In this paper, the three-dimensional flow field around a single bridge pier in an open channel flow is estimated using Ansys Fluent software. Multiphase modeling approach is used to track the free surface of the water. Computations are performed using the two-equation turbulence model, namely the standard k-ε and k-ε RNG model. The models are mainly used to study the characteristics of horseshoe and wake vortices around the pier. Horseshoe and wake vortices are observed in the k-ε RNG model, whereas only wake vortices are observed in the standard k-ε model. On the downstream side of the pier, a wake region is created due to the pressure difference between the upstream and downstream sides of the pier. In this region, generations of wake vortices are clearly seen. The results are compared and validated with the experimental data. Despite the shortcomings of the k-ε model, it performed well, indicating the close agreement of the horizontal velocity component with experimental data. However, the distribution of bed shear stress exhibited a discrepancy between the simulated results and the experimental data. Sensitivity analyses are also carried out for both models to improve the simulated results. The present approach to the estimation of the turbulent characteristics indicates the way forward for the estimation of scouring around the bridge piers in future studies.