Wall bounded turbulent shear flow: Analytic result for an universal amplitude

Details Wall bounded turbulent shear flow: Analytic result for an universal amplitude Wall bounded turbulent shear flow: Analytic result for an universal amplitude

1999-09-21

arxiv.org/abs/cond-mat/9909312v1

Physics

Condensed Matter

Statistical Mechanics

7 pages, no figures, simple latex format

Scientific paper

In the turbulent boundary layer above a flat plate, the velocity profile is known to have the form v=v_0[(1/\kappa) ln z + constant]. The distance from the wall in dimensionless units is z and v_0 is an uniquely defined velocity scale. The number \kappa is universal and measurements over several decades have shown that it is nearly 0.42. We use a randomly stirred model of turbulence to derive the above law and find \kappa=\sqrt{\frac{108} {125 \pi}} \simeq 0.52.

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