Reynolds number dependence in the decay of homogeneous anisotropic turbulence

The Reynolds stress transport (RST) equation is a widely used framework in Reynolds-averaged Navier–Stokes (RANS) modeling, offering improved representation of turbulence anisotropy and history effects compared to eddy viscosity models. Within the RST equation there are several unclosed terms, including the decay of Reynolds stress. Homan et al. (Phys. Rev. Fluids, 2024) proposed a cubic model for the decay term and tuned model coefficients using data from large eddy simulations (LES) of anisotropically forced homogeneous turbulence at infinite Reynolds number. In the present work, we investigate the Reynolds number dependence of the stress decay by performing direct numerical simulations (DNS) of anisotropically forced homogeneous turbulence at a range of finite Re. Our results demonstrate that while the cubic model proposed by Homan et al. accurately captures decay behavior at high Re, deviations emerge as Re decreases. We quantify these deviations and propose Reynolds number dependent corrections to the model coefficients. These corrections improve the predictive performance of the model for practical RANS applications involving moderate Re turbulence.