Transition at dissipative scales in large-Reynolds-number turbulence.
Among the available diagnostics of turbulence, the flatness of the velocity derivatives is particularly interesting because it represents a straightforward test of Kolmogorov theory, and provides a quantitative estimate for intermittency effects. It is commonly considered that the flatness factor increases with the Reynolds number, following a power law at high Reynolds numbers. At variance with this picture, evidence for a transitional behavior, taking place around the Taylor microscale Reynolds number R(lambda)=700, has been recently obtained in several experiments. In the present paper we study this transition in detail, and show it has the characteristics of a second order phase transition. We propose a physical picture for this transition, based on worm vortex breakdown, which leads as to suggest that intense sub-Kolmogorov structures might develop above the transition point. These results indicate that the existence of an asymptotic state at infinite Reynolds number may become questionable and more generally, that our current views on dissipative range intermittency probably need to be revised
Laboratoire de Physique Statistique, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris, France.
Patrick
P
Tabeling
Herve
H
Willaime