Scaling of wall turbulence

Details Scaling of wall turbulence Scaling of wall turbulence

2011-04-04

arxiv.org/abs/1104.0533v1

Physics

Fluid Dynamics

7 pages, 2 figures

Scientific paper

Based on matched asymptotic expansion method the new scaling relations for the mean velocity and Reynolds shear stress in the inner layer (viscous sublayer) are proposed, in which the relevant parameters are friction velocity and the parameter $\lambda$ instead of wall units. Without any propositions about the outer velocity scale $u_o$ it is found that the matching condition for the mean velocity in the overlap region is equivalent to Vincze's functional equation and has the solution in the form of power law. Power law exponent tends to zero in the limit of infinite Reynolds number and only in the case of complete similarity of $u_o$ and $\lambda$. At finite Reynolds numbers the power law exponent is not universal and may be dependent of the flow type.

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