It is well known that in the case of turbulent flow over smooth boundaries, the velocity distribution in the neigh- i bourhood of the wall is given by the law of the wall, c written as
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0001924000056530/resource/name/S0001924000056530_equ01.gif?pub-status=live)
where u is the turbulent mean velocity at a normal distance of y from the boundary, u* is the shear velocity equal to
being the boundary shear stress and ρ the mass density of the fluid and v is the coefficient of kinematic viscosity. In the viscous sublayer, eqn. (1) becomes
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0001924000056530/resource/name/S0001924000056530_equ03.gif?pub-status=live)
and in the turbulent flow region above the sublayer and the transition region, for yu*/v> 30, eqn. (1) becomes
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0001924000056530/resource/name/S0001924000056530_equ04.gif?pub-status=live)
where A and B are coefficients.