Modified log-wake law for turbulent flow in smooth pipes

The Authors have found a clever solution to the discontinuity of the velocity gradient at the axis of uniform turbulent pipe flow in the log-wake model by means of a modification with a cubic correction function. Their modified log-wake law leads to a very good replication of the velocity profiles of a large series of smooth pipe flow experiments (see Fig. 5). Moreover, it leads to a correct eddy viscosity profile in the centre of the pipe that is not obtained with the original log-wake law. This is important for the determination of the diffusion of different quantities in the centre region of the pipe. However the physical reasoning by the Authors is not always convincing.