Some Statistics of Lagrangian and Eulerian Wind Fluctuations

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Abstract
The linear relationship u′(t + τ) = u′(t)R(τ) + u″(t) is shown to be approximately valid for Lagrangian and Eulerian wind speed observations in the planetary boundary layer, where t represents any time and t + τ is some later time, u′ is the turbulent wind speed fluctuation, R(τ) the autocorrelation coefficient, and u″ a random wind speed component assumed to be independent of u′. Eulerian wind data from the Minnesota boundary layer experiment and Lagrangian wind data from tetroon trajectories near Las Vegas and Idaho Falls are analyzed. At extreme values of u′(t) for the Eulerian data, u′(t + τ) tends to be slightly less than that predicted by the above relationship. An application of this formula to the calculation of diffusion yields results in agreement with Taylor's theory.

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