Non-Gaussian statistics of a passive scalar in turbulent flows

The probability density functions (PDFs) of the passive temperature fluctuations theta and the components of the temperature dissipation rate epsilon(theta) conditioned on theta have been measured using a high-resolution compact multi-cold-wire probe in a turbulent plane wake and in a round jet. The wake is generated by a circular cylinder at a characteristic Reynolds number based on cylinder diameter (Re) of about 3000. The jet issues from a nozzle with a smooth contraction at Re approximate to 19,000 based on nozzle exit conditions. The main aims for the study are (1) to investigate the statistical dependence of epsilon(theta) on theta and (2) to examine how this dependence relates to the behavior of p(theta), the PDF of theta. It is shows that epsilon(theta) is strongly dependent on theta in the near wake and that, in the central region of the wake, this dependence weakens with the downstream distance. However, die results suggest that statistical independence of epsilon(theta) and theta never occur even in the self-preserving far wake. Likewise, for the jet flow epsilon(theta) and theta are also not strictly independent, although they are only weakly correlated in the central region of the far field. The present work demonstrates that the departure of p(theta) from Gaussianity reflects the degree of dependence of epsilon(theta) on theta. Also, evidence is provided to support that the statistical independence of the scalar fluctuation theta and its dissipation rate epsilon(theta) is a sufficient and necessary condition for p(theta) to be Gaussian in either homogeneous or inhomogeneous (stationary) turbulence. Thus the independence assumption, often used in combustion modeling, is reasonable only in the flow region where p(theta) is closely Gaussian.