The Eckhaus and Benjamin-Feir resonance mechanisms
The Eckhaus and Benjamin-Feir resonance mechanisms
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Eckhaus 和 Benjamin-Feir 共振机制
DOI：
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发表时间：
1978
期刊：
影响因子：
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通讯作者：
R. DiPrima
中科院分区：
文献类型：
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作者：
J. T. Stuart;R. DiPrima
本文对一维周期性二维流动的稳定性或不稳定性的Eckhaus机制和二维Stokes水波的Benjamin-Feir不稳定性机制作了统一的处理。振幅方程的方法被使用，以下的纽韦尔在相关的上下文中的铅。这种方法可以很容易地分析所谓的边带扰动，这是Eckhaus和Benjamin-Feir共振机制的一个重要特征。特别是，它表明，Eckhaus的结果，即周期性流是稳定的，只有在一个特定的频带内的波数窄于线性化理论的中性曲线的跨度，是唯一有效的特征值和其他参数是真实的。对于复特征值和复系数的一般情况，给出了结果的修正和推广形式。然而，值得注意的是，埃克豪斯的结果是有效的泰勒涡和贝纳德细胞的重要例子。
A unified treatment is given of the Eckhaus mechanism of stability or instability of two-dimensional flows, which are periodic in one spatial dimension, and the Benjamin—Feir instability mechanism of the two-dimensional Stokes water wave. The method of the amplitude equation is used, following the lead of Newell in a related context. This method easily allows the analysis of the so-called side-band perturbations, which are a crucial feature of the Eckhaus and Benjamin—Feir resonance mechanisms. In particular, it is shown that Eckhaus’s result, that a periodic flow is stable only within a particular band of wavenumbers narrower than the span of the neutral curve of linearized theory, is only valid when the eigenvalues and other parameters are real. A corrected and extended form of the result is given for the general case of complex eigenvalues and coefficients. It is noted, however, that Eckhaus’s result is valid for the important examples of Taylor vortices and Bénard cells.