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. Typically, the interface between inner and outer layers does not coincide with the first grid point, and a buffer region is used to allow eddies to be created and develop into physically realistic structures. 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. As a first step we calculate the force due to selected resolvent modes, and add it to the Navier-Stokes equations, that are subsequently solved in a Wall-Resolved LES configuration. The use of a wall-resolving grid allows us to minimize or remove errors due to grid resolution, errors in the sub-filter scale model or in the wall model. We can then isolate the effect of the resolvent-mode forcing on the flow field, prior to their use in an actual WMLES. The resolvent modes are characterized by their wavelengths in streamwise and spanwise directions, by their frequency and, very importantly, by the extent of their support in the wall-normal direction. We find that (1) by changing the wavelengths of the resolvent modes we can affect independently various Reynolds stresses; (2) the resolved stresses adjust to the forcing, both in terms of their magnitude, and spectral distribution of the eddies responsible for the generation of shear stress〈u'v'〉; (3) that resolvent modes that span the inner/outer layer interface are more effective than those that lie entirely below this interface. Future work will concentrate on deploying optimal combinations of resolvent modes to generate eddy content in the buffer region in actual WMLES, for increasing Reynolds numbers and in increasingly complex flow configurations.