Analysis of Velocity and Temperature Fluctuations in Turbulent Shear Flows

Turbulent velocity and temperature fluctuations in the jet-burner mixing-layer were measured. Particular attention was focused on the small scale, high wave number turbulence which strongly affects the optical propagation. Commercial hot-wire sensors involving a newly developed temperature measuring scheme were employed. The velocity and temperature structure functions up to order 18 were measured in the inertial range to establish the power-law relationships, \u3c (Δu)n \u3e ~ \u3c ϵ \u3e n/3 rζn and \u3c (ΔΘ)n \u3e ~ \u3c ϵ \u3e -n/6 \u3c x \u3e n/2 rζr where ζn is the exponent due to intermittency. In contrast to Kolmogorov\u27s theory (1941), both viscous dissipation rate ϵ and thermal dissipation rate X were assumed as random quantities. Measured values of ζn from velocity structure functions were compared with those predicted by lognormal, β-model and a new theory based on gamma statistics for the local dissipation rate ϵr . The present data and past measurements agree more closely with the predictions of gamma model rather than those of the lognormal model. Similarly, the measured values of ζn from temperature structure functions compared more favorably with the predictions of a new theory based on the bivariate gamma distribution for the joint density function of local dissipations (ϵr and xr) than results predicted by bivariate lognormal distribution. Unlike velocity spectra, the measured temperature spectra revealed that at high wave numbers it decreases less rapidly than the k1-5/3 law and has the appearance of a spectral bump just prior to the dissipation ranges. A corresponding bump was also observed in the temperature structure function. By considering the joint fluctuations in the dissipations ϵr and xr, the new analytical spectrum and structure function models based on the bivariate gamma distribution were found to agree well with the present and past experimental data