Local minimal energy landscapes in river networks

Achille Giacometti
Phys. Rev. E 62, 6042 – Published 1 November 2000
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Abstract

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.

  • Received 19 April 2000

DOI:https://doi.org/10.1103/PhysRevE.62.6042

©2000 American Physical Society

Authors & Affiliations

Achille Giacometti

  • INFM Unitá di Venezia, Dipartimento di Scienze Ambientali, Universitá di Venezia, Calle Larga Santa Marta DD2137, I-30123 Venezia, Italy

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Vol. 62, Iss. 5 — November 2000

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