Numerical simulations of a meandering bubble plume in a rectangular flat geometry are presented using the ASTRID code. The simulations are based on a full two-fluid model including turbulence modelling using a k-epsilon model on 2 two-dimensional and 2 three-dimensional grids, For the interfacial forces between the two phases the drag force and virtual mass have been taken into account. The simulations are time dependent and a time step of 50 ms is used. In the 2D case a steady solution is obtained with one large liquid circulation cell. The turbulent viscosity is high, damping all oscillations. In case of 3D simulations the flow becomes transient. If only the drag force is used for the mutual interaction between the phases both the amplitude and the oscillation period are much smaller than observed experimentally. The turbulent viscosity is smaller in the 3D case, consequently the diffusion of the bubble plume is less than in the 2D case. Changing the standard k-epsilon model to a low Reynolds k-epsilon one does not alter the flow behavior significantly. If, however, also the virtual mass is taken into account the oscillations have a period of 34 s and an amplitude for the vertical component of the liquid velocity of about 20 cm/s. This is quite comparable with the experimental finding reported in literature.