Resolvent modes as the foundation for LES wall models

In Wall-Modelled Large-Eddy Simulations (WMLES), the flow away from a solid surface is resolved while the wall-layer is modelled. The present research aims to use Resolvent Analysis to synthesize near-wall eddies that are neglected in WMLES, thereby resulting in a more accurate representation of the momentum exchange between the bypassed near-wall layer and the outer flow. We integrate the Equilibrium Stress Layer (ESL) equation from the wall to the inner/outer layer interface using a mixing-length model to parametrize the turbulence in this region. Resolvent Analysis is used to extract modes that are added to the velocity in the inner layer, resulting in an additional known stress term in the ESL. This term is a time- and space-dependent forcing that increases the wall-stress fluctuations and the turbulent kinetic energy in the wall layer (which is not known when standard wall-models are used). Since the resolvent modes support part of the inner-layer Reynolds stresses, the eddy viscosity must be modified. Additional continuity conditions must be applied at the inner-outer layer interface, which can be used to determine both the eddy-viscosity modifications and the amplitude of the resolvent modes. Several strategies to implement these conditions will be discussed.