Difference-quotient turbulence model: analytical solutions for the core region of plane poiseuille flow

The difference-quotient turbulence model and an explanation in terms of fluid dynamics is presented. With this model an analytical theory for the symmetric core region of turbulent plane Poiseuille flow is derived. The equations and the solutions reveal an order/disorder transition with analogies in other scientific fields where statistical physics applies. At moderate Reynolds numbers the time-averaged profile of the downstream mean velocity and a second-order fluctuation correlation are described in terms of Bessel functions of the first type. At the infinite Reynolds number limit these solutions converge toward functions which can be described by simple geometric figures. Experimental data confirm the model results.