The "law of the wake" for the outer layer of canonical wall-bounded turbulence is revisited, using reference data of channel flow DNS at Ret = 5200. Our focus is thus on the "wake function" F(Y) with Y=y/h: the excess profile one adds to the logarithmic profile to obtain Coles composite profile. For that, the function Q(Y) = Y F'(Y) from the DNS is examined in details. We propose a simple model for Q(Y), which cover the full range up to Y = 1. Its analytical integration then provides a simple and complete model for F(Y), which is seen to recover well the DNS data. The model is then further tested on a ZPG boundary layer: here too, the obtained F(Y) model is seen to recover well the DNS data.
An immersed lifting (and recently also dragging) line model has been developed to efficiently simulate, using the vorticity-velocity formulation, incompressible flows involving slender wings and/or blades and turbulent wakes: our "vortex particle-mesh" (VPM) code. An actuator line method has also been implemented in our 4rth-order staggered-mesh velocity-pressure code; which also allows for realistic atmospheric boundary layer simulations. A few examples of applications involving LES of complex wakes and interactions (also with the ground) will be presented concerning wings, rotorcraft, and wind turbines.