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arXiv 2004.11524physics.flu-dyn
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滑管流的线性稳定性

Linear stability of slip pipe flow

Kaiwen Chen, Baofang Song

摘要:

分别考虑流向滑移和方位滑移作为极限情况,研究了壁面滑移长度各向异性管流的线性稳定性。我们的数值分析表明,流向滑移使流动不稳定,但不会导致不稳定。当雷诺数足够大时,最不稳定模态的指数衰减率为$\propto Re^{-1}$。如果滑移长度足够大,则方位滑移可引起线性不稳定性。临界雷诺数可以减少到几百给定的大滑移长度。除了数值计算,我们提出了一个数学证明的线性稳定性的流动三维但流向独立的干扰任意雷诺数和滑移长度,作为一种替代通常的能量分析。同时给出了特征值和特征向量的解析解,并解释了谱的结构和首特征值与滑移长度的关系。流向独立模式的指数衰减率的标度被证明是严格的$\propto Re^{-1}$。我们的非模态分析表明,整体流向滑移减少非模态增长和方位角滑移有相反的效果。尽管如此,两种滑移情况仍然给出了最大非模态增长的$Re^2$ -标度,并且最大放大的扰动仍然是流向滚转,这在性质上与无滑移情况相同。

英文摘要:

We investigated the linear stability of pipe flow with anisotropic slip length at the wall by considering streamwise and azimuthal slip separately as the limiting cases. Our numerical analysis shows that streamwise slip renders the flow less stable but does not cause instability. The exponential decay rate of the least stable mode appears to be $\propto Re^{-1}$ when the Reynolds number is sufficiently large. Azimuthal slip can cause linear instability if the slip length is sufficiently large. The critical Reynolds number can be reduced to a few hundred given large slip lengths. Besides numerical calculations, we present a mathematical proof of the linear stability of the flow to three-dimensional yet streamwise-independent disturbances for arbitrary Reynolds number and slip length, as an alternative to the usual energy analysis. Meanwhile we derived analytical solutions to the eigenvalue and eigenvector, and explained the structure of the spectrum and the dependence of the leading eigenvalue on the slip length. The scaling of the exponential decay rate of streamwise independent modes is shown to be rigorously $\propto Re^{-1}$. Our non-modal analysis shows that overall streamwise slip reduces the non-modal growth and azimuthal slip has the opposite effect. Nevertheless, both slip cases still give the $Re^2$-scaling of the maximum non-modal growth and the most amplified disturbances are still streamwise rolls, which are qualitatively the same as in the no-slip case.

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