A new divergence-free synthetic eddy method for generating homogeneous isotropic turbulence with a prescribed energy spectrum

• Published in: Computers & fluids 2023-03, Vol.253, p.105788, Article 105788
• Main Authors: Cai, Yunzhu, Wan, Jiawei, Kareem, Ahsan
• Format: Article
• Language: English
• Subjects: Divergence-free; Energy spectrum; Homogeneous isotropic turbulence; Multi-scale; Synthetic eddy method
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2023.105788

A new divergence-free synthetic eddy method (SEM) for the generation of homogeneous isotropic turbulence (HIT) with a prescribed energy spectrum is presented. In the proposed method, the divergence-free consistent synthetic velocity field is generated from the curl of a vector potential field following conventional SEM methodology. A carefully designed formula is constructed for the computation of the local vector potential field induced by each synthetic eddy, with which a desired velocity spectrum tensor can be satisfied for the synthetic incompressible turbulence exactly. The proposed method is characterized by a multi-scale feature in which the length scales of synthetic eddies are determined by a dimensionless random variable satisfying a particular probability distribution function (PDF). The mathematical relation, concerning the energy spectrum of the synthetic turbulence, the shape function of the eddies and the PDF of the eddy-scale-related random variable, is derived. This assists in determining either the shape function or the PDF. The performance of the proposed method is examined by synthesizing HIT satisfying a theoretical energy spectrum model and HIT identified in a wind-tunnel experiment. •A synthetic eddy method for generating homogeneous isotropic turbulence is developed.•The length scales of synthetic eddies are determined by a defined random variable.•The synthetic turbulence satisfies the prescribed velocity spectrum tensor.•All related second-order statistics of the synthetic turbulence are derived analytically.•The enforcement of the divergence-free constraint on a finite volume grid is presented.