On the nature of meander instability

Bend instability is the process whereby perturbations of the planform distribution of a channel relative to a straight configuration may grow, driven by erosion at concave banks and deposition at convex banks, leading to the development of a meandering pattern. Here we investigate the nature of this instability; that is, we ascertain under what conditions bend instability is convective or absolute. In the former case, an initial nonpersistent, small perturbation localized in space is convected away, eventually leaving the flow domain unperturbed. In the latter case, perturbations spread in both the upstream and downstream directions, eventually affecting the whole flow domain. In convective instabilities, the spatial-temporal development of perturbations is somewhat dependent on the characteristics of the initial perturbation which is required to be persistent in time. On the contrary, absolute instabilities are able to amplify perturbations, even if triggered at some initial time and then ceased. If bend instability is convective, planform information migrates only in one direction, while in the absolute regime, information is propagated in both directions. We show that bend instability is most often, though not invariably, convective at both a linear and nonlinear level. Moreover, the group velocity of perturbations changes sign as the width to depth ratio of the channel crosses some threshold value (the resonant value of Blondeaux and Seminara (1985)): Below (above) resonance, information is propagated downstream (upstream). We discuss the implications that these findings have on the morphological characteristics of meandering rivers (in particular, the sense of skewing of meander bends and the direction of meander migration). We also clarify how the choice of appropriate boundary conditions in numerical simulations of planform evolution is crucially dependent on the nature of bend instability and on its subresonant or superresonant regime.