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Local Reynolds number and thresholds of transition in shear flows

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Abstract

Recent experimental and numerical investigations reveal that the onset of turbulence in plane-Poiseuille flow and plane-Couette flow has some similar stages separated with different threshold Reynolds numbers. Based on these observations and the energy equation of a disturbed fluid element, a local Reynolds number Re L is derived to represent the maximum ratio of the energy supplement to the energy dissipation in a cross section. It is shown that along the sequence of transition stages, which include transient localized turbulence, “equilibrium” localized turbulence, spatially intermittent but temporally persistent turbulence and uniform turbulence, the corresponding thresholds of Re L for plane-Couette flow, Hagen-Poiseuille flow and plane-Poiseuille flow are consistent, indicating that the critical (threshold) states during the laminar-turbulent transition are determined by the local properties of the base flow and are independent of global features, such as flow geometries (pipe or channel) and types of driving forces (shear driving or pressure driving).

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Authors and Affiliations

  1. SKLTCS and CAPT, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing, 100871, China

    JianJun Tao, ShiYi Chen & WeiDong Su

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  1. JianJun Tao
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  2. ShiYi Chen
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  3. WeiDong Su
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Correspondence to JianJun Tao.

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Tao, J., Chen, S. & Su, W. Local Reynolds number and thresholds of transition in shear flows. Sci. China Phys. Mech. Astron. 56, 263–269 (2013). https://doi.org/10.1007/s11433-012-4955-7

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