A theory for turbulent pipe and channel flows

A theory for fully developed turbulent pipe and channel flows is proposed which extends the classical analysis to include the effects of finite Reynolds number. The proper scaling for these flows at finite Reynolds number is developed from dimensional and physical considerations using the Reynolds-averaged Navier–Stokes equations. In the limit of infinite Reynolds number, these reduce to the familiar law of the wall and velocity deficit law respectively. The fact that both scaled profiles describe the entire flow for finite values of Reynolds number but reduce to inner and outer profiles is used to determine their functional forms in the ‘overlap’ region which both retain in the limit. This overlap region corresponds to the constant, Reynolds shear stress region (30 300, well outside where it has commonly been sought. The experimental data from the superpipe experiment and DNS of channel flow are carefully examined and shown to be in excellent agreement with the new theory over the entire range 1.8 × 10 2 0, just as for boundary layers. The Reynolds number dependence of the parameters diminishes very slowly with increasing Reynolds number, and the asymptotic behaviour is reached only when R + Gt 10 5 .