A hierarchical model for the formation of eolian

A linear stability analysis of sediment transport by wind or water over an erodible bed shows that perturbations in a narrow range of wavenumbers are ampli ed, leading to the formation of ripples with a wavelength dependent on the roughness length of the bed. The roughness length is proportional to the grain size of the sand and the square of the excess shear velocity at the bed. We propose that this is the instability mechanism for the formation of eolian ripples. In addition, we propose that eolian dunes form by the same instability mechanism with the roughness of the bed at the dune scale proportional to the height of ripples. Similarly, megadunes form as a result of the same instability with the roughness length at the megadune scale proportional to the height of dunes. This model predicts that the spacing between eolian ripples, dunes, and megadunes increases linearly with grain size, quadratically with excess shear velocity, and that the ratio of megadune spacing to dune height, dune spacing to ripple height, and ripple spacing to grain size are all on the order of one thousand. Comparison with observations is complicated by the fact that studies have rarely measured shear velocity. Studies of dune spacing as a function of grain size, for example, have been carried out in sand seas with variable shear velocity conditions, leading to di erent conclusions on graniometric control. We argue that our model is consistent with available data and make speci c suggestions for future eld tests. 2