Meandering River Dynamics: Spatial and Temporal Wave Growth and Non-Periodic Wave Patterns

Abstract:

The evolution of meandering river channels results from interactions amongst turbulent water flow, sediment transport, and channel geometry. Most current physics-based models derive from the meander-morphodynamics equations introduced by Ikeda et al. (1981). Corresponding linear theories have focused almost exclusively on periodic sequences of small-amplitude meanders. Mathematical consideration of the equations shows that boundary conditions must be chosen carefully to yield numerical solutions for a well posed boundary value problem. The numerical algorithms presented in this work yield 2D solutions to the (corrected) Ikeda et al. (1981) equations with second order convergence in both time and space. We explore the characteristics of spatially versus temporally growing waves, as well as the effects of stochastic variations in the upstream boundary condition and in the dimensionless parameter β, which characterizes the strength of secondary flow relative to cross-stream shear. Consideration of the growth patterns for spatially growing waves provides some insight for the design of experimental systems exhibiting self sustaining river meanders.