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首页> 外文期刊>International journal of non-linear mechanics >New analytical approximation forms for non-linear instability of electric porous media
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New analytical approximation forms for non-linear instability of electric porous media

机译：电多孔介质非线性不稳定性的新解析近似形式

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摘要

We study the Kelvin-Helmholtz instability for parallel flow between two dielectric fluids in porous media. A normal electric field stresses the system. A non-linear perturbation technique is introduced. This technique is based on the Fourier transform and the multiple scales method. We discussed the stability conditions for non-Darcian and Darcian flows. A linear analytical dispersion relation and several coupled non-linear equations contain non-linear correction terms in uniform analytical descriptions derived. For non-Darcian, a complex non-linear Ginzburg-Landau equation is used to analyse the stability of the problem obtained. We introduce a simple analytical technique for calculating the non-linear cutoff wavenumber, and a new analytical solution form is derived. The newly derived analytical solution is compared with several previously obtained approximation solutions. The analytical solution is more realistic than the previously proposed descriptions, which were widely used in the past. For some special physical parameters, a non-linear modified diffusion equation for low Reynolds number is obtained. Also, for high Reynolds number we obtain a new analytical non-linear dispersion relation (complex non-linear modified Ginzburg-Landau equation) in terms of the linear analytical dispersion relation. Numerical results and stability diagrams support the analytical proofs. Regions of stability and instability are identified. The non-linear numerical results showed that the linear model is inadequate.
机译：我们研究了多孔介质中两种介电流体之间平行流动的开尔文-亥姆霍兹不稳定性。正常电场会使系统承受压力。介绍了一种非线性摄动技术。该技术基于傅立叶变换和多尺度方法。我们讨论了非Darcian和Darcian流的稳定性条件。线性分析的色散关系和几个耦合的非线性方程式在统一的分析描述中包含非线性校正项。对于非达西人，使用复杂的非线性Ginzburg-Landau方程来分析所获得问题的稳定性。我们介绍了一种用于计算非线性截止波数的简单分析技术，并推导了一种新的解析解形式。将新获得的解析解与几个先前获得的近似解进行比较。该分析解决方案比以前广泛使用的先前提出的描述更现实。对于某些特殊的物理参数，获得了一个低雷诺数的非线性修正扩散方程。同样，对于高雷诺数，我们根据线性解析色散关系获得了新的解析非线性色散关系（复杂的非线性修正的Ginzburg-Landau方程）。数值结果和稳定性图支持分析证明。确定了稳定和不稳定的区域。非线性数值结果表明线性模型是不充分的。

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