HYDRODYNAMIC DESCRIPTION FOR ADVECTIVE SEDIMENT TRANSPORT PROCESSES AND RILL INITIATION

A physically based model for advective sediment transport during rill initiation is developed based on (1) a short-wavelength rescaling of the momentum balance equations for the surface water flux; (2) a deforming coordinate system which characterizes local morphological changes of the surface during erosion; and (3) a generalized transport function for the surface sediment flux which distinguishes the contributions of diffusive and advective transport. A linear stability analysis of the coupled system indicates that an intrinsic minimum transverse length scale for rill initiation is forced by the cross-slope pressure gradient in the surface water. The wavelength of this initial rill spacing is dependent upon the relative significance of the advective component of sediment transport and the hydraulic efficiency of the surface water flux and is independent of the total length of the hillslope. The hydrodynamic model presented can also be used to evaluate the nonlinear development of rills and rill networks, subsequent to initiation.