Nonlinear Dynamical Behavior of the River Meandering Process

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Recent mechanically based treatments flow and erosion in bends indicate that river meandering is a highly nonlinear, autocatalytic process wherein diverse, yet self-organized, meander geometries arise independently of variations in flow and erodibility of valley-floor alluvium. The nonlinearity resides in the fact that the channel configuration at each instant evolves from a previous channel state in accordance with mechanical conditions imposed on the flow (and associated boundary stress field) by that previous state. A suitable equation of motion can be written which describes the essentials of this nonlinear behavior. Numerical simulations will be conducted to clarify how the diversity of bend forms that can occur at any instant, and the tendency for certain of these forms to recur over time, are compatible features of meander trains that naturally arise from the nonlinearity of the process.