Faraday wave patterns on a square cell network

Abstract

We present the experimental observations of the Faraday instability when the vibrated liquid is contained in a network of small square cells for exciting frequencies in the range $10\le F\le 24$ Hz. A sweep of the parameter space has been performed to investigate the amplitudes and frequencies of the driving force for which different patterns form over the network. Regular patterns in the form of square lattices are observed for driving frequencies in the range $10\le F<14$ Hz, while ordered matrices of oscillons are formed for $14<F\le 23$ Hz. At $F>23$ Hz, disordered periodic patterns appear within individual cells for a small range of amplitudes. In this case, the wave field is dominated by oscillating blobs that interact on the capillary–gravity scale. A Pearson correlation analysis of the recorded videos shows that for all ordered patterns, the surface waves are periodic and correspond to Faraday waves of dominant frequency equal to half the excitation frequency (i.e., $f=F/2$). In contrast, the oscillons formed for $14<F\le 23$ Hz are at the first subharmonic ($f=F/2$) and first harmonic ($f=F$) response frequencies, with higher harmonics being negligible or absent as in most cases. The disordered wave fields forming at $F>23$ Hz are not subharmonic and correspond to periodic harmonic waves with $f=nF/2$ (for $n=2,4,\ldots$). We find that the experimentally determined minimum forcing necessary to destabilize the rest state and generate surface waves is consistent with a recent stability analysis of stationary solutions as derived from a new dispersion relation for time-periodic waves with nonzero forcing and dissipation.