Study on time development of horse-shoe vortex diameter and shear stress at bridge pier

Horse-shoe vortex at the bridge pier nose is a final result of reverse pressure gradient at the upstream side of pier and river surface. From literature review different ideas about the formation and initiation of horse-shoe vortex at the bridge pier can be found. These ideas indicated that the horse-shoe vortex is formed before the formation of scour hole, exactly when the scour hole forms and after the formation of scour hole. In present study these ideas are examined with different experimental data selected from previous studies. The experimental data includes equilibrium scour hole to examine the size of horse shoe vortex in comparison with final scour depth and time development of local scour depth to study the variation of horse-shoe vortex diameter with time. Results showed that similar to scour depth development, the logarithmic trend of horse-shoe vortex diameter with time tends to an equilibrium value. In addition, the calculated horse-shoe vortex diameter in equilibrium scour hole condition with different methods is a function of different parameters such as sediment size or bridge pier diameter and varies from 0.3 to 3.3 of equilibrium scour hole. Finally, a new method is presented for calculation of bed shear stress at the bridge pier with regard to diameter of horse-shoe vortex. In this method, by increasing the size of horse-shoe vortex, shear stress at the bridge pier decreases from 4 times of upstream shear stress to critical shear stress of stream bed sediment.