In the subtropical Southeast (SE) Pacific stratocumulus (Sc) regime, the cloud droplet concentration reaches the maximum at the coastal region, and decreases sharply offshore. The strong contrast between the coastal and offshore regions has been considered as a result from the impacts of the anthropogenic aerosol production. Earlier studies proposed that the entrainments of anthropogenic aerosol from the lower free-troposphere contribute to the observed gradients in aerosol and trace gas concentrations, and thereby to the gradients in the cloud droplet concentration. The entrainment processes of the polluted air from above the inversion over the coastal region, however, have just been discussed qualitatively. Understanding and quantifying the entrainment efficiency of the polluted air can help us to clarify how important the anthropogenic aerosol released into the free troposphere to the cloud radiative properties, compared with the surface release of anthropogenic aerosol. This study used an LES model with a two-momentum bulk microphysics scheme to simulate the idealized passive tracer transport in marine Sc under different idealized environment scenarios based on observations over the SE Pacific coastal region. Compared with the in-situ observations, these simulations resolved the sharp inversion at the top of the BL, and captured the general features of the costal Sc layer and the turbulence structures. The preliminary analysis indicated that without considering the large-scale horizontal advection of the tracers (i.e. initially assuming a homogenous tracer layer), 5% - 30% of the passive tracer layer located at 50 m above the inversion can be entrained into the BL within 12 hours. The effects of the vertical wind shear and the moist layer above the inversion are considered in the sensitivity simulations.