Statistical analysis of observed Faraday wave patterns

We present experimental observations of Faraday wave patterns when a liquid in a square recipient is submitted to vertical vibrations with forcing frequencies and amplitudes in the intervals 10 ≤ F ≤ 80 Hz and 0.1 ≤ A ≤ 3 mm, respectively. A sweep of the forcing parameter space is performed to investigate the surface patterns that form for two different sizes of the recipient. The waveforms are obtained by means of a Pearson correlation analysis of a sequence of liquid surface images for each experiment. The Pearson correlation coefficients are then fast Fourier transformed to obtain the power spectra. For 10 ≤ F ≤ 15 Hz, tessellation patterns consisting of ordered arrays of rhomboid-shaped tiles are observed; whereas, for 20 ≤ F ≤ 25, the tessellation patterns become irregular over the entire surface where square, rhomboidal, andhexagonal tilings coexist. At 30 ≤ F ≤ 45 Hz, the patterns correspond to a mixed state where ordered and irregular quadrilateral tessellation patterns coexist. At frequencies between 50 and 80 Hz, the tessellated patterns that form consist of irregularly distributed square-shaped tiles. In all cases, the excited waves are periodic with a dominant subharmonic frequency f = F/2. However, for given forcing parameters, the waveforms and their amplitudes differ markedly when the size of the recipient is changed.