Reynolds dependence of third-order velocity structure functions

Yves Gagne (1) , Bernard Castaing (2) , Christophe Baudet (1) , Yann Malecot (1)

1 LEGI - Laboratoire des Écoulements Géophysiques et Industriels [Grenoble]
2 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

We study the experimental dependence of the third-order velocity structure function on the Taylor based Reynolds number, obtained in different flow types over the range 72⩽Rλ⩽2260. As expected, when the Reynolds number is increasing, the third-order velocity structure functions (plotted in a compensated way) converge very slowly to a possible −4/5 plateau value according to the Kolmogorov 41 theory. Actually, each of these normalized third-order functions exhibits a maximum, at a scale close to the Taylor microscale λ. In this Brief Communication, we show that experimental data are in good agreement with the recent predictions of Qian and Lundgren. We also suggest that, from an experimental point of view, a log-similar plot suits very well to study carefully the behavior of the third-order velocity structure functions with the flow Reynolds number.

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Yves Gagne, Bernard Castaing, Christophe Baudet, Yann Malecot. Reynolds dependence of third-order velocity structure functions. Physics of Fluids, 2004, 16 (2), pp.482-485. ⟨10.1063/1.1639013⟩. ⟨hal-00183628⟩