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COMPARING THE THREE POSSIBLE SCALINGS OF STREAM-WISE NORMAL STRESS IN TURBULENT BOUNDARY LAYERS

Peter A. Monkewitz
Fluid Mechanics Laboratory, Swiss Federal Institute of Technology Lausanne, Station 9, Lausanne, 1015, Switzerland

Hassan M. Nagib
MMAE, Illinois Institute of Technology, Chicago, IL 60616, USA

Vincent Boulanger
MMAE Department Illinois Inst. Technology Chicago, IL 60616, USA

要約

The focus of this contribution is an evaluation against experimental data of three models for the stream-wise normal stress in zero pressure gradient turbulent boundary layers, henceforth abbreviated ZPG TBL's : an inner-scaled, mixed-scaled and outer-scaled model, where the stress is scaled by the square of the friction velocity, the product of friction and free stream velocities, and the square of the free stream velocity, respectively. The inner-scaled model of Monkewitz & Nagib (2015), which implies a decrease of the (negative) outer logarithmic slope of the stream-wise normal stress with increasing Reynolds number and is the only model constructed as a genuine composite asymptotic expansion satisfying the complete momentum equation close to the wall, is found to provide the closest fit to the experimental data. As an aside, it is shown that these data do not collapse in the so-called diagnostic plot.