Bed shear stress inside of a local scour due to a submerged turbulent jet

A scouring experiment was performed and the spatio-temporal evolution of the scour hole was measured. This latter was used as an input for a mathematical model simulating the spatio-temporal evolution of the bed shear stress inside the local scour. The mathematical model is based on a modified Exner equation accounting for the steep slopes of the scour hole. As a consequence the critical bed shear stress, the bed load formulation and the structure of Exner equation are modified. The obtained equation of the bed shear stress is a first order differential equation with the time as a parameter, while the independent variable is the abscissa along the flume. For the performed laboratory experiment, the spatial evolution of the bed shear stress at different scouring stages was calculated and compared with the critical bed shear stress for the corresponding sloping bed. The gap between the calculated and critical bed shear stress decreases as the time increases, till to become negligible at the quasi equilibrium scour condition.