Analytical model for viscous and elastic Rayleigh–Taylor instabilities in convergent geometries at static interfaces
Analytical model for viscous and elastic Rayleigh–Taylor instabilities in convergent geometries at static interfaces
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DOI：
10.1063/5.0096383
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发表时间：
2022-07
期刊：
影响因子：
1.6
通讯作者：
J. Gou;R. Zeng;C. Wang;Y. B. Sun
中科院分区：
文献类型：
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作者：
J. Gou;R. Zeng;C. Wang;Y. B. Sun
收敛几何中的粘性和弹性Rayleigh-Taylor不稳定性，特别是它们的低阶模不对称性，与平面不稳定性有着明显的区别，引起了人们的极大关注。然而，大多数分析集中在静态界面处的不稳定性，排除了Bell-Plesset效应和弹塑性转变的研究，因为它们涉及太复杂的数学。在此，我们利用粘性势流和弹性势流方法对色散关系进行了详细的分析，得到了它们的近似增长率，并与精确增长率进行了比较，结果表明：（1）基于势流方法的近似增长率与精确增长率基本吻合。(ii)提出了一种替代表达式来克服流体/流体界面处低模不对称性的差异。(iii)在固体中必须格外小心，因为最大差异出现在n = 1模式和接近截止的模式。这种非常简单的分析方法是必不可少的，以描述动态界面，包括整体运动的界面的基础上的静态结构，而精确的分析涉及太复杂的数学扩展，包括Bell-Plesset效应和弹塑性性能。总之，近似解析色散关系在收敛的几何形状，有可能处理动态界面的Bell-Plesset效应与弹塑性转变相结合。
Great attention has been attracted to study the viscous and elastic Rayleigh–Taylor instability in convergent geometries, especially for their low mode asymmetries that behave distinctively from the planar counterparts. However, most analyses have focused on the instability at static interfaces that excludes the studies of the Bell–Plesset effects and the elastic–plastic transition since they involve too complex mathematics. Herein, we perform detailed analyses on the dispersion relations by applying the viscous and elastic potential flow method to obtain their approximate growth rates compared with the exact ones to demonstrate: (i) The approximate growth rates based on potential flow method generally coincide with the exact ones. (ii) An alternative expression is proposed to overcome the discrepancy for the low mode asymmetries at fluid/fluid interface. (iii) Extra care must be taken in solids since the maximum discrepancies occur at the n = 1 mode and at the mode proximate to the cutoff. This analytical method of great simplicity is essential to describe the dynamic interface by including the overall motion of the interface based on the static construction, while the exact analysis involves too complex mathematics to be extended by including the Bell–Plesset effects and the elastic–plastic properties. To sum up, the approximate analytical dispersion relations derived in convergent geometries, have the potential for dealing with dynamic interfaces where Bell–Plesset effects are combined with elastic–plastic transition.