Wall Region in Turbulent Shear Flow of Non-Newtonian Fluids

A revision of mixing-length theory for wall-bounded turbulent shear flows is proposed. An analysis of the energy balance of medium-sized eddies (those that scale with the distance from the wall) suggests that the slope of the logarithmic velocity profile should be proportional to the square root of the Reynolds stress at the location where most of the turbulent energy is produced. Application of this prediction to turbulent flow of power-law fluids indicates that the slope of the velocity profile decreases with decreasing flow-behavior index, in excellent agreement with experimental data. Visco-elasticity may change the thickness of the viscous sublayer, but not the slope of the velocity profile.