Golden Ratio Phenomenon of Random Data Obeying von Karman SpectrumReport as inadecuate




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Mathematical Problems in EngineeringVolume 2013 2013, Article ID 130258, 6 pages

Research Article

School of Information Science and Technology, East China Normal University, No. 500, Dong-Chuan Road, Shanghai 200241, China

Department of Computer and Information Science, University of Macau, Avenue Padre Tomas Pereira, Taipa 1356, Macau

Received 9 July 2013; Accepted 26 July 2013

Academic Editor: Ezzat G. Bakhoum

Copyright © 2013 Ming Li and Wei Zhao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

von Karman originally deduced his spectrum of wind speed fluctuation based on the Stokes-Navier equation. Taking into account, the practical issues of measurement and-or computation errors, we suggest that the spectrum can be described from the point of view of the golden ratio. We call it the golden ratio phenomenon of the von Karman spectrum. To depict that phenomenon, we derive the von Karman spectrum based on fractional differential equations, which bridges the golden ratio to the von Karman spectrum and consequently provides a new outlook of random data following the von Karman spectrum in turbulence. In addition, we express the fractal dimension, which is a measure of local self-similarity, using the golden ratio, of random data governed by the von Karman spectrum.





Author: Ming Li and Wei Zhao

Source: https://www.hindawi.com/



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