On the Criterion for the Determination Transition Onset and Breakdown to Turbulence in Wall-Bounded Flows

[+] Author and Article Information
J. Jovanović, M. Pashtrapanska

Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, Cauerstrasse 4, D-91058, Germany

J. Fluids Eng 126(4), 626-633 (Sep 10, 2004) (8 pages) doi:10.1115/1.1779663 History: Received March 12, 2003; Revised March 02, 2004; Online September 10, 2004
Copyright © 2004 by ASME
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Grahic Jump Location
Anisotropy-invariant mapping of the disturbances generated by small, two-dimensional roughness element in a initially laminar flat plate boundary layer from Fischer, Jovanović and Durst 7: (a) specially designed two-component laser-Doppler system for near-wall measurements; (b) schematic of flat plate arrangement in the wind tunnel with layout of two different beam configurations which allowed measurements of all components of the “apparent” stresses of the disturbances; (c) traces of the joint variations of invariants IIa and IIIa across the anisotropy invariant map confirm the two-component nature of the disturbances
Grahic Jump Location
Intermittency (Υ) measurements of the transition process from laminar to turbulent states at the channel centerline from Fischer 8: (a) channel flow test section; (b) transition due to the natural disturbances is accompanied by large hysteresis in the experimental data; (c) transition due to the two-component disturbances implies that for such disturbances the critical Reynolds number may be found by extrapolation data of a fully developed turbulent flow if the transition criterion is known
Grahic Jump Location
Anisotropy invariant map and the asymptotic forms for the unknown correlations involved in the equations for the “apparent” stresses
Grahic Jump Location
Anisotropy invariant mapping of turbulence in a channel flow. Data, which correspond to low Reynolds numbers, show the trend as Re→(Re)crit towards the theoretical solution valid for small, neutrally stable, statistically stationary, axisymmetric disturbances (Jovanović, Hillerbrand and Pashtrapanska 29). The shading indicates the area occupied by the stable disturbances: for such disturbances a laminar regime in the boundary layer will persist up to very high Reynolds numbers.
Grahic Jump Location
Turbulent dissipation rate at the wall normalized with the wall shear velocity and the kinematic viscosity of the flow medium versus the anisotropy of turbulence IIa at the wall. A best-line fit through the numerical data extrapolates fairly well the expected trend ε→0 as the one-component limit (IIa=2/3) is approached.
Grahic Jump Location
Cross plot of Rλ versus Reτ1/2 for fully developed turbulent pipe and channel flows at low Reynolds numbers
Grahic Jump Location
Cross plot of Rλ versus Reτ1/2 for turbulent boundary layer at low Reynolds numbers



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