Localized Faraday patterns under heterogeneous parametric excitation

Héctor Urra, Juan F. Marín, Milena Páez-Silva, Majid Taki, Saliya Coulibaly, Leonardo Gordillo, Mónica A. García-Ñustes

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10 Scopus citations


Faraday waves are a classic example of a system in which an extended pattern emerges under spatially uniform forcing. Motivated by systems in which uniform excitation is not plausible, we study both experimentally and theoretically the effect of heterogeneous forcing on Faraday waves. Our experiments show that vibrations restricted to finite regions lead to the formation of localized subharmonic wave patterns and change the onset of the instability. The prototype model used for the theoretical calculations is the parametrically driven and damped nonlinear Schrödinger equation, which is known to describe well Faraday-instability regimes. For an energy injection with a Gaussian spatial profile, we show that the evolution of the envelope of the wave pattern can be reduced to a Weber-equation eigenvalue problem. Our theoretical results provide very good predictions of our experimental observations provided that the decay length scale of the Gaussian profile is much larger than the pattern wavelength.

Original languageEnglish
Article number033115
JournalPhysical Review E
Issue number3
StatePublished - 27 Mar 2019


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