A straight alluvial channel with erodible banks eventually develops bends, yet the scientific literature still conflicts about what starts and sustains this bending. One line of coupled bar–bank linear stability analysis concludes that riverbed instability (alternate bars) can by itself trigger meandering, with a wavelength longer than fixed-bank bar theory predicts; a physics-based numerical study concludes that meander initiation requires an upstream channel-curvature/inflow perturbation or a reach long enough for a steady alternate bar to form, with sustained high-sinuosity meandering additionally requiring dynamic upstream forcing and bar-to-floodplain conversion; finite-domain linear theory concludes that a continuous boundary perturbation is required for sustained meandering within that linear model class; and flume experiments show that bank erosion begins only after alternate bars exist on the bed. Determining which mechanism (or which combination, under which conditions) initiates and sustains meandering of initially straight rivers remains open.

Background

River meandering — the evolution of an initially straight alluvial channel into a sinuous planform (the channel's shape seen from above) — is a classic problem of fluvial geomorphology, the study of how rivers erode, transport and deposit sediment to shape Earth's surface. Two competing explanations for its origin go back to the 1970s–80s. Parker (1976) attributed meandering to an intrinsic instability of the channel banks, while later linear-stability work (Ikeda, Parker & Sawai 1981; Blondeaux & Seminara 1985) produced the unified bar–bend theory, in which both the bed and the planform can be unstable. Here linear stability analysis means perturbing the coupled depth-averaged flow, sediment-transport (Exner) and bank-erosion equations about a straight reference state and asking which small perturbations grow. Alternate bars are large-scale bedforms whose crests alternate between the left and right side of a straight channel; free bars arise as an intrinsic bed instability and migrate downstream, whereas forced (or steady) bars are fixed in place by an imposed perturbation such as channel curvature, a groyne, or an inflow obstruction. Fixed-bank bar theory (Blondeaux & Seminara 1985; Colombini, Seminara & Tubino 1987) predicts the wavelength of free bars in channels whose banks cannot erode, and Blondeaux & Seminara's planform (bend) instability predicts the wavelength of growing meanders. Which instability actually initiates the bending of a real river, where banks erode, has remained contentious. Flume work sharpened the question: Braudrick, Dietrich, Leverich & Sklar (2009) showed that sustaining meandering in coarse-bed laboratory channels requires suitable bank strength, fine sediment and vegetation; Eaton, Church & Davies (2006) proposed a conceptual bank-perturbation feedback for initiation in bedload streams; and Crosato, Mosselman, Desta & Uijttewaal (2011) found evidence for slow intrinsic nonmigrating bars in straight channels, which they argued dominate incipient meandering only when banks are very resistant, with migrating-bar-induced bank erosion otherwise triggering meandering first. Three conflicting results define the present core of the question. First, Shimada, Shimizu, Hasegawa & Iga (2013) performed a linear stability analysis of a straight channel with erodible non-cohesive banks and concluded that alternate bars can trigger meandering, with meander wavelengths (for example, 12.5 m predicted versus 16.0 m measured in the 50 m laboratory flume case analyzed in that study) well above the classical fixed-bank bar wavelength (about 4 m) and consistent with the observed planform; the classical bend-instability theory alone could not reproduce the simulated meanders. Second, Schuurman, Shimizu, Iwasaki & Kleinhans (2016), using a physics-based depth-averaged morphodynamic model — one that simulates the coupled evolution of flow, bed topography and channel planform — with explicit bank erosion and bar-to-floodplain conversion, concluded that meander initiation from a straight channel requires either an external channel-curvature/inflow perturbation at the upstream boundary or a reach long enough for a steady alternate bar to form, while sustained high-sinuosity meandering additionally requires dynamic upstream forcing together with bar-to-floodplain conversion; free migrating bars alone, in short reaches or without forcing, cause insufficient flow perturbation — their wavelengths are too short and their migration too fast to drive the cascading bank-erosion sequence that grows bends. Third, Kawakami & Watanabe (2016) showed in paired flume experiments that bank erosion under a test discharge begins immediately only where alternate bars pre-exist on the bed, whereas a flat bed produces no bank erosion until bars develop in situ — evidence that bars are the necessary precursor of bank attack. The related bank pull versus bar push dichotomy — whether outer-bank erosion leads inner-bank bar deposition or vice versa during bend growth — was posed by van de Lageweg, van Dijk, Baar, Rutten & Kleinhans (2014) and remains actively studied.

Problem Statement

Determine what physically initiates and sustains the bending of an initially straight alluvial channel with erodible banks. Specifically: can the intrinsic instability of the riverbed (free, migrating alternate bars) alone trigger bank erosion and grow a sustained meandering planform in a finite straight reach, or is an external channel-curvature or inflow perturbation — or a reach long enough for a steady (forced) alternate bar to form — required for meandering to initiate and persist? A complete answer must (i) identify which mechanism(s) operate and establish the temporal order of bar formation, bank deformation, and planform development from an initially straight configuration, and (ii) state the quantitative conditions (e.g. width-to-depth ratio, bank erodibility and resistance, sediment characteristics, reach length, floodplain and vegetation effects) under which each pathway — bars-first triggering, steady-bar triggering, or externally forced triggering — initiates and sustains meandering. The problem is posed in its natural generality, without restriction on channel size, sediment, or flow regime; the predicted meander wavelength and its relation to fixed-bank bar theory and bend-instability theory are part of the target, since the conflicting source results are quantitative as well as qualitative.

References

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