The flow field near bridge piers is analysed using computational fluid dynamics (CFD) models to investigate bridge scour, which is one of the main safety concerns for bridges. Two indicators are used to characterise the scour hole, the horseshoe vortex (HV) core position relative to the bed, and the area of wall shear stress (WSS) above a sediment transport threshold of 1 Pa. The underlying fluid mechanics is detailed, establishing the relation between vorticity generation, the fluid strain rate and the WSS. The CFD models are validated against results in the literature, for the free surface around the pier and for the WSS at the bed. A parametric study with different pier widths, mass flow rates (MFR), and pier shapes is carried out, and these results are compared to an adapted pier with diverting fin inserted in the front. The adaptation shows that the diverting fin reduced the strength of the HV in front of the pier, and also reduces the total area of bed WSS above the threshold.