Efficient non-hydrostatic modelling of flow and bed shear stress in a pier scour hole

Abstract

Predicting 3-D flow in a pier scour hole and the associated bed shear stress τb is important for the safe and economical design of bridge piers. This paper combines layered, hydrostatic hydrodynamic computations with non-hydrostatic pressure corrections, exploring a new modelling approach for efficient and reliable predictions of 3-D flow velocity. The law of the wall method is used for estimating τb. Its suitability for incorporation into layered models for bedload transport and pier scour simulations is also discussed. The predicted flow shows realistic features: strong downward flow adjacent to the upstream nose of a circular pier, vortex motions in the vertical and horizontal direction, and meandering flow wakes. The velocity results compare well with available experimental data. In the approach region, τb is uniform. It attains a local maximum immediately before flow enters the scour hole and then drops non-linearly in the scour-hole region toward the pier. In the wake region, τb has very low values. The τb predictions are consistent with the experimental data. In multi-layer models, when applying the law of wall method, one should use near-bed velocities as opposed to bottom-layer velocities to obtain more reliable τb estimates and avoid noisy results, which can cause a numerical instability problem in bedload transport simulations.