Title: Partial differential equations filtering of forced and decaying homogeneous isotropic turbulent fields

Authors: Waleed Abdel Kareem

Addresses: Department of Mathematics, Faculty of Science in Suez, Suez University, Suez, Egypt; Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia

Abstract: The non-linear diffusion and the fourth order partial differential equations (PDEs) are used to decompose a turbulent flow field into coherent and incoherent fields. The methods are applied against the velocity fields for both forced and decaying homogeneous isotropic turbulence. The aim of this paper is to examine the ability of the partial differential equations in extracting coherent vortices from a turbulent flow field in the spatial domain without transforming the turbulent velocity field into frequency domain. The comparison against the standard methods such as the wavelet and Fourier decompositions are also considered. The three dimensional velocity fields with a resolution of 1283 are generated using the Lattice Boltzmann method (LBM) where the Taylor micro-scale Reynolds numbers are 72 and 29 for forced and decaying fields, respectively. Results show that the coherent field and the random incoherent part contribute to all scales in the inertial range. The two filtering methods approximately identify the coherent fields without any loss of the geometrical structure of the vortices. The statistical properties such as flatness, skewness and spectrum of the extracted fields (coherent and incoherent parts) are also investigated for each filtering method.

Keywords: partial differential equations; nonlinear diffusion; fourth order PDEs; homogeneous turbulence; coherent flows; incoherent flows; filtering; isotropic turbulence; turbulent flow; coherent vortices; Lattice Boltzmann method; LBM.

DOI: 10.1504/PCFD.2013.057099

Progress in Computational Fluid Dynamics, An International Journal, 2013 Vol.13 No.6, pp.346 - 356

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 08 Oct 2013 *

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