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 ch annel migration. Computer simulations give spatial scaling behaviour i n reasonable agreement with geological data from three major river sys tems. A surprising result is that even though our model neglects gravi ty, the simulations give river configurations close to minimal length with the scaling of stretched random walks. The model shows dynamic sc aling with exponents similar to those of the Edwards-Wilkinson model o f interfacial growth. Finally we relate the model to the lattice self- avoiding walk (SAW) and show numerical evidence that the meandering ri ver will always correspond to the subcritical regime.