Camassa-Holm equations as a closure model for turbulent channel and pipe flow

We propose the viscous Camassa-Holm equations as a closure approximation fo r the Reynolds-averaged equations of the incompressible Navier-Stokes fluid . This approximation is tested on turbulent channel and pipe flows with ste ady mean. Analytical solutions for the mean velocity and the Reynolds shear stress are consistent with experiments in most of the now region.