Dynamics of nearly inviscid Faraday waves in almost circular containers

Abstract

Parametrically driven surface gravity-capillary waves in an elliptically distorted circular cylinder are studied. In the nearly inviscid regime, the waves couple to a streaming flow driven in oscillatory viscous boundary layers. In a cylindrical container, the streaming flow couples to the spatial phase of the waves, but in a distorted cylinder, it couples to their amplitudes as well. This coupling may destabilize pure standing oscillations, and lead to complex time-dependent dynamics at onset. Among the new dynamical behavior that results are relaxation oscillations involving abrupt transitions between standing and quasiperiodic oscillations, and exhibiting ‘canards’.