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On the Range of Validity of Taylor's Hypothesis and the Kolmogoroff Spectral Law

U. Oscar LappeNew York University

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Ben DavidsonNew York University

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Abstract

Turbulence measurements obtained from concurrent tower and aircraft observations are analyzed to test G.I. Taylor's hypothesis (1938) of the equivalence between Eulerian space and Eulerian time spectra. The correlation and spectral data (along with data obtained from three other airplane turbulence programs) were also examined to ascertain the validity of Kolmogoroff's prediction (1940) for the behavior of the correlation coefficients and spectral densities in the inertial subrange. At heights of 300–400 ft above the ground, the tower and aircraft observations provide the same turbulence spectrum for wavelengths at least as large as 600 and 900 ft, for mean wind speeds of about 20 and 30 ft sec−1, respectively.

The evidence is that the Kolmogoroff range is not approached for the wavelength range examined in this paper. The shortest wavelength sampled is on the order of 88 ft, at heights above the ground ranging from 200 to 2000 ft. It appears that at these heights, the Kolmogoroff spectrum, if valid, can apply only to wavelengths shorter than 88 ft.

Abstract

Turbulence measurements obtained from concurrent tower and aircraft observations are analyzed to test G.I. Taylor's hypothesis (1938) of the equivalence between Eulerian space and Eulerian time spectra. The correlation and spectral data (along with data obtained from three other airplane turbulence programs) were also examined to ascertain the validity of Kolmogoroff's prediction (1940) for the behavior of the correlation coefficients and spectral densities in the inertial subrange. At heights of 300–400 ft above the ground, the tower and aircraft observations provide the same turbulence spectrum for wavelengths at least as large as 600 and 900 ft, for mean wind speeds of about 20 and 30 ft sec−1, respectively.

The evidence is that the Kolmogoroff range is not approached for the wavelength range examined in this paper. The shortest wavelength sampled is on the order of 88 ft, at heights above the ground ranging from 200 to 2000 ft. It appears that at these heights, the Kolmogoroff spectrum, if valid, can apply only to wavelengths shorter than 88 ft.

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