On von Kármán spectrum from a view of fractal

• Authors: Ming Li , Jianxing Leng
• Languages of publication: EN

Abstracts

EN

Von Kármán originally deduced his spectrum of
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.

Keywords

EN

The von Kármán spectrum; fluctuation ofwind speed; fractional Ornstein-Uhlenbeck process; Kolmogorov’s−5/3 law

• Publisher: De Gruyter Open
• Journal: Waves, Wavelets and Fractals
• Year: 2015
• Volume: 1
• Issue: 1

Dates

online

23 - 11 - 2015

accepted

6 - 10 - 2015

received

9 - 9 - 2015

Contributors

author

Ming Li

• Ocean College, Zhejiang University, Yuhangtang Rd.
  866, Hangzhou 310058, China;

author

Jianxing Leng

• Ocean College, Zhejiang University, Yuhangtang Rd.
  866, Hangzhou 310058, China;

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Identifiers

DOI

10.1515/wwfaa-2015-0004