Mohamadou Alidou, Jiotsa A Kenfack, Kofané T C
Laboratoire de Mécanique, Département de Physique, Faculté des Sciences, Université de Yaoundé I, B.P. 812 Yaoundé, Cameroun.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Sep;72(3 Pt 2):036220. doi: 10.1103/PhysRevE.72.036220. Epub 2005 Sep 28.
The generation of nonlinear modulated waves is investigated in the framework of hydrodynamics using a model of coupled oscillators. In this model, the separatrices between each pair of vortices may be viewed as individual oscillators and are described by a phenomenological one-dimensional discrete complex Ginzburg-Landau equation involving first- and second-nearest neighbor couplings. A theoretical approach based on the linear stability analysis predicts regions of modulational instability, governed by both the first and second-nearest neighbor couplings. From numerical investigations of different wave patterns that may be driven by the modulational instability, it appears that analytical predictions are correctly verified. For wave number in the unstable regions, an initial condition whose amplitude is slightly modulated breaks into a train of unstable patterns. This phenomenon agrees with the description of amplification of the spectral component of the perturbation and its harmonics, as well.
在流体动力学框架内，使用耦合振子模型研究了非线性调制波的产生。在该模型中，每对涡旋之间的分界线可视为单个振子，并由一个包含一阶和二阶最近邻耦合的唯象一维离散复金兹堡 - 朗道方程描述。基于线性稳定性分析的理论方法预测了调制不稳定性区域，该区域由一阶和二阶最近邻耦合共同控制。通过对可能由调制不稳定性驱动的不同波形的数值研究，似乎解析预测得到了正确验证。对于不稳定区域中的波数，振幅略有调制的初始条件会分解为一系列不稳定模式。这种现象也与扰动频谱分量及其谐波放大的描述相符。
