# Secret Hidden in Navier-Stokes Equations: Singularity and Criterion of Turbulent Transition

@article{Dou2014SecretHI, title={Secret Hidden in Navier-Stokes Equations: Singularity and Criterion of Turbulent Transition}, author={Hua-Shu Dou}, journal={arXiv: Fluid Dynamics}, year={2014} }

A new formulation of the Navier-Stokes equation, in terms of the gradient of the total mechanical energy, is derived for the time-averaged flows, and the singular point possibly existing in the Navier-Stokes equation is exactly found. Transition of a laminar flow to turbulence must be implemented via this singular point. For pressure driven flows, this singular point corresponds to the inflection point on the velocity profile. It is found that the stability of a flow depends on the direction of…

## 4 Citations

### Singularity of Navier-Stokes Equations ( 2018-1101 )

- Physics
- 2018

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…

### Analysis of vortex breakdown in an enclosed cylinder based on the energy gradient theory

- PhysicsEuropean Journal of Mechanics - B/Fluids
- 2018

### A universal equation for calculating the energy gradient function in the energy gradient theory

- Physics, Engineering
- 2016

The relationship for the energy variation, work done, and energy dissipation in unit volumetric fluid of incompressible flow is derived. A universal equation for calculating the energy gradient…

### A universal equation for calculating the energy gradient function in shear driven flows using the energy gradient theory.

- Engineering, Physics
- 2020

The energy gradient theory was proposed in our previous studies. The mechanism of flow instability is very different in shear driven flows from pressure driven flows. In present paper, the…

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