【窦华书】NS方程的奇异导致湍流

周华

转发窦华书师兄的一篇关于湍流转捩的文章，供各位老师、同学参考！

Singularity of Navier-Stokes Equations Leading to Turbulence


Abstract. Singularity of Navier-Stokes equations is uncovered for the first time which explains the mechanism of transition of a smooth laminar flow to turbulence. It is found that when an inflection point is formed on the velocity profile in pressure driven flows, velocity discontinuity occurs at this point. Meanwhile, pressure pulse is produced at the discontinuity due to conservation of the total mechanical energy. This discontinuity makes the Navier-Stokes equations be singular and causes the flow to become indefinite. The analytical results show that the singularity of the Navier-Stokes equations is the cause of turbulent transition and the inherent mechanism of sustenance of fully developed turbulence. Since the velocity is not differentiable at the singularity, there exist no smooth and physically reasonable solutions of Navier-Stokes equations at high Reynolds number (beyond laminar flow). The negative spike of velocity and the pulse of pressure due to discontinuity have obtained agreement with experiments and simulations in literature qualitatively.


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2021-1-9 13:33 上传

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窦华书

关于Navier-Stokes 方程的奇异性（Singularity of Navier-Stokes equations）。在下面的这篇文章里，作者采用了另一种方法，泊松方程分析方法，证明了主贴文章里的同一个问题，得到了同样的结论，即对平面Poiseuille flow, 在扰动的作用下，速度剖面会发生畸变，当速度剖面出现拐点或者Kink时，此点就成为了Navier-Stokes方程的奇点。由于奇点的存在，导致Navier-Stokes方程在奇点位置的导数不存在，所以在转捩流动和湍流中，Navier-Stokes方程不存在连续的光滑解。

Dou, H.-S., No existence and smoothness of solution of the Navier-Stokes equation, Entropy, 2022, 24, 339.   https://doi.org/10.3390/e24030339

这篇文章是开源期刊，可以免费下载。在发表时，作者选择了 Reviewers' Reports 和 Authors' responses 全部公开，共有4位审稿专家，经过了2轮评审。读者可以自行查阅，这样读者可以做出自己的判断。