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首页> 外文期刊>Physics of fluids >Rayleigh-Taylor instability at spherical interfaces between viscous fluids: Fluid/vacuum interface
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Rayleigh-Taylor instability at spherical interfaces between viscous fluids: Fluid/vacuum interface

机译：粘性流体之间的球形界面处的瑞利-泰勒不稳定性：流体/真空界面

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For a spherical interface of radius R separating two different homogeneous regions of incompressible viscous fluids under the action of a radially directed acceleration, we perform a linear stability analysis in terms of spherical surface harmonics Y-n to derive the dispersion relation. The instability behavior is investigated by computing the growth rates and the most-unstable modes as a function of the spherical harmonic degree n. This general methodology is applicable to the entire parameter space spanned by the Atwood number, the viscosity ratio, and the dimensionless number B = (a(R)rho(2)(2)/mu(2)(2))(1/3) R (where a(R), rho(2), and mu(2) are the local radial acceleration at the interface, and the density and viscosity of the denser overlying fluid, respectively). While the mathematical formulation herein is general, this paper focuses on instability that arises at a spherical viscous fluid/vacuum interface as there is a great deal to be learned from the effects of one-fluid viscosity and sphericity alone. To quantify and understand the effect that curvature and radial acceleration have on the Rayleigh-Taylor instability, a comparison of the growth rates, under homologous driving conditions, between the planar and spherical interfaces is performed. The derived dispersion relation for the planar interface accounts for an underlying finite fluid region of thickness L and normal acceleration a(R). Under certain conditions, the development of the most-unstable modes at a spherical interface can take place via the superposition of two adjacent spherical harmonics Y-n and Yn+ 1. This bimodality in the evolution of disturbances in the linear regime does not have a counterpart in the planar configuration where the most-unstable modes are associated with a unique wave number. (C) 2015 AIP Publishing LLC.
机译：对于半径为R的球面界面，在径向加速度的作用下将不可压缩粘性流体的两个不同均匀区域分开，我们根据球面谐波Y-n进行线性稳定性分析，以得出色散关系。通过计算增长率和最不稳定的模式作为球谐度n的函数，研究了不稳定性行为。这种通用方法适用于由Atwood数，粘度比和无因次数所覆盖的整个参数空间B =（a（R）rho（2）（2）/ mu（2）（2））（1 / 3）R（其中a（R），rho（2）和mu（2）分别是界面处的局部径向加速度，以及较密的上覆流体的密度和粘度）。尽管此处的数学公式是通用的，但本文只关注在球形粘性流体/真空界面处出现的不稳定性，因为仅从单流体粘度和球形度的影响中可以学到很多东西。为了量化和理解曲率和径向加速度对瑞利-泰勒不稳定性的影响，在相同的驱动条件下，对平面和球形界面之间的增长率进行了比较。导出的平面界面色散关系说明了厚度为L和法向加速度为a（R）的基础有限流体区域。在某些条件下，通过两个相邻的球谐函数Yn和Yn + 1的叠加，可以在球面界面上产生最不稳定的模。平面配置，其中最不稳定的模式与唯一的波数相关联。 （C）2015 AIP Publishing LLC。

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