Three-dimensional linear instability in pressure-driven two-layer channel flow of a Newtonian and a Herschel–Bulkley fluid
Three-dimensional linear instability in pressure-driven two-layer channel flow of a Newtonian and a Herschel–Bulkley fluid
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牛顿流体和赫歇尔-巴尔克利流体压力驱动两层通道流的三维线性不稳定性
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发表时间：
2010
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影响因子：
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通讯作者：
O. Matar
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文献类型：
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作者：
K. Sahu;O. Matar
考虑了压力驱动的两层通道流的三维线性稳定性特性，其中牛顿流体层覆盖赫歇尔-巴尔克利流体层。我们重点关注两层牛顿问题的 Squire 定理不存在的参数范围。使用有效的光谱配置方法导出并求解每层中修正的奥尔-索末菲和斯奎尔方程。我们的结果表明，当粘度比的平方根大于两层厚度比的情况下，存在三维不稳定性；当密度分层不稳定时，也会出现这些“界面”模式的不稳定性。研究二流体非牛顿流的瞬态增长和非线性稳定性的研究人员可能对这些结果特别感兴趣。我们还表明，在足够大的雷诺数下出现的“剪切”模式对于二维扰动是最不稳定的。
The three-dimensional linear stability characteristics of pressure-driven two-layer channel flow are considered, wherein a Newtonian fluid layer overlies a layer of a Herschel–Bulkley fluid. We focus on the parameter ranges for which Squire’s theorem for the two-layer Newtonian problem does not exist. The modified Orr–Sommerfeld and Squire equations in each layer are derived and solved using an efficient spectral collocation method. Our results demonstrate the presence of three-dimensional instabilities for situations where the square root of the viscosity ratio is larger than the thickness ratio of the two layers; these “interfacial” mode instabilities are also present when density stratification is destabilizing. These results may be of particular interest to researchers studying the transient growth and nonlinear stability of two-fluid non-Newtonian flows. We also show that the “shear” modes, which are present at sufficiently large Reynolds numbers, are most unstable to two-dimensional disturbances.