Internal Subharmonic Resonance in Faraday Experiment

摘要

The classical Faraday experiment is a tractable problem in nonlinear physics, and its rich spectrum of nonlinear rnphenomena has made it a prototype in studying nonlinear wave dynamics in general. Here we report the obrnservation of a new type of subharmonic resonances which occurs at some smaller fractional frequencies, such as ν/3, ν/4, and ν/6, where ν is the forcing frequency. As a result of these resonances, the lower-order surface-wave rnmodes whose eigenfrequencies are close to the fractional frequencies participate into the wave motions. Our theory involving quadratically nonlinear mode couplings shows that an already excited mode itself can act as a parametric source on the lower-order primary modes, thus leading to the cascading subharmonic resonances.