A Cusp Catastrophe Model for Alluvial Channel Pattern and Stability

Abstract

The self-adjustment of an alluvial channel is a complicated process with various factors influencing the stability and transformation of channel patterns. A cusp catastrophe model for the alluvial channel regime is established by selecting suitable parameters to quantify the channel pattern and stability. The channel patterns can be identified by such a model in a direct way with a quantified index, which is a 2D projection of the cusp catastrophe surface, and the discriminant function is obtained from the model to distinguish the river state. Predictions based on this model are consistent with the field observations involving about 150 natural rivers of small or medium sizes. This new approach enables us to classify the channel pattern and determine a river stability state, and it paves the way toward a better understanding of the regime of natural rivers to assist decision-making in river management.