Crossover scaling in Scheidegger’s river-network model

Takashi Nagatani
Phys. Rev. E 47, 3896 – Published 1 June 1993
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Abstract

A crossover behavior is investigated in Scheidegger’s river-network model [Bull. Int. Acco. Sci. Hydrol. 12, 1 (1967); 12, 15 (1967)] where a river meanders left with probability p and right with probability 1-p. Near p=1 (or p=0), the crossover phenomenon occurs from linear rivers at smaller length scales than the crossover length tc to the river network of a self-affine fractal at larger length scales than tc. For 0<p<1, the river network always crosses over the self-organized critical state. The mean river size 〈S〉 scales as 〈S〉≊t for t<tc and 〈S〉≊tbd (db=1.50) for t>tc where db is the scaling exponent of the drainage basin area. The crossover length tc scales as tc≊(Δp)1/φ (1/φ=1.033±0.050) where Δp=1-p near p=1 (or Δp=p near p=0). The mean river size is described by the scaling form 〈S〉=tf(t/tc) where f(x)≊1 for x≪1 and f(x)≊xbd-1 for x≫1. For a sufficiently small Δp, the mean river size 〈S〉 also scales as 〈S〉≊Δpγ (γ=0.484±0.020). The cumulative river size distribution NS scales as NS≊(Δp)2γ/3S1/3.

  • Received 23 November 1992

DOI:https://doi.org/10.1103/PhysRevE.47.3896

©1993 American Physical Society

Authors & Affiliations

Takashi Nagatani

  • College of Engineering, Shizuoka University, Hamamatsu 432, Japan

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Issue

Vol. 47, Iss. 6 — June 1993

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