Sediment transport on the lee sides of aeolian dunes involves a combination of grain-fall deposition on the upper portion of the slip face until a critical angle is exceeded, transport of a portion of those sediments down the slip face by grain flows and, finally, deposition at an angle of repose. We measured the mean critical and repose angles and the rate of slip-face avalanching using terrestrial laser scanning (TLS) on two barchans of different size in Jericoacoara, Brazil. Wind speeds and sand fluxes were measured simultaneously at the dune crests. We found that the mean critical angle decreased with increasing wind speed. We attribute this effect to turbulent shear stresses, the magnitude of which we quantified using 3-D large eddy simulation modeling, that randomly act down the slip face (i.e., in the direction of gravity) to trigger grain flows at lower angles than would be possible with gravity stresses alone. We developed and tested a new predictive model for the frequency of avalanching that depends on both the sediment flux delivered to the slip face and changes in the critical angle with time. In this model, increasing turbulent shear stresses drive avalanching even in the absence of sand flux delivered to the slip face if the critical angle decreases below the slope angle. We also document that the mean critical angle decreases slightly with increasing slip-face height. These results have important implications for aeolian dune evolution, interpretations of aeolian stratigraphy, and granular mechanics.