Assessment of confinement effects on decay terms of Reynolds-stress transport equations*

The Reynolds stress transport equations provide a valuable framework for developing second-order closure models for the unclosed terms in Reynolds-averaged Navier-Stokes equations. In this work, we specifically focus on the unclosed terms associated with the decay of Reynolds stresses. To study these terms in isolation, we consider a canonical setup of forced turbulence with walls encompassing a wide range of turbulence anisotropies. In this setting, only the decay of the Reynolds-stress terms needs to be closed due to the absence of mean velocity gradients. However, due to the confinement effect of the walls, the decay rate of Reynolds stress and its anisotropy is modified. We present a systematic study of these modifications by analyzing the exact Reynolds-stress equations for various volumetrically forced high-fidelity simulations.