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 to the river network of a self-affine fractal at larger length scales than . 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< and 〈S〉≊ (=1.50) for t> where is the scaling exponent of the drainage basin area. The crossover length scales as ≊(Δp (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/) where f(x)≊1 for x≪1 and f(x)≊-1 for x≫1. For a sufficiently small Δp, the mean river size 〈S〉 also scales as 〈S〉≊Δ (γ=0.484±0.020). The cumulative river size distribution scales as ≊(Δp.
- Received 23 November 1992
DOI:https://doi.org/10.1103/PhysRevE.47.3896
©1993 American Physical Society