Bifurcations of limit cycles in surface waves due to resonant forcing

Abstract

Experiments on surface waves in cylindrical container subject to resonant horizontal oscillation have been carried out, and behaviors of the waves associated with the increase of forcing period are examined in detail. We have found several kinds of periodic or irregular modulations of surface waves corresponding to limit cycles or chaotic attractors. Furthermore, a few kinds of bifurcations (period-doubling, symmetry-breaking, and homoclinic ones) of these limit cycles are observed. Many of these behaviors in the experiment agree well with the solutions in the theory developed by Miles. That is, all the above bifurcations are also found in the theoretical solutions. Moreover, most of the chaotic attractors and limit cycles obtained in the experiments have corresponding partners in the theory. It is suggested that a few discrepancies found between the experiment and the theory are caused by the variation of an effective damping coefficient in the experiment and a subtle asymmetry with respect to the axis of oscillation in the experimental system.