Modified Einstein Sediment Transport Method to Simulate the Local Scour Evolution Downstream of a Rigid Bed

The present study consists of a new mathematical-numerical modeling formulation to simulate the spatial and temporal scour development downstream of a rigid bed for both a noncohesive sediment bed and a cohesive sediment mixture with relatively small percentage of cohesive material. Laboratory tests were conducted in a rectangular tilting flume having a recessed box filled with the selected bed sediments and placed downstream of a rigid rough bed. The scour pattern was accurately acquired with a three-dimensional laser scanner at various time instants. The numerical code was calibrated through the scour profile data obtained under steady-state flow condition and then validated on the basis of scour patterns acquired under both steady and unsteady flow conditions (symmetric and asymmetric hydrographs). Contrary to most previous studies conducted with an issuing jet, the present study’s experiments were performed under non–strictly uniform flow conditions. The numerical model utilized information concerning the erosive turbulent flow characteristics as well as physical and mechanical properties of the movable-bed materials. The mathematical framework of the numerical model was a second-order partial differential parabolic equation in which the form of the scoured bed was assumed as an unknown parameter. Instantaneous near-bed velocity data, acquired with an acoustic Doppler velocimeter, was used to modify the Einstein sediment transport method, leading to a significant improvement of the simulated longitudinal scour profiles. Simulated temporal evolution of the scour profiles was in good agreement with the measured ones for both cohesive and noncohesive bed materials under steady and unsteady flow conditions.