Physical Sciences and Mathematics Commons^™

Resonances And Superlattice Pattern Stabilization In Two-Frequency Forced Faraday Wave, Chad M. Topaz, Mary Silber

Chad M. Topaz

We investigate the role weakly damped modes play in the selection of Faraday wave patterns forced with rationally related frequency components $m\omega$ and $n\omega$. We use symmetry considerations to argue for the special importance of the weakly damped modes oscillating with twice the frequency of the critical mode, and those oscillating primarily with the “difference frequency” $|n−m| \omega$ and the “sum frequency” $(n+m) \omega$. We then perform a weakly nonlinear analysis using equations of Zhang and Viñals [J. Fluid Mech. 336 (1997) 301] which apply to small-amplitude waves on weakly inviscid, deep fluid layers. For weak damping and forcing and …