Extended local balance model of turbulence and Couette-Taylor flow

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.