Phenomenological model of weakly damped Faraday waves and the associated mean flow

A phenomenological order parameter model of parametric surface waves in the limit of weak viscous dissipation to mean flows was coupled. The importance of mean flows in the Faraday wave system for small viscous damping was illustrated by determining the stability boundaries of the base pattern of standing waves against long-wavelength perturbations. Mean flows are induced by perturbation of the stripes and their coupling to the order parameter equation affects the stability of stripe solutions. The eigenvectors corresponding to the oscillatory instability show that the associated mean flow consists of large-scale rolls with their axis oriented parallel to the surface.