An analytical approach of finding out the equilibrium scour depth at a cylindrical pier when the current is making an angle with the wave

Abstract

The present work describes the development of a mathematical model for the evaluation of the equilibrium scour depth around a single cylindrical pier under the influence of co-existing waves and current. The presented equation includes the effect of the Keulegan–Carpenter number and Froude number on the formation of scour hole. The principle of energy balance is used to form a nonlinear equation of scour, where the energy of incoming flow when collided with the pier is equated with the weight of the sediments moving away from the vicinity of the pier to establish an equilibrium scour depth. An effort has been made to capture the nature of the flow along x-, y-, and z-directions when the current is inclined at an angle θ with the direction of progress of the wave. Further, the scour profile chosen can incorporate any shape and size of the scour hole. The model has been tested against published experimental data pertaining to two cases, namely when the waves are following the current and when the waves are traveling normal to the current. Here, only linear wave is considered while deriving the equation.