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An Empirical Investigation of Scaling Behavior in the Atmospheric Turbulence for Understanding the Underlying Cascade Process

We study the scaling behaviors in the wind velocity time series collected at the atmospheric surface layer and compare them with two commonly used cascade models, the truncated stable distribution and the log-normal model. Results show that although both models can describe the change of probability density functions from non-Gaussian to Gaussian like distributions with the increase of time scale, they can not fit the scaling behaviors observed in the probability of return and in the moments at the same time. This work provides some clues on the understanding of cascade process in the atmospheric turbulence.