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IS IT POSSIBLE TO DETERMINE SELF-SIMILARITY IN ISOTROPIC TURBULENCE BY THE OBSERVATION OF THE DECAY REGIME CHARACTERISTICS?

Marcello Meldi
Institut Jean Le Rond D'Alembert, UMR 7190 Université Pierre et Marie Curie 4 place Jussieu 75005 Paris, France

Pierre Sagaut
Institut Jean Le Rond D'Alembert, UMR 7190 Université Pierre et Marie Curie 4 place Jussieu 75005 Paris, France; Laboratoire de Mecanique, Modelisation et Procedes Propres UMR CNRS 7340 Aix-Marseille Universite IMT La Jetee, Technopole de Chateau-Gombert 38, rue Frederic Joliot-Curie 13451 Marseille Cedex 13, France

Résumé

The time evolution of initially non-self-similar regimes in isotropic turbulence decay is investigated by both theoretical analysis and EDQNM simulations. The breakdown of self-similarity is recovered by the analysis of a three-range energy spectrum, with two different slopes at scales larger than the integral length scale.
The results of the analysis indicate that, depending on the initial conditions, the solution can bifurcates toward a true self-similar decay regime, or sustain a lasting non-selfsimilar state. These non-self-similar regimes can not be detected restricting the observation to the time exponent of turbulence statistical properties such as the turbulent kinetic energy or the energy dissipation rate. In fact, it is shown that the decay of the physical quantities is governed by the large scales close to the energy spectrum peak only. In particular, the shape of the energy spectrum near its peak, which may be related to the turbulence production mechanisms, is of pivotal importance. As a conclusion, information about the very large scales of the energy spectrum can not be derived from the observation of the decay regimes characteristics, as those scales have a negligible impact over energy transfer.
Another relevant result is that classical self-similarity theories, which link the asymptotic behaviour the energy spectrum E(k→0) and the turbulence decay exponent, are not fully relevant when the large scale spectrum shape exhibits more than one range.