Controls on the Height and Spacing of Transverse Eolian Bedforms

Transverse eolian bedforms occur at three distinct spatial scales: ripples, dunes, and megadunes. Within each of these bedform types, field observations suggest that bedform height and spacing increases with bedform age, grain size, and excess shear velocity. How each of these factors influence bedform size and whether bedforms ever reach a steady state condition without further growth, however, is still unknown. In this paper, the controls on transverse eolian bedform height and spacing are further constrained using a numerical model for the formation of eolian bedforms from an initially flat surface. This bedform evolution model combines the basic elements of Werner's (1995) cellular automaton model for dune formation with a realistic model for boundary-layer flow over complex topography. Particular attention is paid to the nonlinear relationship between bed shear stress and slope angle on the windward side of evolving bedforms. Beginning with a flat bed, the model forms ripples that achieve a steady state condition. The steady state ripple height and spacing predicted by the model are proportional to grain size and excess shear velocity. In the model, grain size and excess shear velocity control the steady state height and spacing through the aerodynamic roughness length. The speedup ratio of incipient ripples is a maximum for roughness length values approximately one tenth of the ripple width. In this way, incipient ripples with a wavelength to roughness length ratio of approximately ten grow preferentially. Once steady-state ripples form, they become the dominant roughness element on the surface (superceding grains) and dunes form with the same mechanism at a larger scale. The model predicts that transverse eolian ripples, dunes, and megadunes are genetically related and it makes predictions consistent with available field data.