Modelling Stream Braiding Over a Range of Scales

Abstract

Modelling of fully developed braiding using conventional PDE techniques has been hindered by the difficulty of solving a nonlinear system of equations on a complex, constantly deforming domain. Simplified cellular models can reproduce many of the main features of braiding but their parameters are difficult to constrain. These two approaches are examples respectively of reductionism and synthesism, two approaches to modelling complex systems whose relative merits are being debated across a range of fields. Future research should aim at a marriage of these approaches, and at developing models capable of handling the full range of natural river types from braided to meandering. Another important parallel goal is the development of models for the mean behaviour of braided river systems. The first goal is to predict mean slope, depth, velocity, etc. from total water and sediment fluxes, and grain-size distribution. One can average the shallow-water and sediment-flux equations in a manner analogous to Reynolds averaging. This produces viable models, but just as for turbulence, adds new parameters that must be measured or estimated from physical arguments. Application of such averaging techniques to modelling rivers is only just beginning.