Wall-bounded turbulent shear flow: Analytic result for a universal amplitude

In the turbulent boundary layer above a hat plate, the velocity profile is known to have the form nu = nu (0)[(1/kappa )ln z+const]. The distance from the wall in dimensionless units is z and v(0) is a uniquely defined velocity scale. The number kappa is universal, and measurements over several decades have shown that it is nearly 0.42. We use a randomly stirred model of turbulence to derive the above law and find kappa= root 108/125 pi similar or equal to0.52.