Camassa-Holm Equations as a Closure Model for Turbulent Channel and Pipe Flow

We propose the viscous Camassa-Holm equations as a closure approximation for the Reynolds-averaged equations of the incompressible Navier-Stokes fluid. This approximation is tested on turbulent channel and pipe flows with steady mean. Analytical solutions for the mean velocity and the Reynolds shear stress are consistent with experiments in most of the flow region. {copyright} {ital 1998} {ital The American Physical Society}