The life of a meander bend: Connecting shape and dynamics via analysis of a numerical model

Abstract

Analysis of bend‐scale meandering river dynamics is a problem of theoretical and practical interest. This work introduces a method for extracting and analyzing the history of individual meander bends from inception until cutoff (called “atoms”) by tracking backward through time the set of two cutoff nodes in numerical meander migration models. Application of this method to a simplified yet physically based model provides access to previously unavailable bend‐scale meander dynamics over long times and at high temporal resolutions. We find that before cutoffs, the intrinsic model dynamics invariably simulate a prototypical cutoff atom shape we dub simple. Once perturbations from cutoffs occur, two other archetypal cutoff planform shapes emerge called long and round that are distinguished by a stretching along their long and perpendicular axes, respectively. Three measures of meander migration—growth rate, average migration rate, and centroid migration rate—are introduced to capture the dynamic lives of individual bends and reveal that similar cutoff atom geometries share similar dynamic histories. Specifically, through the lens of the three shape types, simples are seen to have the highest growth and average migration rates, followed by rounds, and finally longs. Using the maximum average migration rate as a metric describing an atom's dynamic past, we show a strong connection between it and two metrics of cutoff geometry. This result suggests both that early formative dynamics may be inferred from static cutoff planforms and that there exists a critical period early in a meander bend's life when its dynamic trajectory is most sensitive to cutoff perturbations. An example of how these results could be applied to Mississippi River oxbow lakes with unknown historic dynamics is shown. The results characterize the underlying model and provide a framework for comparisons against more complex models and observed dynamics.

Model predictions of long-lived storage of organic carbon in river deposits

“…In order to account for the effects of variable migration rates, we normalized all storage durations by the time required for the channel to migrate laterally to the point of meander bend cutoff (T cut ). In our model simulations, we explicitly tracked meander bends from growth to cutoff following the approach of Schwenk et al (2015). While the cutoff time varied in the model runs, the peak of the probability distribution function occurred for T cut = 350 years.…”

Multiscale structure of meanders

“…Equation is less sensitive to noise in the input coordinates when the derivatives are approximated with centered differences [cf. Schwenk et al , ]. The calculation of curvature is notably affected by noise and often requires some level of smoothing.…”

Sinuosity evolution along an incising channel: New insights from the Jordan River response to the Dead Sea level fall

“…In their review, Blum et al (2013) concluded that lateral migration is the primary process widening incised channels into valleys in response to base-level fall. This conclusion corresponds to positive relationships between channel-bed slope and lateral bend migration, which is widely implemented in numerical simulations of channel meandering (Howard and Knutson, 1984;Gran et al, 2013;Schwenk et al, 2015). Most of the models are restricted to simulations of neck cutoffs, as a result of the difficulty of predicting and simulating chute cutoffs (Seminara, 2006).…”