African Journal of Physics

Full Length Research Paper

Physics of irregularity flow and tumultuous conversion in shear flows

Irene Gourt

Temasek Laboratories, National University of Singapore, Singapore 117411. E-mail: [email protected].

Accepted 18 May, 2013

Abstract

Turbulent transition is of great significance in modern sciences and industrial applications. The physics of flow instability and turbulent transition in shear flows is studied by analyzing the energy variation of fluid particles under the interaction of base flow with a disturbance. A simple model derived from physics is proposed to show that the flow instability under finite amplitude disturbance leads to turbulent transition. The proposed model is named as “energy gradient method”. It is demonstrated that it is the transverse energy gradient that leads to the disturbance amplification while the disturbance is damped by the energy loss due to viscosity along the streamline. The threshold of disturbance amplitude obtained is scaled with the Reynolds number by an exponent of -1, which is in good agreement with experiments in literature for pipe flow with injection disturbance. Experimental data for wall bounded parallel flows indicate that the critical value of the so called energy gradient parameter K_{m ax} is same at turbulent transition (at least for pressure driven flows). The location of instability initiation accords well with the experiments for both pipe Poiseuille flow (r/R=0.58) and plane Poiseuille flow (y/h=0.58). It is also inferred from the proposed method that the transverse energy gradient can serve as the power for the self-sustaining process of wall bounded turbulence. Finally, the relation of “energy gradient method” to the classical “energy method” based on Rayleigh-Orr equation is also discussed.

Key words: Turbulent transition, shear flows, energy gradient, energy loss, critical Reynolds number.