Scaling laws and dissipation scale of a passive scalar in fully developed turbulence

Abstract

The scaling laws of the temperature structure functions and their relation with those of velocity have been experimentally studied. The relationship between the dissipative scales for velocity and the temperature is first investigated. In agreement with recent numerical simulations of Pumir (1994), it is found that, for Prandtl number close to 1, the dissipation scale for a scalar is smaller than that of velocity. Thus temperature structure functions present a larger scaling interval than that of the velocity. The intermittent corrections of scaling are then analyzed. It is shown that, as proposed in literature (R. Benzi et al., 1992), the second-order structure function is affected only by the velocity intermittency. This structure function is then used as the reference for testing the applicability of the extended self-similarity (ESS) to the passive scalar case. ESS holds, but in a narrower interval than that observed in velocity statistics. Finally, a hierarchy for the temperature structure functions, similar to that proposed by She and Leveque (1994) for the velocity field, is introduced and experimentally tested.