The Dynamics of a Meandering River

TL;DR

This paper develops a statistical model of meandering rivers incorporating non-linear dynamics and terrain heterogeneity, analyzing stability and steady states through analytical and numerical methods, with validation against field data.

Contribution

It introduces a novel stochastic model capturing river channel migration and ox-bow lake formation, providing insights into river stability and steady-state behavior.

Findings

River motion is inherently unstable without ox-bow lake formation.

Inclusion of ox-bow lakes stabilizes the river system.

Model predictions align with field measurements.

Abstract

We present a statistical model of a meandering river on an alluvial plane which is motivated by the physical non-linear dynamics of the river channel migration and by describing heterogeneity of the terrain by noise. We study the dynamics analytically and numerically. The motion of the river channel is unstable and we show that by inclusion of the formation of ox-bow lakes, the system may be stabilised. We then calculate the steady state and show that it is in agreement with simulations and measurements of field data.