The cornea of the human eye is cooled by the surrounding air and by evaporation of the tear film. The temperature difference between the cornea and the iris (at core body temperature) causes circulation of the aqueous humor in the anterior chamber of the eye. Others have suggested that the circulation pattern governs the shape of the Krukenberg spindle, a distinctive vertical band of pigment on the posterior cornea surface in some pathologies. We modeled aqueous humor flow the human eye, treating the humor as a Boussinesq fluid and setting the corneal temperature based on infrared surface temperature measurements. The model predicts convection currents in the anterior chamber with velocities comparable to those resulting from forced flow through the gap between the iris and lens. When paths of pigment particles are calculated based on the predicted flow field, the particles circulate throughout the anterior chamber but tend to be near the vertical centerline of the eye for a greatest period of time. Further, the particles are usually in close proximity to the cornea only when they are near the vertical centerline. We conclude that the convective flow pattern of aqueous humor is consistent with a vertical pigment spindle.