Protostellar disks are intrinsically unstable against thermal convection in the direction normal to the plane of the disk. Because the origin of effective disk viscosity is unknown it is of great theoretical interest to investigate the effect of convection on the transport of angular momentum. To study this effect we present here results of direct two-dimensional simulations of compressible convection in axisymmetric accretion disks. In order to make the problem tractable an underlying viscosity (possibly due to shear instabilities and/or smaller scale convection) is used such that the calculations are performed for a Rayleigh number 10 times the critical value for marginal stability. Under these conditions the results show that the convection cells cross the equatorial plane and extend over the entire vertical height. They have, for the chosen underlying viscosity, a radial extension comparable to but somewhat less than the disk height. We show that the convection modifies both the heat and angular momentum transport. The modification is such that in order to transmit a given outward angular momentum flux coming from a stable region, the structure adjusts such that the mean viscous flux is increased, this being counterbalanced by a negative advected flux. This suggests that the nonlinear viscous dissipation and mixing associated with large-scale axisymmetric convective motions leads to an inward flux of angular momentum. However, we point out that this result may not apply to the convective motion when the underlying viscosity is much smaller or when nonaxisymmetric modes are considered.