Probability Density Functions of Velocity Increments in the Atmospheric Boundary Layer |
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| Authors: | Lei Liu Fei Hu Xue-Ling Cheng Li-Li Song |
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| Institution: | (1) Hillsdale College, 33 East College, Hillsdale, MI 49242, USA;(2) Ludwig von Mises Institute, 518 W. Magnolia Avenue, Auburn, AL 36832, USA |
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| Abstract: | The probability density functions (pdf’s) of the wind increments are measured under different weather conditions in the atmospheric
boundary layer, including the extreme weather of a typhoon and sand storm. It is found that in each case the measured pdf’s
with respect to different time lags coincide by suitable scaling transformation. This property is similar to that of the stable
distributions. However, fitting results show that the tails of the stable distributions are generally heavier than that of
the measured ones. Beside, the stable distributions (except for the Gaussian distribution) have infinite variance, which implies
infinite average kinetic energy. In fact, it can be proved that if the tails of the pdf’s are heavy enough, the variance will
be infinite. Therefore, the tail-truncated stable distributions with finite variances are introduced to fit the data and the
fitting results are excellent. |
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| Keywords: | |
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