Derivation of the nonlinear dependence of aeolian sand flux on wind speed

Aeolian transport, in which turbulent wind shearing over a granular bed causes grains to hop or roll along the bed, is a major mechanism controlling bedform evolution and desertification processes. Predictions of transport rates have significantly advanced in recent years, but none of the theoretical models has managed to provide accurate predictions of aeolian transport over a wide range of wind conditions. Here, we develop a theory, based on the physics of different transport regimes, that accounts for the linear and nonlinear scaling exhibited by aeolian sand transport, capturing quantitatively the contribution of these regimes to the total transport for a wide range of wind velocities. Our theoretical predictions are in very good agreement with experimental results for a large range of wind strengths.