Energy dissipation in shear driven turbulence

The Navier-Stokes equations are utilized to derive upper bounds on the turbulent energy dissipation rate for an incompressible Newtonian fluid confined between parallel comoving plates. These estimates provide a rigorous foundation for one of the basic scaling ideas of turbulence theory, namely, the independence of the dissipation rate and the viscosity at high Reynolds number. The bounds are compared to experiments on turbulence in the Couette-Taylor system.