Phenomenological Characterization of Vortex Induced Scour

A series of experiments, investigating vortex induced scour formation, show that the scour hole geometry induced by a rotating fluid flow, can be explained within the concept that the granular bed is eroded as the imposed shear stress overcomes a certain critical value inherent in the liquid/bed pair. The situation is seemingly kindred to that observed in the pseudoplastic Bingham fluids and the first experiment, investigating cylindrical scour, is conducted using a high viscous Bingham fluid with a low yield stress. Two other experiments investigating the two and three dimensional scour formation for the stationary flow regime are also conducted using a fluid and grain substrate pair. A simple model for vortex induced scour is derived for an infinitely long axisymmetric vortex with circular streamlines surrounded by a deformable boundary. The Navier–Stokes equations are solved by using a polynomial approximation of the tangential velocity. The model is then extended to two and three dimensional stationary flow situations by considering the torque balance between the fluid motion and the critical bed shear stress. The quantified results agree well with experimental results obtained in both the one dimensional Bingham fluid experiment and the two and three dimensional fluid/grain experiments.