受均匀斜磁场影响的粘性液体层和亚音速气体层之间表面波的非线性不稳定性

A. Assaf, Noha M. Hafez
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引用次数: 0

摘要

讨论了粘性液体层和不粘性气体层之间表面波的非线性不稳定性。这两种流体都具有磁性,并受到均匀的斜磁场作用。气体是亚音速的,粘性是通过粘性势近似引入的。通过多尺度技术推导了边缘态附近和边缘态上的演化方程。通过调制思想获得了波的稳定性标准。分散方程的许多特殊情况以及可解性条件与文献中的类似情况完全吻合。对各种数值应用进行了研究,以揭示参数对系统稳定性的影响。线性结果显示了磁场、倾角总和和渗透率的双重影响,而液体中的波长、气体运动和倾角则倾向于破坏流动的稳定性。非线性应用显示了气体厚度的双重作用,而它具有线性稳定作用。此外,非线性还显示了粘度和液体厚度的双重作用,而根据线性理论,这两者没有任何影响。与线性理论相比,使用非线性理论研究稳定性似乎更能准确地描述(不)稳定的影响因素。目前的工作可能有助于更准确地理解稳定性过程,并通过设计合适的装置来控制模型参数,从而获得所需的稳定性条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Nonlinear instability of surface waves between viscous–liquid and subsonic‐gas layers subject to uniform oblique magnetic field
Nonlinear instability of surface waves between viscous–liquid and inviscid‐gas layers is discussed. The two fluids are magnetic and subjected to uniform oblique magnetic field. The gas is subsonic and the viscosity is introduced by viscous potential approximation. The evolution equations near and on the marginal state are derived by means of multiple scales technique. The stability criteria of the waves are obtained by the modulation idea. Many special cases of dispersion equation as well as solvability conditions correspond well the similar ones in the literature. Various numerical applications have been investigated to reveal the parameters effects on the system stability. Linear results show dual influences for magnetic field, sum of inclination angles and permeability ratio whereas the wavelength, gas motion, and inclination angle in the liquid tend to destabilize the flow. Nonlinear applications reveal dual role for the gas thickness, while it has a linear stable‐role. Moreover, nonlinearity shows dual roles for viscosity and liquid thickness, which have no influences according to linear theory. The investigation of stability using nonlinear theory seems more accurate to describe the (un)stable influences comparing with the linear one. The current work may be useful to give more accurate comprehension of stability process as well as to obtain the required conditions of stability by designing suitable devices, which control the model parameters.
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