论文标题
滑水管的线性稳定性
Linear stability of slip pipe flow
论文作者
论文摘要
我们通过将流向和方位角滑移作为极限情况来研究，研究了壁上具有各向异性滑移长度的管道流动的线性稳定性。我们的数值分析表明，流式滑移使流量较低，但不会导致不稳定。当雷诺数足够大时，最低稳定模式的指数衰减率似乎是$ \ propto re^{ - 1} $。如果滑动长度足够大，方位角滑动可能会导致线性不稳定性。给定较大的滑动长度可以将临界雷诺数减少到几百个。除了数值计算外，我们还提供了数学证明，证明了流动到任意雷诺数和滑移长度的三维但不依赖于流的独立干扰的线性稳定性，作为通常的能量分析的替代方法。同时，我们向特征值和特征向量得出了分析溶液，并解释了光谱的结构以及领先特征值对滑动长度的依赖性。流向独立模式的指数衰减率的缩放表明是严格的$ \ propto re^{ - 1} $。我们的非模式分析表明，总体流动滑移会降低非模式的生长，而方位角滑移具有相反的效果。然而，这两个滑动案例仍然给出了最大非模式增长的$ re^2 $尺度，并且最大的干扰仍然是流向卷，其质量上与无扫描案例相同。
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.
