The fine-scale structure of the turbulent velocity field

Abstract

The existence of universal similarity of the fine-scale structure of turbulent velocity fields and the validity of the original Kolmogorov local similarity theory and the later reformulations were investigated. Recent studies of the fine-scale velocity field for many different flows, e.g. grid flows, wakes, jets and the atmospheric boundary layer, are shown to provide considerable evidence for the existence of Kolmogorov normalized spectral shapes which are universal in the sense that they describe the high wave-number spectral behaviour of all turbulent flow fields with a similar value of the turbulence Reynolds number R λ . The normalized spectral shapes vary with R λ in a manner consistent with the later reformulations. The Reynolds number dependence of the normalized spectra is demonstrated for the R λ range from about 40 to 13 000. Expressions for the Kolmogorov normalized spectral functions are presented for three values of R λ . Also revealed in this study is the importance of considering effects on spectra caused by deviations from Taylor's approximation in high intensity turbulent flows. Lumley's (1965) model is used to correct the high frequency portion of the measured one-dimensional spectra for these effects. An analytical solution to Lumley's expression is presented and applied to the data.