A Minimalist Turbulent Boundary Layer Model.pdf

a r X i v : 0 8 0 9 .0 8 7 8 v 1 [ p h y s i c s .f l u - d y n ] 4 S e p 2 0 0 8 A Minimalist Turbulent Boundary Layer Model L. Moriconi Instituto de F??sica, Universidade Federal do Rio de Janeiro, C.P. 68528, 21945-970, Rio de Janeiro, RJ, Brazil We introduce an elementary model of a turbulent boundary layer over a flat surface, given as a vertical random distribution of spanwise Lamb-Oseen vortex configurations placed over a non-slip boundary condition line. We are able to reproduce several important features of realistic flows, such as the viscous and logarithmic boundary sublayers, and the general behavior of the first statistical moments (turbulent intensity, skewness and flatness) of the streamwise velocity fluctuations. As an application, we advance some heuristic considerations on the boundary layer underlying kinematics that could be associated with the phenomenon of drag reduction by polymers, finding a suggestive support from its experimental signatures. PACS numbers: 47.27.-i, 47.27.nb, 47.27.De Turbulent boundary layers have been a central topic of interest in fluid dynamic research for long years [1, 2]. Nevertheless their obvious technological importance, a satisfactory description of the physical mechanisms which underlie the boundary velocity fluctuations remains elu- sive to date. As the result of intensive computational and experimental efforts carried out mainly along the last two decades, it is by now clear that the turbulent boundary layer is the stage for the production and the complex interaction of coherent structures [3], a fact that was for- merly antecipated by Theodorsen [4] and Townsend [5]. Standard phenomenological formulations of the tur- bulent boundary layer problem aim at solving self- consistent equations for the expectation values of veloc- ity and the Reynolds stress tensor components, relevant quantities in engineering applications [2, 6]. At the very conception of these models no fundamental role is given to the who