Fourier Decomposition and Anisotropic Diffusion Filtering of Forced Turbulence

Abstract

The Fourier decomposition and the anisotropic diffusion filtering model are used to extract various flow field scales and their coherent and incoherent parts. The different flow field scales are identified using the Fourier decomposition. Three cutoff wavenumbers are chosen to extract large, medium and fine scale velocity fields, respectively. Then, the anisotropic diffusion model is applied against the obtained velocity fields for each scale to define the coherent and incoherent parts. The forced turbulent velocities are simulated using the lattice Boltzmann method with resolutions [Formula: see text] and [Formula: see text], respectively. The Fourier decomposition of the velocity fields make the filtering process very difficult, so the anisotropic diffusion parameters should be chosen carefully to overcome the problems arising from the sharp cutoffs process. Although of such difficulties, results show that the anisotropic diffusion model successfully isolate the incoherent parts for each scale. It is shown that the incoherent parts are existed everywhere in the flow fields and they are not limited to the fine scales. The coherent fields that are identified by the anisotropic diffusion filtering method are found similar to the extracted scales by the Fourier decomposition. The incoherent regions are fewer in the large scale fields compared with that found in the intermediate and fine fields. The statistical characteristics of the three flow field scales as well as their coherent and incoherent parts are studied and compared with the universal characteristics of turbulence.