DOI: 10.1615/TSFP8
IS IT POSSIBLE TO DETERMINE SELF-SIMILARITY IN ISOTROPIC TURBULENCE BY THE OBSERVATION OF THE DECAY REGIME CHARACTERISTICS?
SINOPSIS
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.