Nonlinear instability of Hele-Shaw flows with smooth viscous profiles
Nonlinear instability of Hele-Shaw flows with smooth viscous profiles
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DOI：
10.1016/j.jde.2008.07.012
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发表时间：
2008-10
影响因子：
2.4
通讯作者：
P. Daripa;H. Hwang
中科院分区：
文献类型：
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作者：
P. Daripa;H. Hwang
我们严格推导出Hele-Shaw流动的非线性不稳定性的存在下，光滑的粘度分布，上游的粘度低于下游的粘度以恒定的速度移动。这是一个没有任何物质界面的单层问题。基本流的不稳定性是由粘度梯度驱动的，这与传统的界面Saffman-Taylor不稳定性相反，在传统的界面Saffman-Taylor不稳定性中，不稳定性是由跨界面的粘度跃变驱动的。本文采用现有的分析技术来建立非线性失稳。
We rigorously derive nonlinear instability of Hele-Shaw flows moving with a constant velocity in the presence of smooth viscosity profiles where the viscosity upstream is lower than the viscosity downstream. This is a single-layer problem without any material interface. The instability of the basic flow is driven by a viscosity gradient as opposed to conventional interfacial Saffman–Taylor instability where the instability is driven by a viscosity jump across the interface. Existing analytical techniques are used in this paper to establish nonlinear instability.