How does wall modeling impact the momentum transfer of the modeled wall turbulence?

As a modeled representation of the high-resolution solutions, wall-modeled large-eddy simulation (WMLES) is supposed to represent the projected solutions in a low-resolution solution space. However, the utilization of a wall model is essentially a restriction on the solution space. For example, an underlying assumption of the wall model is that the mean profile is applicable to the instantaneous flow field. The recent development and application of the WMLES mainly focus on matching the low-order statistics, which could be case-specific.

To explore the generalizability of a wall model, the dynamical-system point of view is adopted. I examine the structures in the channel flow that are resolved in WMLES. Specifically, I focus on the modeled momentum transfer of the near-wall turbulence by those structures. It turns out that the wall model is not necessarily restricting an accurate prediction of the flow at the matching location, but its interaction with the subgrid-scale (SGS) model leads to possible inaccuracy far from the wall.