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Reconsidering Kolmogov for Non-stationary Turbulent Flows

William K George

Marie Curie Intra European Principal Research Fellow
Department of Aeronautics
Imperial College of Science, Technology and Medicine
South Kensington Campus, Exhibition Road
SW7 2AV London, UK

One of the most important contributions to turbulence over the past century was theory of Kolmogorov 1941. Since its introduction to the western world by Batchelor in 1946 it has dominated turbulence, both the interpretation of experiments and the development of turbulence models and scaling laws. It has been commonly assumed since the tidal channel measurements of Grant et al. 1961 that experiments have been uniformly supportive and that the coefficients are universal. Unfortunately the most important parameter, the turbulent dissipation, can almost never be measured directly and quite frequently is determined by `fitting' the measured data to the `established' results. Thus the `perfect' agreement is largely illusory, and in fact there is a considerable disagreement about what the `universal' constants are (or even if they are universal). Also it is seldom pointed out that almost all of the experiments cited are in statistical equilibrium, so that Kolmogorov's crucial first hypothesis of `local' equilibrium is satisfied identically. Thus none of these experiments can be regarded as a test of its generality. Worse, recent experiments and DNS in non-stationary turbulence show signicant departures from Kolmolgorov behavior. These non-stationary homogeneous experiments are, however, consistent with the equilibrium similarity theory of George 1992 for these flows. So together the non-stationary theory and experiments provide some confidence in these iconoclastic results. Therefore they present by counter-example a challenge to the Kolmogorov-based ideas for non-stationary flows, suggesting that we need to modify at least one of our fundamental beliefs.