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Study of isotropic structure in atmospheric boundary layer turbulence Webster, Ian Taylor

Abstract

The two purposes of this study were to determine at what turbulent scales in a high Reynold's number shear flow the transition to isotropy occurs and at what scales Taylor's 'frozen field' hypothesis is applicable. The flow studied was the wind at a height of z = 2 m. above a flat land surface. Four hot wire anemometers were mounted in a three dimensional array to collect data on the downwind turbulent velocity fluctuations. Cross spectra were computed from the observed data between three pairs of hot wires having the same spacing in different directions; these were varied between 1.8 m. and 2 cm. Knowing the observed spectrum of downwind velocity fluctuations and assuming the turbulence is isotropic, incompressible, and obeys Taylor's hypothesis, theoretical cross spectra were computed. The results of the comparison between the observed and theoretical cross spectra for different spacings revealed that in the flow studied the behaviour of the turbulence is consistent with the assumptions of both isotropy and Taylor's hypothesis for k₁z > 20, but for wave numbers less than this range either or both of the assumptions are not valid. However, between k₁z = 4 and k₁z = 20 the turbulence appears to be at least axisymmetric about the downstream direction and for k₁z > 3 that part of Taylor's hypothesis relating observed frequency at a stationary sensor to the downstream wave number component appears to be justified.

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