On the Structure of Wind near the Ground, III

Abstract

The several correlation functions of fluctuations in wind velocity are closely connected with the spectral functions of wind. Assuming the negative five-thirds power law for turbulence spectrum, the author obtains the functional forms of correlations as follows:
R(t)=1-(t/T⁰)_??_,
f(r)=1-(r/Λ₀)^2/3,
g(r)=1-(4/3)(r/Λ₀)^2/3,
These results are compared with the practical observations carried out in the natural wind. T₀ and Λ₀ mean the pass-time and scale of the effective largest turbulon, and their quantities are proportional to the time duration T of observation. Some characteristic quantities of turbulent state measured in the natural wind are also related to the time duration T, and it is shown that the turbulent diffusion coefficient is proportional to T^4/3. Finally, in the natural wind, the smallest eddy defined by G. I. Taylor is pointed out to be by no means the absolute length, and to be proportional to T^1/3.