Anisotropic Diffusion for Filtering of Forced Homogeneous Isotropic Turbulence

The anisotropic diffusion model (ADM) that proposed for noise removal of band-pass signals is developed to a three dimensional model to decompose forced homogeneous turbulence into coherent and incoherent parts. The incoherent part represents the noisy data in the flow field, however the coherent part represents the important data for turbulence studies. The velocity flow field is generated by the Lattice Boltzmann method with resolutions of 128 3 and 256 3 grid points, respectively. The high rotational method, namely the Q-identifying method, is used to identify the vortical structures. The scalar tensor Q is the second invariant of the velocity gradient tensor (u). The ADM filtering model is applied against the scalar field Q. Results show that the model is a promising tool for fluid dynamics applications. The method identifies the coherent vortices with similar geometrical shapes to the vortices in the original field. The proposed filtering method also isolates the non-organized structureless regions successfully. The phenomenon of turbulence was discovered physically and is still largely need to explore by mathematical techniques. The analysis of turbulent flow field is too much complicated than that of laminar flows. So, extraction and filtering of homogeneous isotropic turbulence are important processes. The extraction process depends on identifying different scales of the flow, however the filtering process divides the fluid flow field into the coherent and incoherent parts. Most of filtering methods for turbulent problems are applied using the frequency analysis such as the wavelet and Fourier decompositions. These methods are applied against 2D and 3D velocity fields to extract the organized coherent and the random incoherent fields. Wavelets method has significantly impacted many areas of science and engineering (e.g., signal and image processing, speech recognition, and computer graphics). This unification has its own dynamics, allowing scientific cooperation between researchers from very various fields and modifying deeply the scientific perception of many issues in each of these fields. In fluid mechanics, wavelets were first used in the early 1990s, almost since their invention, to analyze the structure and dynamics of two dimensional flow (M. Farge. (1), M. Farge et al. (2), (3), (4),