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, and hexagonal 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. (c) 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0155502