INNER REGION OF SMOOTH PIPES AND OPEN CHANNELS

The eddy viscosity function, proposed in this note, is characterized b y a damping coefficient, Gamma(o), the asymptotic value for a large Re ynolds number. It is related to the Reynolds stress in the near-wall r egion. As the Reynolds number decreases in pipes and subcritical open- channel flow, the velocity profile is progressively displaced from the universal log-linear relation, which is accounted for by increasing v alues of the damping coefficient. The inverse relation between the Rey nolds number and the damping coefficient follows from an analytical so lution of the velocity profile, which is composed of both a viscous an d a turbulent component. The inverse relation, derived from the logari thmic gradient of the viscous component, also yields the minimum Reyno lds number for completely turbulent flow. Furthermore, it provides the basis for the correlation of various characteristics in the laminar-t urbulent transition and of heat and mass transfer coefficients. All of these relations, which are singular functions of the asymptotic value of the damping coefficient, Gamma(o), support the cubic, rather than the quartic, variation of Reynolds stress and eddy viscosity in the ne ar-wall region.