22nd IFIP TC 7 Conference on System Modeling and Optimization Turin, Italy, July 18-22, 2005 Self-similarity of the turbulences mixing with a constant in time macroscale gradient D.Tordella 1 , M.Iovieno 1 1) Politecnico di Torino, Dipartimento di Ingegneria Aeronautica e Spaziale, Corso Duca degli Abruzzi 24, 10129 Torino daniela.tordella@polito.it, michele.iovieno@polito.it Key words : turbulence, transport, similarity Abstract In the absence of kinetic energy production, we consider that the influ- ence of the initial conditions is characterized by the presence of an energy gradient or by the concurrency of an energy and a macroscale gradient on turbulent transport. Here, we present a similarity analysis that in- terprets two new results on the subject recently obtained by means of numerical experiments on shearless mixing (Tordella & Iovieno, 2005). In short, the two results are: i – The absence of the macroscale gradient is not a sufficient condition for the setting of the asymptotic Gaussian state hypothesized by Veeravalli and Warhaft (1989), where, regardless of the existence of velocity variance distributions, turbulent transport is mainly diffusive and the intermittency is nearly zero up to moments of order four. In fact, it was observed that the intermittency increases with the energy gradient, with a scaling exponent of about 0.29; ii – If the macroscale gradient is present, referring to the situation where the macroscale gra- dient is zero but the energy gradient is not, the intermittency is higher if the energy and scale gradients are concordant and is lower if they are opposite. The similarity analysis, which is in fair agreement with the previous experiments, is based on the use of the kinetic energy and the two-point correlation equations, which contain information on the second and third order moments of the velocity fluctuations. The analysis is based on two main hypotheses: first, the decays of the turbulences be- ing mixed are nearly equal (as suggested by the experiments), second, the pressure-velocity correlation is almost proportional to the convective transport associated to fluctuations (Yoshizawa, 2002). 1