LANDSCAPE EVOLUTION IN FLOOD - A MATHEMATICAL-MODEL

We present analytical and numerical studies for the evolution of a landscape in flood. Our model is based on the assumption that the local fluxes of both water and sediment depend only (and simply) on the gradient of the water surface and local depth of flood. Nonlinear differential equations for water conservation dictate the distribution of flood-water. The divergence of the sediment flux then determines the net rise (deposition) or fall (erosion) of the underlying landscape. We present linear stability analysis for an initially planar slope, with uniform water flow: the dominant instability is the development of corrugations at an angle oblique to the flow direction. Numerical results are presented for the long time evolution of a system with periodic boundary conditions, and no net gain or loss of either water or sediment. The resulting landscape resembles that of a braided river bed, and analysis of the contours shows quantitative agreement with the experimental power law distribution of island sizes for the Zaire and Rakaia river systems and the outwash drainage system at Vatnajokull.