Multiresolution and nonlinear diffusion filtering of homogeneous isotropic turbulence

Waleed Abdel Kareem, Tamer Nabil, Seiicherio Izawa, Yu Fukunishi

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


The multiresolution (Gabor and wavelet transforms) and nonlinear diffusion filtering (NDF) methods are investigated to extract the coherent and incoherent parts of a forced homogeneous isotropic turbulent field. The aim of this paper is to apply two different analyses to decompose the turbulent field into organized coherent and random incoherent parts. The first analysis filtering process (Gabor and wavelet transforms) is based on the frequency domain; however the second NDF filtering analysis is implemented in the spatial domain. The turbulent field is generated using the Lattice Boltzmann method (LBM) with a resolution of 1283, and the Q-identification method is used to extract the elongated vortical structures. The three filtering methods are applied against the scalar Q-field rather than a vector field (velocity or vorticity fields). The Gabor transform and the orthogonal wavelet with approximately symmetric basis are applied to filter out incoherent noise. Filtering in the Gabor domain is done in the highest quarter frequency values, whereas filtering in the wavelet domain is done using sub-band dependent thresholding. The NDF method is based on explicit finite-difference discretization in the spatial domain. Results indicate that the three filtering methods smoothly identify the coherent and incoherent parts. Although the NDF method isolates the incoherent part more smoothly, the cross sections of the vortices in the coherent part are changed. Also, the Gabor filtering method can remove few incoherent points from the flow field, compared with the other two methods. The wavelet method tends to identify the coherent vortices and remove the incoherent noise without any change in the physical structure of the turbulent field.

Original languageEnglish
Article number1350054
JournalInternational Journal of Computational Methods
Issue number1
Publication statusPublished - 2014 Feb
Externally publishedYes


  • Gabor transform
  • Homogeneous isotropic turbulence
  • nonlinear diffusion method
  • wavelet decomposition

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Computational Mathematics


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