  Wall modelling in large-eddy simulation (LES) is necessary to overcome the
prohibitive near-wall resolution requirements in high-Reynolds-number turbulent
flows. Most existing wall models rely on assumptions about the state of the
boundary layer and require a priori prescription of tunable coefficients. They
also impose the predicted wall stress by replacing the no-slip boundary
condition at the wall with a Neumann boundary condition in the wall-parallel
directions while maintaining the no-transpiration condition in the wall-normal
direction. In the present study, we first motivate and analyse the Robin (slip)
boundary condition with transpiration (nonzero wall-normal velocity) in the
context of wall-modelled LES. The effect of the slip boundary condition on the
one-point statistics of the flow is investigated in LES of turbulent channel
flow and flat-plate turbulent boundary layer. It is shown that the slip
condition provides a framework to compensate for the deficit or excess of mean
momentum at the wall. Moreover, the resulting nonzero stress at the wall
alleviates the well-known problem of the wall-stress under-estimation by
current subgrid-scale (SGS) models. Secondly, we discuss the requirements for
the slip condition to be used in conjunction with wall models and derive the
equation that connects the slip boundary condition with the stress at the wall.
Finally, a dynamic procedure for the slip coefficients is formulated, providing
a dynamic slip wall model free of a priori specified coefficients. The
performance of the proposed dynamic wall model is tested in a series of LES of
turbulent channel flow, non-equilibrium three-dimensional channel flow, and
flat-plate turbulent boundary layer. The results show that the dynamic wall
model is able to accurately predict one-point turbulence statistics for various
flow configurations, Reynolds numbers, and grid resolutions.
