Local Minimal Energy Landscape in River Networks

The existence and stability of a universality class associated with local minimal energy landscapes is investigated. Using extensive numerical simulations, we first study the dependence on a parameter γ of a partial differential equation, which was proposed to describe the evolution of a rugged landscape toward a local minimum of the dissipated energy. We then compare the results with those obtained by an evolution scheme based on a variational principle (the optimal channel networks). It is found that both models yield qualitatively similar river patterns and similar dependences on γ. However, the aggregation mechanism is strongly dependent on the value of γ. A careful analysis suggests that scaling behaviors may depend weakly on both γ and on initial conditions, but in all cases are within observational data predictions. Consequences of our results are finally discussed, and the most plausible scenario is presented.