Joint statistics of a passive scalar and its dissipation in turbulent flows

Abstract

The statistical relationship between a passive scalar and its dissipation is important for both a basic understanding of turbulence small-scale properties and for various aspects of turbulent combustion modelling. This problem is studied in two different flows through spectral analysis as well as probability density functions using temperature as a passive scalar. Particular attention is paid to the experimental determination of the three squared derivatives involved in the temperature dissipation. As a first step, it is found that basic properties such as the correlation coefficient between temperature and its dissipation are strongly related to the asymmetry of the scalar fluctuations, so that the usually assumed statistical independence between these variables is not justified. These trends are the same for the two flows investigated here, a boundary layer and a jet. This connection appears to be related to fluctuations of small amplitude for both quantities which are associated with relatively low frequencies lying between the integral scale and the Taylor microscale. In regions where the temperature skewness factor is nearly zero, the correlation coefficient is also very small, and several tests show that the assumption of independence is then fully justified. Thus, the main parameter influencing joint statistics of temperature and its dissipation is the asymmetric feature of temperature fluctuations, but the asymmetry of the longitudinal temperature derivative, which results from the flow boundary conditions and is usually felt through the presence of the so-called temperature ramps, is also involved. Even though the magnitude of the derivative skewness factor is almost uniformly distributed in both flows, the secondary effect becomes the dominant one in flow regions where the influence of the temperature asymmetry is relatively weak.