UNSPECIFIED (2000) Nonlinear RDT theory of near-wall turbulence. PHYSICA D, 139 (1-2). pp. 158-176. ISSN 0167-2789

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Abstract

A WKB method was recently used to extend rapid distortion theory (RDT) to initially inhomogeneous turbulence strained by irrotational mean flows [S.V. Nazarenko, N. Kevlahan, B. Dubrulle, J. Fluid Mech. 390 (1999) 325]. This theory takes into account the feedback of turbulence on the mean flow, and it was used by Nazarenko ct al. to explain the effect of strain reduction caused by turbulence observed by Andreotti et al. [B. Andreotti, S. Douady,Y. Couder, in: O. Boratav, A. Eden, A. Erzan (Eds.), Turbulence Modeling and Vortex Dynamics, Proceedings of a Workshop held at Istanbul, Turkey, 2-6 September 1996, pp. 92-108]. In this paper, we develop a similar WKB RDT approach for shear flows. We restrict ourselves to problems where the turbulence is small-scale with respect to the mean flow length-scale and turbulence vorticity is weak compared to the mean shear. We show that the celebrated log-law of the wall exists as an exact analytical solution in our model if the initial turbulence vorticity (debris of the near-wall vortices penetrating into the outer regions) is statistically homogeneous in space and shortly correlated in time. We demonstrate that the main contribution to the shear stress comes from very small turbulent scales which are close to the viscous cut-off and which are elongated in the stream-wise direction (streaks). We also find that anisotropy of the initial turbulent vorticity changes the scaling of the shear stress, but leaves the log-law essentially unchanged. (C) 2000 Elsevier Science B.V. All rights reserved.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Journal or Publication Title:	PHYSICA D
Publisher:	ELSEVIER SCIENCE BV
ISSN:	0167-2789
Date:	1 May 2000
Volume:	139
Number:	1-2
Number of Pages:	19
Page Range:	pp. 158-176
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/13534

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