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A system of two-dimensional, two coupled Faraday interfacial waves isexperimentally observed at the two interfaces of the three layers of fluids(air, pure ethanol and silicon oil) in a sealed Hele-Shaw cell with periodicvertical vibration. The upper and lower Faraday waves coexist: the uppervibrates vertically, but the crests of the lower one oscillate horizontallywith unchanged wave height and a frequency equal to the half of the forcing oneof the vertically vibrating basin, while the troughs of the lower one alwaysstay in the same place (relative to the basin). Besides, they are stronglycoupled: the wave height of the lower Faraday wave is either a linear function(in the case of a fixed forcing frequency) or a parabolic function (in the caseof a fixed acceleration amplitude) of that of the upper, with the same wavelength. In addition, the upper Faraday wave temporarily loses its smoothness ataround $t=T/4$ and $t=3T/4$, where $T$ denotes the wave period, and thus hasfundamental difference from the traditional one. To the best of our knowledge,this system of the two coupled Faraday waves has never been reported.

Observation of two coupled Faraday waves in a vertically vibrating Hele-Shaw cell with one of them oscillating horizontally