AN EQUILIBRIUM RELATIONSHIP FOR SHEAR VELOCITY AND APPARENT ROUGHNESS LENGTH IN AEOLIAN SALTATION

An equilibrium relationship between shear velocity and apparent surface roughness is established for aeolian saltation. Velocity profiles of wind over blowing sand were digitized from eleven published data sets. The 106 profiles were analyzed to obtain estimates of shear velocity and apparent surface roughness lengths. These values were used to test Charnock's relationship for suitability in aeolian environments. The results indicate that z0 = 0.0091 u*2/g. Modifying Charnock's model to describe wind over an equilibrium saltation field yields z0 - (2D50/30) = 0.0252 (u* - u*t)2/g. The latter result is used to demonstrate that the focal point concept proposed by Bagnold stems from the increase in apparent roughness with increased shear velocity. The results demonstrate an excellent example of threshold-controlled equilibrium in dynamic systems.