JOINT STATISTICS OF A PASSIVE SCALAR AND ITS DISSIPATION IN TURBULENTFLOWS

The statistical relationship between a passive scalar and its dissipat ion is important for both a basic understanding of turbulence small-sc ale properties and for various aspects of turbulent combustion modelli ng. This problem is studied in two different flows through spectral an alysis as well as probability density functions using temperature as a passive scalar. Particular attention is paid to the experimental dete rmination 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 variab les is not justified. These trends are the same for the two flows inve stigated here, a boundary layer and a jet. This connection appears to be related to fluctuations of small amplitude for both quantities whic h are associated with relatively low frequencies lying between the int egral scale and the Taylor microscale. In regions where the temperatur e 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 s tatistics of temperature and its dissipation is the asymmetric feature of temperature fluctuations, but the asymmetry of the longitudinal te mperature 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 s kewness factor is almost uniformly distributed in both flows, the seco ndary effect becomes the dominant one in flow regions where the influe nce of the temperature asymmetry is relatively weak.