Title: Applicability of double power law model for the statistical analysis of meteorological wind velocity time series data

Authors: Shashank Bhardwaj; Sammedkumar Patil; Vijesh V. Joshi

Addresses: Hero MotoCorp, Tada, 524401, Andhra Pradesh, India ' Powervector Tech. Pvt. Ltd., Karnataka, 590001, India ' School of Mechanical Engineering, Vellore Institute of Technology, Vellore, 632014, Tamil Nadu, India

Abstract: This paper is devoted to the statistical analysis of wind velocity variance time-series data obtained over the Bay of Bengal to investigate the turbulent energy cascade. The spectral distribution of wind velocity variance followed two different power laws. It was proposed that these power laws express the inertial subrange and the dissipation range. So, to cover these spectral ranges of frequencies, a double power-law(DPL) model was employed. The statistical analysis conducted on the power spectrum provided equations of both the power laws with high confidence levels. The Heaviside functions helped to formulate a single equation describing the entire spectral density. It was observed that the DPL model was very compliant with the -5/3 power law, and the statistical tests concluded that this model was a better fit with a close to 96% R² score when compared to a 90% R² score of -5/3 power law.

Keywords: Kolmogorov Energy Spectra; DPL; double power law; -5/3 power law; turbulence; inertial subrange; time series analysis.

DOI: 10.1504/IJCSM.2023.133632

International Journal of Computing Science and Mathematics, 2023 Vol.18 No.2, pp.152 - 161

Received: 23 Jul 2021
Received in revised form: 04 Aug 2022
Accepted: 05 Aug 2022
Published online: 26 Sep 2023 *

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