Interaction between curvature-driven width oscillations and channel curvature in evolving meander bends. (English) Zbl 1430.86008

Summary: We study the morphodynamics of channel width oscillations associated with the planform development of river meander bends. With this aim we develop a novel planform evolution model, based on the framework of the classical bend theory of river meanders by S. Ikeda et al. [ibid. 112, 363-377 (1981; Zbl 0512.76052)], that accounts for local width changes over space and time, tied to the local hydro-morphodynamics through a two-way feedback process. We focus our attention on “autogenic” width variations, which are forced by flow nonlinearities driven by channel curvature dynamics. Under the assumption of regular, sinusoidal width and curvature oscillations, we obtain a set of ordinary differential equations, formally identical to those presented by G. Seminara et al. [ibid. 438, 213-230 (2001; Zbl 1034.76017)], with an additional equation for the longitudinal oscillation of the channel width. The proposed approach gives insight into the interaction between autogenic width variations and curvature in meander development and between forcing and damping effects in the formation of width variations. Model outcomes suggest that autogenic width oscillations mainly determine wider-at-inflection meandering river patterns, and affect their planform development particularly at super-resonant aspect ratios, where the width oscillation reaches its maximum and reduces meander sinuosity and lateral floodplain size. The coevolution of autogenic width oscillation and curvature occurs through temporal hysteresis cycles, whereby the peak in channel curvature lags behind that of width oscillation. Width oscillation amplitudes predicted by the model are consistent with those extracted from remotely sensed data.


86A05 Hydrology, hydrography, oceanography
76E20 Stability and instability of geophysical and astrophysical flows


