Turbulent velocity profiles : a new law for narrow channels

Abstract

The determination of velocity profiles in turbulent narrow open channels is a difficult task due to the significant effects of the anisotropic turbulence that drives the Prandtl’s second kind of secondary flow in the cross section. Due to these currents the maximum velocity appears below the free surface. This is called the dip phenomenon. The classical log law describes the velocity distribution in the inner region of the turbulent boundary layer. The Coles law and its wake function are not able to predict the velocity profile in the outer region of narrow channels. This paper relies on an analysis of the Navier-Stokes equations and yields a new formulation of the vertical velocity profile in the outer region of the boundary layer in the central cross section area of steady, fully developed turbulent flows in open channels. This formulation is able to predict primary velocity profiles for both narrow and wide open channels. This new law is a modification of the classical one, it involves an additional parameter CAr that is a function of the position of the maximum velocity ξdip and roughness height (kS).ξdip may be derived either from measurements or from an empirical equation given in this paper. A wide range of longitudinal velocity profile data for narrow open channel has been used for validating the new law. The agreement between the experimental data and the profile given by the law is very good, despite the simplification used.