Lagrangian statistical quantities related to the dispersion of heavy particles were studied numerically by following particle trajectories in a random flow generated by Fourier modes. An experimental fluid velocity correlation was incorporated into the flow. Numerical simulation was performed with the use of nonlinear drag. The simulation results for glass beads in a nondecaying turbulent air showed a difference between the horizontal dispersion coefficient and vertical dispersion coefficient. This difference was related to the differences of both the velocity scale and the time scale between the two direction. It was shown that for relatively small particle sizes the particle time scale ratio dominates the value of the diffusivity ratio. For large particles, the velocity scale ratio reaches a value of $1/2$ and thus fully determines the diffusivity ratio. Qualitative explanation was provided to support the numerical findings. The dispersion data for heavy particles in grid-generated turbulences were successfully predicted by the simulation when flow decay was considered. As a result of the reduction in effective inertia and the increase in effective drift caused by the flow decay, the particle dispersion coefficient in decaying flow decreases with downstream location. The particle rms fluctuation velocity has a slower decay rate than the fluid rms velocity if the drift parameter is large. It was also found that the drift may substantially reduce the particle rms velocity.

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