The Role of Law-of-the-Wall and Roughness Scale in the Surface Stress Model for LES of the Rough-wall Boundary Layer.

Large-eddy simulation (LES) of the high Reynolds number rough-wall boundary layer requires both a subfilter-scale model for the unresolved inertial term and a ``surface stress model'' (SSM) for space-time local surface momentum flux. Standard SSMs assume proportionality between the local surface shear stress vector and the local resolved-scale velocity vector at the first grid level. Because the proportionality coefficient incorporates a surface roughness scale $z_{0}$ within a functional form taken from law-of-the-wall (LOTW), it is commonly stated that LOTW is ``assumed,'' and therefore ``forced'' on the LES. We show that this is not the case; the LOTW form is the ``drag law'' used to relate friction velocity to mean resolved velocity at the first grid level consistent with $z_{0}$ as the height where mean velocity vanishes. Whereas standard SSMs do not force LOTW on the prediction, we show that parameterized roughness does not match ``true'' $z_{0}$ when LOTW is not predicted, or does not exist. By extrapolating mean velocity, we show a serious mismatch between true $z_{0}$ and parameterized $z_{0}$ in the presence of a spurious ``overshoot'' in normalized mean velocity gradient. We shall discuss the source of the problem and its potential resolution.