On the spectral instability of parallel shear flows
On the spectral instability of parallel shear flows
复制标题
平行剪切流的谱不稳定性
DOI：
10.5802/slsedp.82
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Toan T. Nguyen
中科院分区：
文献类型：
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作者：
E. Grenier;Yan Guo;Toan T. Nguyen
这篇短文是为了宣布我们最近的结果[2，3]，它为海森堡（1924），C.C. Lin和Tollmien（1940年代），以及其他著名的物理学家。准确地说，我们构造了关于有界通道（通道流）或半空间（边界层）中一般定常剪切流的线性化Navier-Stokes方程的增长模，其中雷诺数R → ∞足够大。这种不稳定性与Tollmien-Schlichting波的出现有关，Tollmien-Schlichting波描述了从层流到湍流过渡的早期阶段。
This short note is to announce our recent results [2, 3] which provide a complete mathematical proof of the viscous destabilization phenomenon, pointed out by Heisenberg (1924), C.C. Lin and Tollmien (1940s), among other prominent physicists. Precisely, we construct growing modes of the linearized Navier-Stokes equations about general stationary shear flows in a bounded channel (channel flows) or on a half-space (boundary layers), for sufficiently large Reynolds number R → ∞. Such an instability is linked to the emergence of Tollmien-Schlichting waves in describing the early stage of the transition from laminar to turbulent flows.