Singularity of Navier-Stokes Equations

Hua-Shu Dou

Published 2018-05-30Version 1

The physics of transition of a smooth laminar flow to turbulence is still a great challenge in fluid dynamics. There is discontinuity in time-averaged Navier-Stokes equations from laminar flow to turbulence. In this paper, the singularity of Navier-Stokes equations is discovered by the derivation of the Navier-Stokes equations and the analysis of the velocity profile. It is the inflection point on the velocity profile which leads to the discontinuity and the instability. This singularity is the origin of the spanwise vortex and the genesis of the vortex head of the hairpin vortex formed afterwards. The singularity of the Navier-Stokes equations is the cause of turbulent transition and the inherent mechanism of sustenance of full developed turbulence.