Moderate and steep Faraday waves: instabilities, modulation and temporal asymmetries
Moderate and steep Faraday waves: instabilities, modulation and temporal asymmetries
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DOI：
10.1017/s0022112096008920
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发表时间：
1996-12
影响因子：
3.7
通讯作者：
Lei Jiang;C. Ting;M. Perlin;W. Schultz
中科院分区：
文献类型：
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作者：
Lei Jiang;C. Ting;M. Perlin;W. Schultz
在窄矩形柱体中产生了基模的轻度到陡峭的驻波，该矩形柱体经历垂直振荡，强迫频率为3.15 Hz至3.34 Hz。一个精确的，非侵入性的光学波剖面测量系统与波探头一起使用沿着，以准确地量化空间和时间的表面高程。这些驻波也模拟了二维谱柯西积分代码。实验结果表明，接触线效应提高了粘性固有频率，改变了中性稳定曲线。因此，正如预期的那样，添加润湿剂Photo Flo显著改变了响应图中的稳定性曲线和滞后。实验上，我们发现强调制的波振幅高于3.30赫兹的一些强迫频率。通过添加Photo-Flo减少接触线效应抑制了这些调制。扰动分析预测，这种调制的一部分是由通过“边带共振”的强迫信号中的噪声引起的，即，引入小的边带强迫可以产生法拉第波的大调制。我们的数值模拟和物理实验验证了分析。最后，我们观察实验一种新形式的陡峭的驻波与一个大的对称双峰波峰，而模拟相同的强迫条件下的结果比以前看到的更尖锐的波峰。这两种驻波形式出现在一个有限的波陡度远小于经典驻波的最大陡度和表面张力远小于威尔顿涟漪。在物理和数值实验中，更强的二次谐波（在时间上）和波形的时间不对称性表明由于非常规的四重相互作用而产生1：2共振。在物理实验中，波陡的增加导致了一种新的破驻波形式。
Mild to steep standing waves of the fundamental mode are generated in a narrow rectangular cylinder undergoing vertical oscillation with forcing frequencies of 3.15 Hz to 3.34 Hz. A precise, non-intrusive optical wave profile measurement system is used along with a wave probe to accurately quantify the spatial and temporal surface elevations. These standing waves are also simulated by a two-dimensional spectral Cauchy integral code. Experiments show that contact-line effects increase the viscous natural frequency and alter the neutral stability curves. Hence, as expected, the addition of the wetting agent Photo Flo significantly changes the stability curve and the hysteresis in the response diagram. Experimentally, we find strong modulations in the wave amplitude for some forcing frequencies higher than 3.30 Hz. Reducing contact-line effects by Photo-Flo addition suppresses these modulations. Perturbation analysis predicts that some of this modulation is caused by noise in the forcing signal through ‘sideband resonance’, i.e. the introduction of small sideband forcing can generate large modulations of the Faraday waves. The analysis is verified by our numerical simulations and physical experiments. Finally, we observe experimentally a new form of steep standing wave with a large symmetric double-peaked crest, while simulation of the same forcing condition results in a sharper crest than seen previously. Both standing wave forms appear at a finite wave steepness far smaller than the maximum steepness for the classical standing wave and a surface tension far smaller than that for a Wilton ripple. In both physical and numerical experiments, a stronger second harmonic (in time) and temporal asymmetry in the wave forms suggest a 1:2 resonance due to a non-conventional quartet interaction. Increasing wave steepness leads to a new form of breaking standing waves in physical experiments.