In the framework of the two-fluid model of dilute dusty gases, the present paper gives the governing equations for dusty atmospheric flows, where the two-way coupling is taken into account in the source terms. The similarity criteria are derived for dynamical behaviors of the carrier- and dispersed-phase and they include seven parameters such as the Froude number, the dust mass loading and so on. As a model problem, the aerodynamic entrainment of the dust and sand particles in the fully developed turbulent atmospheric boundary layer over an erodible surface are studied and the aerodynamic drag as well as the Saffman lifting and gravity forces are considered. To overcome the difficulties associated with the non-uniqueness of the flow parameters due to the intersection of particle trajectories, the continuity equation of the dispersed phase is introduced in the Lagrangian coordinates. The motion characteristics and concentration distributions of the dispersed phase are simulated numerically at two different wind speeds and four different particle sizes and the effects of wind velocity and dust size are discussed in detail. These results are also relevant to the energy exchange process between the two phases in the atmospheric boundary layer. The equations, criteria and method may be useful in interpretation of some natural disaster phenomena such as wind erosion and sand-dust storm.