  Insights gained from modal analysis are invoked for predictive large-eddy
simulation (LES) wall modeling. Specifically, we augment the law of the wall
(LoW) by an additional mode based on a one-dimensional proper orthogonal
decomposition (POD) applied to a 2D turbulent channel. The constructed wall
model contains two modes, i.e., the LoW mode and the POD-based mode, and the
model matches with the LES at two, instead of one, off-wall locations. To show
that the proposed model captures non-equilibrium effects, we perform a-priori
and a-posteriori tests in the context of both equilibrium and non-equilibrium
flows. The a-priori tests show that the proposed wall model captures extreme
wall-shear stress events better than the equilibrium wall model. The model also
captures non-equilibrium effects due to adverse pressure gradients. The
a-posteriori tests show that the wall model captures the rapid decrease and the
initial decrease of the streamwise wall-shear stress in channels subjected to
suddenly imposed adverse and transverse pressure gradients, respectively, both
of which are missed by currently available wall models. These results show
promise in applying modal analysis for turbulence wall modeling. In particular,
the results show that employing multiple modes helps in the modeling of
non-equilibrium flows.
