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A phenomenological model of parametric surface waves (Faraday waves) isintroduced in the limit of small viscous dissipation that accounts for thecoupling between surface motion and slowly varying streaming and large scaleflows (mean flow). The primary bifurcation of the model is to a set of standingwaves (stripes, given the functional form of the model nonlinearities chosenhere). Our results for the secondary instabilities of the primary wave showthat the mean flow leads to a weak destabilization of the base state againstEckhaus and Transverse Amplitude Modulation instabilities, and introduces a newlongitudinal oscillatory instability which is absent without the coupling. Wecompare our results with recent one dimensional amplitude equations for thissystem systematically derived from the governing hydrodynamic equations.

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