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wind speed fluctuation based on the Stockes-Navier equation.

That derivation, however, is insufficient to exhibit

the fractal information of time series, such as wind velocity

fluctuation. This paper gives a novel derivation of

the von Kármán spectrum based on fractional Langevin

equation, aiming at establishing the relationship between

the conventional von Kármán spectrum and fractal dimension.

Thus, the present results imply that a time series

that follows the von Kármán spectrum can be taken as

a specifically fractional Ornstein-Uhlenbeck process with

the fractal dimension 5/3, providing a new view of the famous

spectrum of von Kármán’s from the point of view

of fractals. More importantly, that also implies a novel relationship

between two famous spectra in fluid mechanics,

namely, the Kolmogorov’s spectrum and the von Kármán’s.

Consequently, the paper may yet be useful in practice,

such as ocean engineering and shipbuilding.

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online

23 - 11 - 2015

accepted

6 - 10 - 2015

received

9 - 9 - 2015

References

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YADDA identifier

bwmeta1.element.-psjd-doi-10_1515_wwfaa-2015-0004

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