, a much richer set of dynamics. The linear instability of
plane waves is studied, and the dominant unstable wave numbers are identified. The
subsequent fully nonlinear evolution of these perturbed plane waves is investigated by direct
numerical simulations. The Fermi – Pasta – Ulam recurrence phenomenon is observed.