Smart Structures and Systems

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Hierarchical structure parameters in three dimensional turbulence: She-Leveque model

  • Ahmad, Imtiaz (Department of Mathematics, Mirpur University of Science and Technology (MUST)) ;
  • Hadj-Taieb, Lamjed (College of Engineering, Department of Mechanical Engineering, Prince Sattam Bin Abdulaziz University) ;
  • Hussain, Muzamal (Department of Mathematics, Government College Universit Faisalabad) ;
  • Khadimallah, Mohamed A. (Civil Engineering Department, College of Engineering, Prince Sattam Bin Abdulaziz University) ;
  • Taj, Muhammad (Department of Mathematics, University of Azad Jammu and Kashmir) ;
  • Alshoaibi, Adil (Department of Physics, College of Science, King Faisal University)
  • Received : 2020.09.16
  • Accepted : 2022.04.02
  • Published : 2022.05.25
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Abstract

Hierarchical structure parameters, proposed in She-Leveque model, are investigated for velocity components obtained from different flow types over a large range of Reynolds numbers 255 < Re𝜆 < 720. The values of intermittency parameter 𝛽, with respect to a fixed velocity component, are observed nearly same for all four types of turbulence. The parameter 𝛾, for streamwise velocity components is nearly the same but significantly different for vertical components in different flows. It is also observed that for both parameters, an obvious relation between the longitudinal and transverse components 𝛽T < 𝛽L (and 𝛾T < 𝛾L) always holds. However, the difference between 𝛽L and 𝛽T is found very small in all types of turbulent flows, we studied here. It is evidenced that at low Reynolds numbers, the deviations from K41 scaling are mainly due to the most intense structures and slightly because of more heterogeneous hierarchy of fluctuation structures. However, at higher Reynolds numbers the deviations seem as a consequence of the most intense structures only. Over all, the study suggests that the hierarchy parameter 𝛽 may be consider as a universal constant.

Keywords

Acknowledgement

This project was supported by the Deanship of Scientific Research at Prince Sattam Bin Abdulaziz University under research project no. 2019/01/10886

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