Analysis of Velocity and Temperature Fluctuations in Turbulent Shear Flows.
Abstract
Turbulent velocity and temperature fluctuations in the jetburner mixinglayer were measured. Particular attention was focused on the small scale, high wave number turbulence which strongly affects the optical propagation. Commercial hotwire 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 powerlaw relationships, <(Delta u)^{n }> ~ <epsilon> ^{n/3} r ^{zeta_ {n}} and <( Deltatheta)^{n} > ~ <epsilon> ^{rm n/6} <chi >^{rm n/2} rm r ^{zeta_rm n}, where zeta_{n} is the exponent due to intermittency. In contrast to Kolmogorov's theory (1941), both viscous dissipation rate epsilon and thermal dissipation rate chi were assumed as random quantities. Measured values of zeta_{n} from velocity structure functions were compared with those predicted by lognormal, beta model and a new theory based on gamma statistics for the local dissipation rate epsilon_ {r}. 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 zeta _{rm n} 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 ( epsilon_{r} and chi_{r}) 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 k_sp{1} {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 epsilon_ {r} and chi_ {r}, 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.
 Publication:

Ph.D. Thesis
 Pub Date:
 March 1989
 Bibcode:
 1989PhDT........39J
 Keywords:

 Engineering: Mechanical; Physics: Atmospheric Science; Physics: Fluid and Plasma