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

Abstract

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.