Abstract

In this talk I will describe the theory and present numerical evidence for a new type of nonlinear resonant interaction using Rossby and surface gravity waves as examples. The resonance constitutes a generalisation of the usual ‘exact’ resonance as we show that exchanges of energy between the waves can be enhanced when the linear frequency mismatch, or detuning, is non-zero i.e. ω1 ± ω2 ± ω3 ≠ 0. This is possible because the resonance condition is now a match between the so-called ‘precession frequency’ of a given triad interaction and an existent nonlinear frequency in the system. In the limit of weak nonlinearity this precession frequency is simply due to the linear ‘drift’ of the triad phase; therefore, it tends toward the detuning. This means precession resonance of this type can occur at finite amplitudes, with nonlinear corrections contributing to the resonance. In the Rossby wave case we find precession resonance leads to a collective state of synchronised oscillation, giving enhanced cascades at intermediate nonlinearity. In the water wave case we find triads can resonate, not quartets as normal, and we discuss ongoing physical experiments in collaboration with Marc Perlin in Michigan.