A new framework for modeling the migration of meandering rivers

Many models of river meander migration rely upon a simple formalism, whereby the eroding bank is cut back at a rate that is dictated by the flow, and the depositing bank then migrates passively in response, so as to maintain a constant bankfull channel width. Here a new model is presented, in which separate relations are developed for the migration of the eroding bank and the depositing bank. It is assumed that the eroding bank consists of a layer of fine-grained sediment that is cohesive and/or densely riddled with roots, underlain by a purely noncohesive layer of sand and/or gravel. Following erosion of the noncohesive layer, the cohesive layer fails in the form of slump blocks, which armor the noncohesive layer and thereby moderate the erosion rate. If the slump block material breaks down or is fluvially entrained, the protection it provides for the noncohesive layer diminishes and bank erosion is renewed. Renewed bank erosion, however, rejuvenates slump block armoring. At the depositing bank, it is assumed that all the sediment delivered to the edge of vegetation due to the transverse component of sediment transport is captured by encroaching vegetation, which is not removed by successive floods. Separate equations describing the migration of the eroding and depositing banks are tied to a standard morphodynamic formulation for the evolution of the flow and bed in the central region of the channel. In this model, the river evolves toward maintenance of roughly constant bankfull width as it migrates only to the extent that the eroding bank and depositing bank 'talk' to each other via the medium of the morphodynamics of the channel center region. The model allows for both (a) migration for which erosion widens the channel, forcing deposition at the opposite bank, and (b) migration for which deposition narrows the channel forcing erosion at the opposite bank.