On von Kármán spectrum from a view of fractal

• Autorzy: Ming Li , Jianxing Leng
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Waves, Wavelets and Fractals
• Rocznik: 2015
• Tom: 1
• Numer: 1

Daty

otrzymano

2015-09-09

zaakceptowano

2015-10-06

online

2015-11-23

Twórcy

autor

Ming Li

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

autor

Jianxing Leng

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

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Identyfikatory

DOI

10.1515/wwfaa-2015-0004