Non-gaussian statistics of a passive scalar in turbulent flows

Abstract

The probability density functions (PDFs) of the passive temperature fluctuations θ and the components of the temperature dissipation rate εθ conditioned on θ 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≈19,000 based on nozzle exit conditions. The main aims for the study are (1) to investigate the statistical dependence of εθ on θ and (2) to examine how this dependence relates to the behavior of p(θ), the PDF of θ. It is shown that εθ is strongly dependent on θ in the near wake and that, in the central region of the wake, this dependence weakens with the downstream distance. However, the results suggest that statistical independence of εθ and θ never occur even in the self-preserving far wake. Likewise, for the jet flow, εθ and θ 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(θ) from Gaussianity reflects the degree of dependence of εθ on θ. Also, evidence is provided to support that the statistical independence of the scalar fluctuation θ and its dissipation rate εθ is a sufficient and necessary condition for p(θ) 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(θ) is closely Gaussian.