Simulations of the Faraday instability in a rectangular-shaped vessel with well, filled with a viscous fluid, are presented. Oscillations promoted by applying a vertical vibration of a given frequency and amplitude show the following features: (i) unstable waves become increasingly localized in the well as the amplitude of vibration increases, (ii) the threshold amplitude for an arbitrary well width is bounded by the thresholds of a vessel with no well and liquid layers thicknesses equal to those in either the plateau or in the well region, and (iii) below threshold, a weak horizontal component triggers harmonic oscillations. Experiments carried out in a vessel filled with ethanol allowed to observe wave localization and, below threshold, the harmonic wave. Below threshold, the harmonic wave had been previously observed as the only possible wave in a square vessel with an immersed concentric square well. Novel theoretical tools are developed to investigate this system: A generalized Mathieu equation is used to handle the case without well, whereas a numerical transfer matrix method is applied to the case with well.

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