Modeling the law of the wake using an offset from the wall

Wall-bounded turbulence is present in many flows, with the famous ``law of the wall'' of von Karman followed by the also famous ``law of the wake'' of Coles. A new model for the ``wake function'' is proposed and calibrated using direct numerical simulation data of channel flow and zero pressure gradient boundary layer at high Reynolds numbers. The model uses an explicit offset from the wall (thus preserving a logarithmic overlap layer) and is shown to fit the data very well. As an added contribution, the model of Coles is also improved by adding the offset.