Bed shear in equilibrium scour around a circular cylinder embedded in a loose bed

Abstract

The bed shear stress for a horseshoe vortex in the equilibrium scour hole around the base of a circular cylinder, embedded in a loose bed with a uniform approach flow under a clear water regime, is computed from turbulent boundary layer analysis by integrating the Navier-Stokes equations. Inside the thin boundary layer, which is developed by the reverse flow at the bed due to swirl motion, Pohlhausen's method is applied with an arbitrary 1/7th power distribution of velocity, as was assumed by Weber in solving turbulent boundary layer. Outside the boundary layer, the expressions of 3-D flow field given by Dey are used. Finally the above technique produces two unknowns, namely bed shear stress and boundary layer thickness. The expression of wall shear stress given by Blasius for turbulent flow in pipes as well as over flat plates is assumed for solving boundary layer thickness, and subsequently bed shear stress. The computational results of bed shear stress and boundary layer thickness are presented.