Odd-viscosity-induced instability of a thin film with variable density
Odd-viscosity-induced instability of a thin film with variable density
复制标题
变密度薄膜的奇数粘度引起的不稳定性
DOI：
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
S. Chattopadhyay
中科院分区：
文献类型：
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作者：
S. Chattopadhyay
讨论了沿均匀加热斜面排出时反对称性破裂的二维重力驱动的粘性牛顿流体的稳定性。具有奇粘性系数的柯西应力张量奇数部分的存在给流体流动带来了新的特征。建立了表面张力随温度变化的理论模型，该模型还考虑了不同热差下液体密度的变化。从解析和数值两方面研究了奇异粘度、变密度和表面张力的耦合效应。采用系统渐近展开的方法，导出了自由面的非线性演化方程。进行了线性稳定性分析，给出了长波扰动下发生失稳的临界条件。新的有趣的结果说明了临界雷诺数如何依赖于奇粘性以及其他各种无量纲参数。此外，基于多尺度方法进行了弱非线性稳定性分析，得到了一个复杂的Ginzburg-Landau方程。观察到，该膜不仅有超临界稳定区和亚临界不稳定区，而且还有无条件稳定区和爆炸区。结果还表明，边带扰动对应的空间均匀解在不稳定区域可能是稳定的。采用周期域中的Crank-Nicolson方法，数值分析了模型在不同奇粘性和其它流动参数下的时空演化。非线性仿真结果与线性和弱非线性稳定性分析结果吻合较好。研究结果有助于相关实验的进一步开展。
The stability of a two-dimensional gravity-driven thin viscous Newtonian fluid with broken time-reversal-symmetry draining down a uniformly heated inclined plane is discussed. The presence of the odd part of the Cauchy stress tensor with an odd viscosity coefficient brings new characteristics in fluid flow. A theoretical model is implemented, which captures the dependence of the surface tension on temperature, and the model also allows for variation in the density of the liquid with a thermal difference. The coupled effect of odd viscosity, variable density, and surface tension has been investigated both analytically and numerically. A nonlinear evolution equation of the free surface is derived by the method of systematic asymptotic expansion. A linear stability analysis is carried out, which yields the critical conditions for the onset of instability in long-wave perturbations. New interesting results illustrating how the critical Reynolds number depends on the odd viscosity as well as other various dimensionless parameters have been obtained. In addition, a weakly nonlinear stability analysis is performed based on the method of multiple scales from which a complex Ginzburg–Landau equation is obtained. It is observed that the film not only has supercritical stable and subcritical unstable zones, but also unconditional stable and explosive zones. It has been also shown that the spatial uniform solution corresponding to the sideband disturbance may be stable in the unstable region. Employing the Crank–Nicolson method in a periodic domain, the spatiotemporal evolution of the model has been analyzed numerically for different values of the odd viscosity as well as other flow parameters. Nonlinear simulations are found to be in good agreement with the linear and weakly nonlinear stability analysis. The results are conducive to the further development of related experiments.
具有奇粘度的非线性浅水动力学
影响因子：
2.7
作者：
Monteiro, Gustavo M.;Ganeshan, Sriram
通讯作者：
Ganeshan, Sriram