  A phenomenological model of parametric surface waves (Faraday waves) is
introduced in the limit of small viscous dissipation that accounts for the
coupling between surface motion and slowly varying streaming and large scale
flows (mean flow). The primary bifurcation of the model is to a set of standing
waves (stripes, given the functional form of the model nonlinearities chosen
here). Our results for the secondary instabilities of the primary wave show
that the mean flow leads to a weak destabilization of the base state against
Eckhaus and Transverse Amplitude Modulation instabilities, and introduces a new
longitudinal oscillatory instability which is absent without the coupling. We
compare our results with recent one dimensional amplitude equations for this
system systematically derived from the governing hydrodynamic equations.
