Taylor's Hypothesis and High–Frequency Turbulence Spectra

Abstract

Lumley's model for interpreting frequency spectra of streamwise velocity in high-turbulence level flows assumes 1) that the convection velocity fluctuations and the convected finestructure are statistically independent, and 2) that the characteristic function of convection velocity fluctuations can be represented by the first two terms of its series expansion. The first assumption is consistent with numerous experimental results, and we test the second with an alternative assumption: that the convection velocity fluctuations are Gaussian. The two models are found to agree well up to moderately high fluctuation levels, thus giving support for Lmnley's model in atmospheric boundary layer applications. We generalize his model to spectra of lateral velocity and a scalar, and calculate how various large-wavenumber spectral properties are disturbed by convection velocity fluctuations. The inertial subrange spectra are found to be affected relatively little, but serious spectral distortion is found at larger wavenumbers.