Harmonic analysis filtering techniques for forced and decaying homogeneous isotropic turbulence

  • Authors:

  • Waleed Abdel Kareem;Tamer Nabil;Seiichiro Izawa;Yu Fukunishi

  • Affiliations:

  • Suez University, Faculty of Science, Department of Mathematics, Suez, Egypt and King Khalid University, Faculty of Science, Department of Mathematics, P. Box 9004, Abha, Saudi Arabia;Suez Canal University, Faculty of Computers and Informatics, Basic Science Department, Ismailia, Egypt and King Khalid University, Faculty of Science, Department of Mathematics, P. Box 9004, Abha, ...;Graduate School of Engineering, Department of Mechanical Systems and Design, Tohoku University, Sendai 980-8579, Japan;Graduate School of Engineering, Department of Mechanical Systems and Design, Tohoku University, Sendai 980-8579, Japan

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2013

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Abstract

Harmonic analysis filtering methods are used to decompose 3D forced and decaying turbulent fields into coherent and incoherent parts. The filtering methods are the curvelets, wavelet and dual-tree complex wavelet filtering techniques. The methods are applied against the velocity fields of forced and decaying homogeneous isotropic turbulence. The velocity fields are generated using the Lattice Boltzmann Method (LBM) with a resolution of 128^3 where the Taylor micro-scale Reynolds numbers are 72 and 29 for forced and decaying fields, respectively. The main objective of this study is to use other different filtering methods rather than depending only on wavelet and Fourier decompositions. Using different filtering methods may help in turbulence modeling, improving our knowledge about the structure of turbulent flow, choosing the appropriate filtering method and extracting general characteristics of the flow under study. Results show that the coherent and the random incoherent fields contribute to all scales in the inertial range, but the statistical behavior is different for each field. The three filtering methods approximately identify the coherent fields with the same geometrical shapes of the organized vortical structures. The statistical properties such as flatness, skewness and spectrum of the extracted fields (coherent and incoherent parts) are also investigated for each filtering method. The joint PDFs between the third and second invariants of the velocity gradient tensor are also studied. The joint PDFs for the coherent parts are found similar to previous topological studies of isotropic turbulence; however the incoherent PDFs show different topological features.