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Vortical structures in the turbulent boundary layer: a possible route to a universal representation

type de publication      article in an international journal with refereeing comitee
date de publication 2008
auteur(s) Stanislas Michel; Perret Laurent; Foucaut Jean-Marc
journal (abréviation) Journal of Fluid Mechanics (J Fluid Mech)
volume (numéro) 602
  
pages 327 – 382
résumé A study of streamwise oriented vortical structures embedded in turbulent boundary layers is performed by investigating an experimental database acquired by Stereoscopic Particle Image Velocimetry (SPIV) in a plane normal both to the mean flow and the wall (K¨ahler et al. 2000; Carlier & Stanislas 2005). The characteristics of the experimental data allow to focus on the spatial organization within the logarithmic region for Reynolds numbers Re up to 15 000. On the basis of the now well–admitted hairpin model, relationships and interaction between streamwise vortices are first investigated via computation of two–point spatial correlations and the use of Linear Stochastic Estimation (LSE). These analysis confirm that the shape of the most probable coherent structures corresponds to an asymmetric one–legged hairpin vortex. Moreover, two regions of different dynamics can be distinguished: the near–wall region below y+ = 150, densely populated with strongly interacting vortices and the region above y+ = 150 where interactions between eddies happen less frequently. Characteristics of the detected eddies, such as probability density functions of their radius and intensity, are then studied. It appears that Reynolds number as well as wall–normal independences of these quantities are achieved when a scaling with the local Kolmogorov scales is performed. The most probable size of the detected vortices is found to be about 10 times the Kolmogorov length scale. These results lead to revisit the equation for the mean square vorticity fluctuations, as studied by Tennekes & Lumley (1972), and to propose a new balance of this equation in the near wall region. This analysis and the above results allow, in the discussion, to propose a new description of the near wall region, leading to a new scaling which seems to have a good universality in the Reynolds number range investigated. The possibility to reach a universal scaling at high enough Reynolds number, based on the external velocity and the Kolmogorov length scale is underscored.
mots clés couche limite turbulente, PIV, structures tourbillonnaires
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