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. |