Amplitude equation and pattern selection in Faraday waves
Amplitude equation and pattern selection in Faraday waves
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DOI：
10.1103/physreve.60.559
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发表时间：
1999-07-01
影响因子：
2.4
通讯作者：
Viñals, J
中科院分区：
文献类型：
--
作者：
Chen, PL;Viñals, J
提出了一种不局限于小粘性耗散的参数表面波（法拉第波）模式选择的非线性理论。利用阈值附近的多尺度渐近展开，导出了控制方程的驻波振幅方程。振幅方程是梯度形式，相关的Lyapunov函数的系数作为粘性阻尼参数γ的函数计算了各种对称的规则图案。对于类似于1的伽马，所选的波型包括单个驻波（条纹波）。对于远小于1的伽马，在毛细区（大频率）获得方形对称的模式。在较低的频率下（重力-毛细管混合状态），六倍（六边形），八倍，…预测模式。对于更低的频率（重力波），再次选择条纹模式。我们对各种图案的稳定区域的预测与最近在大纵横比系统中进行的实验在定量上一致。[s1063 - 651 x(99) 08607 - 9]。
A nonlinear theory of pattern selection in parametric surface waves (Faraday waves) is presented that is not restricted to small viscous dissipation. By using a multiple scale asymptotic expansion near threshold, a standing wave amplitude equation is derived from the governing equations. The amplitude equation is of gradient form, and the coefficients of the associated Lyapunov function are computed for regular patterns of various symmetries as a function of a viscous damping parameter gamma. For gamma similar to 1, the selected wave pattern comprises a single standing wave (stripe pattern). For gamma much less than 1, patterns of square symmetry are obtained in the capillary regime (large frequencies). At lower frequencies (the mixed gravity-capillary regime), a sequence of sixfold (hexagonal), eightfold, ... patterns are predicted. For even lower frequencies (gravity waves) a stripe pattern is again selected. Our predictions of the stability regions of the various patterns are in quantitative agreement with recent experiments conducted in large aspect ratio systems. [S1063-651X(99)08607-9].