The critical layer in pipe flow at high Reynolds number
The critical layer in pipe flow at high Reynolds number
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高雷诺数管流的临界层
DOI：
10.1098/rsta.2008.0225
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Divakar Viswanath
中科院分区：
文献类型：
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作者：
Divakar Viswanath
本文报道了Re= 75000以下管道流动的行波解族的计算。在所有的低分支解决方案中，条纹和滚动在这些解决方案中具有突出的特点。对于大Re，这些解决方案在壁外形成一个关键层。虽然解是线性不稳定的，但当Re→∞时，两个不稳定特征值以Re - 0.41和Re - 0.87给出的速率趋近于0；令人惊讶的是，随着流体的粘性降低，溶液变得更加稳定。临界层的形成及Re→∞极限的其他方面对剪切流的下分支解具有普适性。给出了用于计算这些解及其谱的GMRES-hookstep和Arnoldi迭代的实现细节，同时指出了我们方法的新方面。
We report the computation of a family of travelling wave solutions of pipe flow up to Re=75 000. As in all lower branch solutions, streaks and rolls feature prominently in these solutions. For large Re, these solutions develop a critical layer away from the wall. Although the solutions are linearly unstable, the two unstable eigenvalues approach 0 as Re→∞ at rates given by Re−0.41 and Re−0.87; surprisingly, the solutions become more stable as the flow becomes less viscous. The formation of the critical layer and other aspects of the Re→∞ limit could be universal to lower branch solutions of shear flows. We give implementation details of the GMRES-hookstep and Arnoldi iterations used for computing these solutions and their spectra, while pointing out the new aspects of our method.