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

Abstract

Turbulence measurements obtained from concurrent tower and aircraft\robservations are analyzed to test G.I. Taylor's hypothesis (1938) of the\requivalence between Eulerian space and Eulerian time spectra. The\rcorrelation and spectral data (along with data obtained from three other\rairplane turbulence programs) were also examined to ascertain the\rvalidity of Kolmogoroff's prediction (1940) for the behavior of the\rcorrelation coefficients and spectral densities in the inertial\rsubrange. At heights of 300-400 ft above the ground, the tower and\raircraft observations provide the same turbulence spectrum for\rwavelengths at least as large as 600 and 900 ft, for mean wind speeds of\rabout 20 and 30 ft sec1, respectively.The evidence is that\rthe Kolmogoroff range is not approached for the wavelength range\rexamined in this paper. The shortest wavelength sampled is on the order\rof 88 ft, at heights above the ground ranging from 200 to 2000 ft. It\rappears that at these heights, the Kolmogoroff spectrum, if valid, can\rapply only to wavelengths shorter than 88 ft.