A physical basis of the slip-wall model for wall-modeled large-eddy simulations

Conducting large-eddy simulations (LES) implies the use of LES filters, which are commensurate with the local grid spacing. For wall modeled LES (WMLES) where the grid spacing in the wall-normal direction scales with the local boundary layer height, the near-wall turbulence is typically not well resolved. Because of the poorly-resolved near-wall region, the no-slip condition no longer applies; and a near-wall closure (an LES wall model) must be used. Recently S. T. Bose & P. Moin (Physics of Fluids, 26, 015104, 2014, DOI: http://dx.doi.org/10.1063/1.4849535) proposed to use a Robin-type near-wall closure u_i -l_p∂u_i/∂ y = 0, where u_i's are the slip velocities at the wall, l_p is a slip length and the subscript i = 1, 2, 3 indicate the streamwise, wall-normal and spanwise directions respectively. Different from most physics-based LES wall models, this slip wall model is based on the use of a differential LES filter. In the present work, we provide a physics-based interpretation for this Robin-type wall closure. We show that the model is compatible with arbitrary LES filter and it can be motivated by the same considerations that lead to the equilibrium wall model. The possibility of explicitly accounting for non-equilibrium effects is briefly discussed. The model is tested in turbulent channel flow and its performance is compared against other wall models. The flow quantities of interest here include the mean velocity, the variance of the streamwise velocity fluctuation and the instantaneous wall shear stress.