Asymptotic analysis of turbulent boundary-layer flow of purely viscous non-Newtonian fluids

• Asymptotic structure of purely viscous non-Newtonian boundary layers is studied.
• Hypotheses are based on order of magnitude of the terms in the equations of motion.
• Results show that a two-layered structure remains valid for a power law fluid.
• The thickness of the viscous layer depends on the power law index.
• Linear coefficient of the log-law is shown to vary with the reciprocal of n.

The asymptotic structure of turbulent boundary layers of purely viscous non-Newtonian systems is investigated through the intermediate variable technique. The cases of power-law and Carreau fluids are discussed in detail. Results show that a classical two-layered structure persists, with a viscous layer thickness that is dependent on the power-law index, n, and a logarithmic solution in the fully turbulent region. For Carreau fluids, in general, a three-layered structure emerges, with two nested viscous sub-layers. Experimental and numerical data from other authors are used to determine the functional behaviour of the linear coefficient of the log-law with n.