Taylor's hypothesis and spectra of velocity and temperature derivatives in a turbulent shear flow

Abstract

Spectral densities of temporal velocity and temperature derivatives, measured in the atmospheric turbulent boundary layer and on the axis of a turbulent plane jet, are compared with the spectral densities of the ratios of these derivatives and of the local longitudinal instantaneous velocity. The comparison between the spectral densities, when both are normalized such that the areas under the spectra are equal, shows that the corrected spectrum is lower than the measured spectrum at frequencies larger than about one-seventh of the Kolmogorov frequency while the opposite trend is observed at low frequencies. A qualitatively similar result has been obtained when the measured velocity derivative spectrum is compared with that corrected using Lumley's method. While the unnormalized spectral densities and moments of the derivatives, as corrected by Lumley's method are smaller than the corresponding measured quantities, the opposite trend is found when the correction is made by dividing the temporal derivative by the longitudinal instantaneous velocity.