The role of bulk eddy-viscosity variation on the log-layer mismatch observed in wall-modeled large-eddy simulations

We investigate the role of the bulk eddy-viscosity variation on the well-known log-layer mismatch problem. An analysis of the mean momentum-balance shows that the modeled stress term close to the wall can dominate because of the bulk eddy-viscosity. Consequently, the momentum-balance equation lacks a degree-of-freedom and the mean velocity conforms to an incorrect profile to satisfy the momentum-balance. We show that zonal enforcement of the target mass flow-rate can be an effective strategy to introduce an additional degree of freedom to the mean momentum-balance, which led to a significant reduction in the log-layer mismatch. When the mass flow-rate is enforced zonally, the filtered velocity field attains its own constant velocity-scale above the Reynolds-averaged field, supporting the hypothesis that there exists an artificial boundary layer above the Reynolds-averaged region. We simulate turbulent channel flows at friction Reynolds numbers of 2000 and 5200 on coarse meshes that would put the first point away from the wall well into the logarithmic layer. Second-order turbulence statistics and one-dimensional velocity spectra agree well with the direct numerical simulation benchmark data when results are normalized by the velocity-scale extracted from the filtered velocity field. Additionally, the error in the skin-friction coefficient for friction Reynolds numbers of 2000 decreased from $14.1\%$ to $2.5\%$ when we enforced the mass flow-rate zonally.