The Walker Function

The quantitative description of turbulent flows is known to be severely hampered by the extremely rapid variations in the mean and higher-order statistics in the near-wall region. Some very early studies [1, 2, 3] showed that the basic structure of an attached turbulent boundary layer consists of a viscous wall layer, in which the turbulent and laminar stresses are of comparable magnitude, and a defect layer, in which the velocity profile may be expressed in terms of a small perturbation to the external flow solution [4]. Also, [1, 2, 3] showed that this structure naturally leads to a universal velocity solution that has logarithmic behavior and depends on the velocity and length scales based on the friction velocity.