An extended local balance model of turbulence, based on a new transport equation for the dissipation rate with a negative diffusion coefficient, is presented. Analytical solutions for the mean velocity and the dissipation rate for the turbulent Couette-Taylor problem are derived. The dependence of torque on the Reynolds number is obtained. These solutions depend only on two constants k=0.4 and C=9.5 of the turbulent boundary layer and, within the limits of a narrow channel, are reduced to the well-known von Karman's solutions for planar Couette flow. Strange attractor behavior in this limit is also observed.
The article is focused on one of the ways to apply the generalized local balance turbulence model for Couette-Taylor flow. The ultimate resistance law can be expressed in terms of the Lambert W function, and its asymptotic behaviour at very large Taylor and Reynolds numbers can be easily obtain using the asymptotes of this function. Comparison with the recent theoretical approaches and some experiments are made.
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