We carried out a wind tunnel experiment on aeolian transport of sand. Fluorescence-dyed grains of sand were embedded in the sand bed in a wind tunnel, and their dispersion was recorded by a video camera. Dispersion of colored sand both downwind and in the crosswind direction are examined. The concentration of colored sand decreases as an exponential function of the downwind distance y, Ae-κy, whereas the cross-sectional distribution is approximated by a Gaussian distribution with the standard deviation proportional to $sqrt{y}$. The characteristic length scale is 1000 times greater in the downwind than in the crosswind direction. A simple stochastic model is proposed to explain these findings. We also found that our experimental results conform to the assumptions of the Werner model, which reproduces aeolian dune dynamics well. We derived conditions on the parameters of the Werner model from the experimental results and suggest the applicability of the Werner model to real problems such as sandy coasts, deserts, and regions whose surface is contaminated.