BIFURCATIONS AND NONLINEAR DYNAMICS OF SURFACE-WAVES IN FARADAY RESONANCE

The nonlinear dynamics of nonlinear modulated cross-waves of resonant frequency omega(1) and carrier frequency omega approximate to omega(1) is investigated. In a long channel of width b, that contains fluid of depth d and which is subjected to a vertical oscillation of frequency 2 omega, the wave can appear in solitary form. As has been shown prev iously, the solitary wave is only stable in a certain parameter regime ; depending on damping and driving amplitudes the wave becomes unstabl e. The nonlinear development of the instabilities of solitary waves is the central problem of this paper. It is shown how instabilities are saturated following generic routes to chaos in time with spatially coh erent structures. Finally, the case of time-modulated driving amplitud es is also considered. In most cases it appears that nonlinear waves o f simple spatial structures take part in the nonlinear dynamics, but a few cases of spatial chaos are also reported.