Designing LES of the Atmospheric Boundary Layer to Capture Law-of-the-Wall: Surface Stress Model and the von Kármán Constant

As discussed in another abstract, large-eddy simulation (LES) of the atmospheric boundary layer (ABL) has been plagued by an inability to capture the law-of-the-wall (LOTW) in mean wind through the surface layer when shear dominated. LES systematically over-predicts the mean velocity gradient in the inertial surface layer creating an "overshoot" with a number of negative consequences of predictions of ABL related mechanical and thermo dynamics. We describe in the other abstract the fundamental source of the overshoot and a process for its elimination. This requires the simulation to be systematically adjusted within a parameter space until three parameters exceed critical values that depend on the constant within the subfilter-scale (SFS) stress model and the aspect ratio of the grid. This is necessary to remove the influence of a spurious length scale that arises in the transition from the exact continuous dynamical system on paper to the discretized dynamical system advanced on the computer.

However, in addition to the model for SFS stress, LES of the rough surface ABL also includes a model for the horizontal components of the total stress tensor on the rough surface. This model cannot be exact, thus producing another potential source for the introduction of spurious scales that can interfere with LOTW, at the surface rather than within the computational domain. We show that current models do, in fact, introduce additional deviations from LOTW scaling at the surface. The effect is obscured then the spurious SFS frictional effect is strong and an overshoot exists. It appears when as the overshoot is removed and further adjustments are made to move the simulation into the supercritical region of the parameter space to capture LOTW. As the spurious influence of the surface stress model appears it grows in severity as the LES moves further into the supercritical region of the parameter space. In this discussion we analyze the details of current surface stress models and show that the source of the spurious influence is in the fluctuating component of the surface stress models, typically make proportional to fluctuating velocity at the first grid level. We show that a spurious sink in velocity variance exists in current surface stress models that negatively influences the LOTW at the surface. We show how current models can be reformulated to remove the sink and that the removal has two significant influences: (1) it significantly improves prediction of LOTW and (2) it influences the prediction of the von Kármán constant. In particular, the von Kármán constant increases by 5.6% as the sink is removed. We also explore further influences on the von Kármán constant prediction and show that, for both the Smagorinsky and one equation eddy viscosity models, there exists a second parameter space between model constant and grid aspect ratio, and that the von Kármán constant is weakly influenced by the position in this parameter space. Thus, the design of large-eddy simulation of the atmospheric boundary layer should take into account the position of the LES within two interrelated parameter spaces and the structure of the surface stress model.