Resonant interactions between propagating gravity wave packets

Abstract

The spatial and temporal evolution of gravity wave packet interactions is studied numerically. It is shown that through the resonant parametric excitation an upgoing gravity wave packet can cause the growth of two secondary waves from noise level up to a significant intensity in several hours. The primary wave packet is apparently deformed as it decays. The energy transfer among the interacting waves is no longer reversible since their amplitudes are localised. Therefore the characteristic time for the interactions is of a particular significance; it represents a time during which the principal energy transfer arises. Beyond the characteristic time the net energy transfer among the interacting waves becomes rather weak, but the local change in the wave energy densities can be considerable. Only a part of the initial energy of the primary wave packet is transferred to the secondary waves during the parametric excitation. The amounts of energy, which each of the two secondary waves extract from the primary wave, are different, exhibiting a parameter preference in the energy transfer. The parametric excitation process can be completed in the propagation time. For the resonant interaction with two gravity wave packets initially having large amplitudes, the evolution rate is faster than that in the parametric excitation. The primary wave packet can lose most of its energy and finally be reduced to a small fluctuation. The viscous dissipation not only decreases the wave energies but also strongly affects the local energy transfer among the interacting gravity wave packets.