Basins of attraction on random topography - art. no. 026112

We investigate the consequences of fluid flowing on a continuous surface up on the geometric and statistical distribution of the flow. We find that the ability of a surface to collect water by its mere geometrical shape is pro portional to the curvature of the contour line divided by the local slope. Consequently, rivers tend to lie in locations of high curvature and flat sl opes. Gaussian surfaces are introduced as a model of random topography. For Gaussian surfaces the relation between convergence and slope is obtained a nalytically. The convergence of flow lines correlates positively with drain age area, so that lower slopes are associated with larger basins. As a cons equence, we explain the observed relation between the local slope of a land scape and the area of the drainage basin geometrically. To some extent, the slope-area relation comes about not because of fluvial erosion of the land scape, but because of the way rivers choose their path. Our results are sup ported by numerically generated surfaces as well as by real landscapes.