Criteria Of Turbulent Transition In Parallel Flows

TL;DR

This paper proposes criteria for turbulent transition in parallel flows based on the energy gradient method, linking flow profile features to transition conditions and suggesting control strategies.

Contribution

It introduces specific criteria for turbulent transition in pressure and shear driven flows using the energy gradient method, connecting flow inflection points and zero velocity gradients to transition.

Findings

Transition occurs at flow inflection points or zero velocity gradients.

Singularity in the energy gradient function relates to chaos and transition.

Turbulence can be controlled by modulating energy gradient distribution.

Abstract

Based on the energy gradient method, criteria for turbulent transition are proposed for pressure driven flow and shear driven flow, respectively. For pressure driven flow, the necessary and sufficient condition for turbulent transition is the presence of the velocity inflection point in the averaged flow. For shear driven flow, the necessary and sufficient condition for turbulent transition is the existence of zero velocity gradient in the averaged flow profile. It is shown that turbulent transition can be effected via a singularity of the energy gradient function which may be associated with the chaotic attractor in dynamic system. The role of disturbance in the transition is also clarified in causing the energy gradient function to approach the singularity. Finally, it is interesting that turbulence can be controlled by modulating the distribution of the energy gradient function.