Stability and bifurcations of Parametrically excited Thin Liquid films
Stability and bifurcations of Parametrically excited Thin Liquid films
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参数激发液体薄膜的稳定性和分岔
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
A. Oron
中科院分区：
文献类型：
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作者：
O. Gottlieb;A. Oron
研究了参数激振液体薄膜的稳定性和分岔问题。一个最近导出的二维时空动力学的非线性演化方程被扩展到低阶傅立叶模态。验证了四阶模态动力系统，得到了由Benney方程描述的基本落膜动力学的初级分岔结构，并准确预测了时间调制Benney方程（TMBE）的准周期结构。本文对基本稳态解和周期解的稳定性进行了解析和数值研究，揭示了非周期调制行波对应的非平稳解和混沌解的阈值。通过对演化方程的数值模拟，验证了该简化模态动力系统可以构造出一个全面的分岔结构。
We investigate the stability and bifurcations of parametrically excited thin liquid films. A recently derived nonlinear evolution equation for the two-dimensional spatio-temporal dynamics of falling liquid films on an oscillating vertical wall is expanded to low order Fourier modes. A fourth-order modal dynamical system is validated to yield the primary bifurcation structure of the fundamental falling film dynamics described by the Benney equation, and accurately predicts the quasi-periodic structure of the temporally modulated Benney equation (TMBE). The stability of fundamental steady and periodic solutions is analytically and numerically investigated so as to reveal the threshold for nonstationary and chaotic solutions corresponding to aperiodic modulated traveling waves. The reduced modal dynamical system enables construction of a comprehensive bifurcation structure, which is verified by numerical simulation of the evolution equation.