A nonlinear return-to-isotropy model with Reynolds number and anisotropy dependency

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Abstract
A new computational model for the return to isotropy is presented. In order to reproduce the significant role of the third invariant III b (=b ij b jk b ki ) of the Reynolds stressanisotropyb ij [=u iu j /(2k)−(1/3)δ ij ] in the return‐to‐isotropy process, a nonlinear return‐to‐isotropy model is formulated by a Taylor series expansion up to fifth power of b ij . Then the strong realizability condition for non‐negativity of the component energies is utilized to reduce the number of model constants produced. Correction for the low Reynolds number effect is then included by investigating an energy‐weighted average time scale of eddies over the three‐dimensional energy spectrum. Superiority of the proposed model performance is exemplified by a number of test computations of homogeneous relaxing turbulence in a wide range of turbulenceReynolds number and III b .