In general, the flow in a wide open-channel is two-dimensional in the region away from the sidewall. However, the same flow over a mobile bed is three-dimensional, showing a series of pairs of counter-rotating vortices over longitudinal bedforms. This is due to the cellular secondary currents formed over the entire cross section. The initiation mechanism of such cellular secondary currents has not yet been clearly demonstrated. The interaction between the pre-existing vortex created by the sidewall and the bottom sediment is thought to be related to the initiation of those secondary currents. The presence of the free surface and sidewall as well as the non-uniformity of sediment particles are also known to strengthen the cellular secondary currents. In the present paper, turbulent open-channel flows over sand ridges and troughs are numerically simulated. The Reynolds-averaged Navier-Stokes equations are solved with the non-linear k-ε model. This turbulence model was selected mainly due to its speed in computation. Mean flows and turbulence statistics are presented. The simulated secondary currents clearly showed upflows and downflows over the ridges and troughs, respectively, and the simulated results are compared with experimental data sets available in the literature. The modeling presented here is an important step in investigating the initiation mechanism of cellular secondary currents in a wide open-channel.