A lattice model of the meandering river.

We present a lattice model of a meandering river on an alluvial plane which is motivated by the physical non-linear dynamics of the river channel migration. Computer simulations give spatial scaling behaviour in reasonable agreement with geological data from three major river systems. A surprising result is that even though our model neglects gravity, the simulations give river configurations close to minimal length with the scaling of stretched random walks. The model shows dynamic scaling with exponents similar to those of the Edwards-Wilkinson model of interfacial growth. Finally we relate the model to the lattice self-avoiding walk (SAW) and show numerical evidence that the meandering river will always correspond to the subcritical regime.