# Séminaire de Mécanique d'Orsay

## Le Jeudi 31 mai à 14h00 - Salle de conférences du LIMSI

### Statistically non-stationary turbulence

## William K. George

Dept Aeronautics, Imperial College, London

The Kolmogorov theory of turbulence has dominated out thinking about turbulence since it was first introduced to the West by Batchelor after the Second World War. Of all the assumptions in Kolmogorov 1941 the most fundamental is the assumption (or postulate) that the smallest scales of the turbulence are in statistical equilibrium. This is usually justified by heuristic arguments based on the decreasing time scales as the eddy size is decreased relative to that of the energy containing eddies so that they can be assumed to be in local equilibrium (c.f., Batchelor 1953). This argument can be shown to be fundamentally awed since it does not account for the decreasing energy of the smaller scales. Moreover there are well-documented counter-examples to local equilibrium in non-stationary ows. It is argued that the K41 scaling arguments (or variations upon it) for the dissipative scales are in fact only applicable to ows in strict statistical equilibrium (i.e., statistically stationary), and should not be expected to apply to non-equilibrium ows. At least three types of non-equilibrium ows will be identified, one of which curiously enough satisfies Kolmogorov scaling at all scales. Finally it will be demonstrated how we were led into believing something that wasn't really true, and why we continued to believe it for so long.