Tetragonal modulation cells at the parametric excitation of the weakly damped capillary waves

The parametric excitation of two mutually orthogonal pairs of the quasi-monochromatic (modulated) capillary waves on the surface of a vertically vibrating liquid layer (the Faraday waves) is studied. The quasi-steady wave patterns with tetragonal cells of modulation containing the indications of disorder, which agree well with former experimental observations for weakly damped waves, are revealed using numerical solution of the coupled wave equations. The problem of maintenance of the narrow-bend spectra of the excited waves over a broad instability range is also considered. In this connection, the condition of the “external instability” first introduced by Zakharov et al. (1970) [1] and L’vov (1971) [2] is analyzed for a steady state with four spatially uniform waves and validity of the obtained solution is confirmed numerically for averaged specific intensity of the modulated waves.