Numerical simulation of scour by a free falling jet

In this paper the numerical simulation of scour by a free falling jet is presented. It is assumed that the flow is two-dimensional, the alluvium is cohesionless, and that at the beginning of a run, i.e. at t = 0, the movable bed is flat. The scour simulation involves three basic steps: simulation of a turbulent flow in the stilling basin of a free falling jet, determination of distribution of sand concentration, and computation of bed deformation. The flow simulation rests on the momentum equations, the continuity equation, and on the k-ε equations for turbulent flows. A general 2-D non-orthogonal curvilinear computational domain is used; the solution is by the finite volume method, with a non-staggered grid arrangement. The SIMPLE scheme is used for pressure correction and the checkerboard problem is solved with a momentum interpolation scheme. The distribution of sand concentration is determined on the basis of the convection-diffusion equation. An appropriate boundary condition for concentration at the bed, which takes into account the effect of bed-load, is implemented. The bed deformation is computed with the aid of the sediment continuity equation. The aforementioned steps are repeated until the equilibrium bed surface (i.e. the equilibrium scour hole) is reached. The results of the numerical simulation appear to compare favourably with experiment.