The determination of eddy diffusivity from measurements of turbulent energy

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Abstract
Two existing methods of deriving eddy diffusivity from measurements of turbulent energy are briefly reviewed, one based on the theory of the inertial sub‐range and therefore concerned with high‐frequency energy, the other purely empirical and concerned with total energy. A third method, based on the statistical theory of diffusion of particles and concerned with low‐frequency energy, is suggested.The three methods are applied in terms of some recent broad‐band spectrum measurements of the vertical component near the ground in neutral conditions, and the results compared with the eddy diffusivity K derived from the wind‐profile. The high‐frequency and total‐energy methods give the smallest spread (standard deviation near 10 per cent) in the individual estimates of K. On average K is given by the lowfrequency method (using a constant derived independently) within a few per cent, but the high‐frequency method (using one particular estimate of a constant term) underestimates by about 36 per cent. The latter discrepancy is in agreement with an earlier related test, made by R. J. Taylor, against observations of shearing stress and structure functions. Taylor's analysis suggests that the high‐frequency method should otherwise be useful in non‐neutral conditions also, but confirmation of this and thorough testing of the other methods requires further observations.

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