Basins of attraction on random topography
Abstract
We investigate the consequences of fluid flowing on a continuous surface upon 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 proportional to the curvature of the contour line divided by the local slope. Consequently, rivers tend to lie in locations of high curvature and flat slopes. Gaussian surfaces are introduced as a model of random topography. For Gaussian surfaces the relation between convergence and slope is obtained analytically. The convergence of flow lines correlates positively with drainage area, so that lower slopes are associated with larger basins. As a consequence, we explain the observed relation between the local slope of a landscape and the area of the drainage basin geometrically. To some extent, the slopearea relation comes about not because of fluvial erosion of the landscape, but because of the way rivers choose their path. Our results are supported by numerically generated surfaces as well as by real landscapes.
 Publication:

Physical Review E
 Pub Date:
 February 2001
 DOI:
 10.1103/PhysRevE.63.026112
 arXiv:
 arXiv:condmat/0009383
 Bibcode:
 2001PhRvE..63b6112S
 Keywords:

 05.90.+m;
 92.40.Fb;
 92.40.Gc;
 Other topics in statistical physics thermodynamics and nonlinear dynamical systems;
 Erosion and sedimentation;
 sediment transport;
 Condensed Matter  Statistical Mechanics;
 Physics  Geophysics
 EPrint:
 doi:10.1103/PhysRevE.63.026112