Statistics of fine-scale velocity in turbulent plane and circular jets

Abstract

Higher-order statistics of the streamwise velocity derivative have been measured on the centre-line of turbulent plane and circular jets. The instrumentation and sources of error are discussed to establish the accuracy of the data and convergence of statistics. The optimum setting for the low-pass filter cut-off was found to be 1·75 times the Kolmogorov frequencyfK, in contrast with the majority of previous investigations where it was set equal tofK. The magnitude of the constant μ in Kolmogorov's revised hypothesis is obtained using statistics derived from the instantaneous velocity derivative or its squared value. The correlation and spectrum of fluctuations of the squared velocity derivative and the Reynolds-number variation of the skewness and flatness factors of the velocity derivative are consistent with μ ≃ 0·2, while the most popular value used is 0·5. Second-order moments of the locally averaged dissipation, assumed proportional to the squared streamwise velocity derivative, and breakdown coefficients also suggest a value of μ of about 0·2. Higher-order correlations and spectra of the dissipation are in closer agreement with the Novikov-Stewart or β-model than with Kolmogorov's lognormal model. Higher-order moments of locally averaged values of the dissipation rate are more closely represented by the lognormal than the β-model.