Resonant triad dynamics in weakly damped Faraday waves with two-frequency forcing

PHYSICA D-NONLINEAR PHENOMENA

卷:190

Article

Porter, J ; Silber, M

关键词: resonant triads;    Faraday waves;    pattern formation;    symmetry-breaking;   

DOI  :  10.1016/j.physd.2003.09.044

来源: Elsevier

【 摘 要 】

Many of the interesting patterns seen in recent multi-frequency Faraday experiments can be understood on the basis of three-wave interactions (resonant triads). In this paper we consider two-frequency forcing and focus on a resonant triad occurring near the bicritical point where two pattern-forming modes with distinct wavenumbers onset simultaneously. This triad has been observed directly (in the form of rhomboids) and has also been implicated in the formation of quasipatterns and superlattices. We show how the symmetries of the undamped unforced problem (time translation, time reversal, and Hamiltonian structure) can be used, when the damping is weak, to obtain general scaling laws and additional qualitative properties of the normal form coefficients governing the pattern selection process near onset; such features help to explain why this particular triad is seen only for certain low forcing ratios, and predict the existence of drifting solutions and heteroclinic cycles. We confirm the anticipated parameter dependence of the coefficients and investigate its dynamical consequences using coefficients derived numerically from a quasipotential formulation of the Faraday problem due to Zhang and Vinals. (C) 2003 Elsevier B.V. All rights reserved.

【 授权许可】

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