Three freely meandering rivers in the Amazon basin were analyzed for statistical scaling properties and oxbow lake size-frequency distributions. The rivers are the Purus (central Amazon, planform data), Juruá (central Amazon, planform and oxbow lake data), and Madre de Dios (Peruvian Amazon, oxbow lake data). Long reaches were found to be power-law scaling over more than two orders of magnitude. These river planforms are self-affine fractals. Oxbow lake data suggest that the lakes are sampled from a skewed hyperbolic (Pareto) size-frequency distribution.

To examine the long-term behavior of freely meandering rivers, a deterministic continuum model of meandering rivers has been used for extensive simulations of free meandering motion. The simulation outcomes are consistent with a dynamical state of self-organized criticality, which has the following characteristic behavior: (1) stationary mean sinuosity of the final state; (2) robustness, in the sense that the same final state is reached from any initial conditions; and (3) formation of a spatiotemporal fractal structure.

Sensitivity tests showed that this behavior is not affected by valley confinement down to a valley width of 50 w (river width), and by chute cutoffs of mature meanders up to 3 w long, but the average sinuosity value reached in the final state is sensitive to valley width less than 100 w, and chutes longer than 1.5 w.

Comparison with empirical data confirmed the validity of the simulations as models of river meandering. All tests found data and simulation results to be in close agreement.

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