Year: 2021
Author: Hua-Shu Dou
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 3 : pp. 527–553
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0063
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 3 : pp. 527–553
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Navier-Stokes equations singularity discontinuity total mechanical energy turbulence.
Author Details
-
Turbulence generation in the transitional wake flow behind a sphere
Niu, Lin | Dou, Hua-Shu | Zhou, Changquan | Xu, WenqianPhysics of Fluids, Vol. 36 (2024), Iss. 3
https://doi.org/10.1063/5.0199349 [Citations: 0] -
Origin of Turbulence
Energy Gradient Theory for Parallel Flow Stability
Dou, Hua-Shu
2022
https://doi.org/10.1007/978-981-19-0087-7_4 [Citations: 0] -
Origin of Turbulence
Scaling of Disturbance for Turbulent Transition and Turbulence
Dou, Hua-Shu
2022
https://doi.org/10.1007/978-981-19-0087-7_7 [Citations: 0] -
Origin of Turbulence
Turbulent Transition Through Velocity Discontinuity
Dou, Hua-Shu
2022
https://doi.org/10.1007/978-981-19-0087-7_5 [Citations: 0] -
Dynamics of fiber optic airgun bubbles for micropropulsion
Li, Hanyang | Yang, Xulong | Zhou, Gaoqian | Sun, Jiapeng | Chen, Ying | Tang, Xianqi | Ge, YangApplied Physics Letters, Vol. 123 (2023), Iss. 24
https://doi.org/10.1063/5.0186165 [Citations: 2] -
Origin of Turbulence
Stability and Transition of Boundary Layer Flow
Dou, Hua-Shu
2022
https://doi.org/10.1007/978-981-19-0087-7_6 [Citations: 1] -
Origin of Turbulence
Fundamental of Stability of Parallel Flows
Dou, Hua-Shu
2022
https://doi.org/10.1007/978-981-19-0087-7_3 [Citations: 0] -
Origin of Turbulence
Stability of Taylor-Couette Flow Between Concentric Rotating Cylinders
Dou, Hua-Shu
2022
https://doi.org/10.1007/978-981-19-0087-7_9 [Citations: 3] -
Origin of Turbulence
Methods for Prediction of Turbulent Transition
Dou, Hua-Shu
2022
https://doi.org/10.1007/978-981-19-0087-7_10 [Citations: 0] -
Origin of Turbulence
Stability of Non-Newtonian Fluid Flows
Dou, Hua-Shu
2022
https://doi.org/10.1007/978-981-19-0087-7_15 [Citations: 0] -
Effect of a perforation on the flow characteristics of corrugated wall
Yu, Linmeng | Sun, Jiao | Sun, Kangfu | Yuan, Pengda | Chen, WenyiExperimental Thermal and Fluid Science, Vol. (2024), Iss. P.111358
https://doi.org/10.1016/j.expthermflusci.2024.111358 [Citations: 0] -
From Patterns to Cocktails: A Novel Visualization Method for Turbulent Flow Fields in Stirred Reactors
Meng, Tong | Wang, Yu | Qin, Shuang | Liu, Peiqiao | Zhang, Qian | Wang, Yundong | Tao, Changyuan | Liu, ZuohuaIndustrial & Engineering Chemistry Research, Vol. 63 (2024), Iss. 44 P.19320
https://doi.org/10.1021/acs.iecr.4c02919 [Citations: 0] -
Extensions to the Navier–Stokes equations
Wang, Shisheng
Physics of Fluids, Vol. 34 (2022), Iss. 5
https://doi.org/10.1063/5.0087550 [Citations: 13] -
Origin of Turbulence
Introduction
Dou, Hua-Shu
2022
https://doi.org/10.1007/978-981-19-0087-7_1 [Citations: 2]