Faraday waves in 2:1 internal resonance
Faraday waves in 2:1 internal resonance
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2:1 内部共振法拉第波
DOI：
10.1017/s0022112091001179
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发表时间：
1991
影响因子：
3.7
通讯作者：
J. Miles
中科院分区：
文献类型：
--
作者：
D. Henderson;J. Miles
本文报道了圆柱体中的法拉第波的实验结果。圆柱体的内共振模式可以是次谐波模式（频率等于强迫的1/4），也可以是超谐波模式（频率等于强迫的1/4）。对于亚谐共振，两种模式都实现了相当的振幅是稳定的，或调制一个或两个周期，或表现出准周期或混沌运动。这些响应的稳定性图。线性稳定性和增长率的理论预测进行了测试。给出了稳态振幅、极限环频率和破碎时波斜率的测量结果。一些测得的相平面轨迹示出具有理论上的对应物。对于超谐波共振，超谐波的振幅永远不能与法拉第波的振幅相比。对于低模的能量交换发生在增长的初始阶段，和一个岁差不稳定性，有时发展。对于频率和波数都在2：1比率的高模式，超谐波共振不可再现地发生;它似乎被可能的法拉第波模式之间的1：1相互作用所压倒。
Experiments are reported on Faraday waves in a circular cylinder, which are internally resonant with either the subharmonic mode (with frequency ¼ that of the forcing) or the superharmonic mode (with frequency equal to that of the forcing). For subharmonic resonance both modes achieved comparable amplitudes that were steady, or were modulated with one or two periods, or exhibited quasi-periodic or chaotic motions. A stability map of these responses is presented. Theoretical predictions of linear stability and growth rates are tested. Measurements of steady amplitudes, limit-cycle frequencies and wave slopes at breaking are presented. Some of the measured phase-plane trajectories are shown to have theoretical counterparts. For superharmonic resonance the amplitude of the superharmonic was never comparable with that of the Faraday wave. For low modes an energy exchange occurred during the initial period of growth, and a precession instability sometimes developed. For high modes for which both frequencies and wavenumbers are in a 2:1 ratio, superharmonic resonance occurred irreproducibly; it appeared to be overwhelmed by 1:1 interactions among the possible Faraday-wave modes.