On von Kármán spectrum from a view of fractal

Ming Li; Jianxing Leng

Waves, Wavelets and Fractals (2015)

  • Volume: 1, Issue: 1
  • ISSN: 2449-5557

Abstract

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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.

How to cite

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Ming Li, and Jianxing Leng. "On von Kármán spectrum from a view of fractal." Waves, Wavelets and Fractals 1.1 (2015): null. <http://eudml.org/doc/276614>.

@article{MingLi2015,
abstract = {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.},
author = {Ming Li, Jianxing Leng},
journal = {Waves, Wavelets and Fractals},
keywords = {The von Kármán spectrum; fluctuation of wind speed; fractional Ornstein-Uhlenbeck process; Kolmogorov’s −5/3 law},
language = {eng},
number = {1},
pages = {null},
title = {On von Kármán spectrum from a view of fractal},
url = {http://eudml.org/doc/276614},
volume = {1},
year = {2015},
}

TY - JOUR
AU - Ming Li
AU - Jianxing Leng
TI - On von Kármán spectrum from a view of fractal
JO - Waves, Wavelets and Fractals
PY - 2015
VL - 1
IS - 1
SP - null
AB - 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.
LA - eng
KW - The von Kármán spectrum; fluctuation of wind speed; fractional Ornstein-Uhlenbeck process; Kolmogorov’s −5/3 law
UR - http://eudml.org/doc/276614
ER -

References

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