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[1] Bagnold, R. A., An Approach to the Sediment Transport Problem from General Physics, (1966), US government printing office
[2] Blondeaux, P.; Seminara, G., A unified bar-bend theory of river meanders, J. Fluid Mech., 157, 157, 449-470, (1985)
[3] Braudrick, C. A.; Dietrich, W. E.; Leverich, G. T.; Sklar, L. S., Experimental evidence for the conditions necessary to sustain meandering in coarse-bedded rivers, Proc. Natl Acad. Sci. USA, 106, 40, 16936-16941, (2009)
[4] Brice, J. C.1975 Air photo interpretation of the form and behaviour of alluvial rivers. Tech. Rep. U.S. Army Research Office.
[5] Brown, P. N.; Byrne, G. D.; Hindmarsh, A. C., Vode: a variable-coefficient ode solver, SIAM J. Sci. Stat. Comput., 10, 5, 1038-1051, (1989) · Zbl 0677.65075
[6] Camporeale, C.; Perona, P.; Porporato, A.; Ridolfi, L., On the long-term behavior of meandering rivers, Water Resour. Res., 41, 12, 1-13, (2005)
[7] Chen, D.; Duan, J. G., Modeling width adjustment in meandering channels, J. Hydrol., 321, 1-4, 59-76, (2006)
[8] Colombini, M., Tubino, M. & Whiting, P.1992Topographic expression of bars in meandering channels. In Dynamics of Gravel Bed rivers (ed. Wiley, J. & Ltd., Sons), pp. 457-474. Wiley.
[9] Constantine, J. A.; Dunne, T.; Ahmed, J.; Legleiter, C.; Lazarus, E. D., Sediment supply as a driver of river meandering and floodplain evolution in the amazon basin, Nature Geosci., 7, 12, 899-903, (2014)
[10] Crosato, A., Physical explanations of variations in river meander migration rates from model comparison, Earth Surf. Process. Landf., 34, 15, 2078-2086, (2009)
[11] Darby, S. E.; Alabyan, A. M.; Van de Wiel, M. J., Numerical simulation of bank erosion and channel migration in meandering rivers, Water Resour. Res., 38, 9, 1163, (2002)
[12] Darby, S. E.; Rinaldi, M.; Dapporto, S., Coupled simulations of fluvial erosion and mass wasting for cohesive river banks, J. Geophys. Res., 112, (2007)
[13] Duan, J. G.; Julien, P. Y., Numerical simulation of the inception of channel meandering, Earth Surf. Process. Landf., 30, 1093-1110, (2005)
[14] Dubón, S. A. L.2018 Width variations in river meandering evolution and chute cutoff process. PhD thesis, Università degli Studi di Padova.
[15] Eke, E. C.; Czapiga, M. J.; Viparelli, E.; Shimizu, Y.; Imran, J.; Sun, T.; Parker, G., Coevolution of width and sinuosity in meandering rivers, J. Fluid Mech., 760, 127-174, (2014)
[16] Eke, E. C.; Parker, G.; Shimizu, Y., Numerical modeling of erosional and depositional bank processes in migrating river bends with self-formed width: Morphodynamics of bar push and bank pull, J. Geophys. Res., 119, 2, 1455-1483, (2014)
[17] Frascati, A.; Lanzoni, S., A mathematical model for meandering rivers with varying width, J. Geophys. Res., 118, 3, 1641-1657, (2013)
[18] Güneralp, I.; Abad, J. D.; Zolezzi, G.; Hooke, J., Advances and challenges in meandering channels research, Geomorphology, 163, 1-9, (2012)
[19] Hooke, J. M., The significance of mid-channel bars in meandering channels, Sedimentology, 33, 839-850, (1986)
[20] Ikeda, S.; Parker, G.; Sawai, K., Bend theory of river meanders. Part 1. Linear development, J. Fluid Mech., 112, 363-377, (1981) · Zbl 0512.76052
[21] Jang, C. L.; Shimizu, Y., Numerical simulation of relatively wide, shallow channels with erodible banks, J. Hydraul. Engng, 31, 7, 565-575, (2005)
[22] Jones, E., Oliphant, T. & Peterson, P.2001 SciPy: Open source scientific tools for Python.
[23] Kinoshita, R.1961 Investigation of channel deformation in the Ishikari River. Tech. Rep. 36. Nat. Resour. Div., Ministry of Science and Technology of Japan.
[24] Knighton, A. D., Changes in a braided reach, Geol. Soc. Am. Bull., 83, 3813-3822, (1972)
[25] Lagasse, P. F., Zevenbergen, L. W., Spitz, W. J., Thorne, C. R., Associates, A. & Collins, F.2004 Handbook for Predicting Stream Meander Migration. Tech. Rep. National cooperative highway research program.
[26] Lauer, J. W.; Parker, G., Net local removal of floodplain sediment by river meander migration, Geomorphology, 96, 1-2, 123-149, (2008)
[27] Luchi, R.; Bolla Pittaluga, M.; Seminara, G., Spatial width oscillations in meandering rivers at equilibrium, Water Resour. Res., 48, 5, (2012)
[28] Luchi, R.; Hooke, J. M.; Zolezzi, G.; Bertoldi, W., Width variations and mid-channel bar inception in meanders: River Bollin (UK), Geomorphology, 119, 1-2, 1-8, (2010)
[29] Luchi, R.; Zolezzi, G.; Tubino, M., Modelling mid-channel bars in meandering channels, Earth Surf. Process. Landf., 35, 8, 902-917, (2010)
[30] Luchi, R.; Zolezzi, G.; Tubino, M., Bend theory of river meanders with spatial width variations, J. Fluid Mech., 681, 311-339, (2011) · Zbl 1241.76226
[31] Meyer-Peter, E. & Müller, R.1948Formulas for bed-load transport. In Proc. 2nd Meeting IAHSR, pp. 1-26.
[32] Monegaglia, F.; Zolezzi, G.; Güneralp, I.; Henshaw, A. J.; Tubino, M., Automated extraction of meandering river morphodynamics from multitemporal remotely sensed data, Environ. Model. Software, 105, 171-186, (2018)
[33] Mosselman, E.1992 Mathematical modelling of morphological processes in rivers with erodible cohesive banks. Tech. Rep. Delft Univ. of Technol.
[34] Mosselman, E., Morphological modelling of rivers with erodible banks, Hydrol. Process., 12, 8, 1357-1370, (1998)
[35] Motta, D.; Abad, J. D.; Garcia, M. H., A simplified 2D model for meander migration with physically-based bank evolution, Geomorphology, 163-164, 10-25, (2012)
[36] Parker, G., Surface-based bedload transport relation for gravel rivers, J. Hydraul Res., 28, 4, 417-436, (1990)
[37] Parker, G.; Shimizu, Y.; Wilkerson, G. V.; Eke, E. C.; Abad, J. D.; Lauer, J. W.; Paola, C.; Dietrich, W. E.; Voller, V. R., A new framework for modeling the migration of meandering rivers, Earth Surf. Process. Landf., 36, 1, 70-86, (2011)
[38] Partheniades, E.; Paaswell, R. E., Erodibility of channels with cohesive boundary, J. Hydraul. Div., 96, 3, 755-771, (1970)
[39] Repetto, R.; Tubino, M.; Paola, C., Planimetric instability of channels with variable width, J. Fluid Mech., 457, 79-109, (2002) · Zbl 1112.76348
[40] Richards, K., Channel width and the riffle-pool sequence, Geol. Soc. Am. Bull., 87, 883-890, (1976)
[41] Rüther, N.; Olsen, N. R. B., Modeling free-forming meander evolution in a laboratory channel using three-dimensional computational fluid dynamics, Geomorphology, 89, 3-4, 308-319, (2007)
[42] Seminara, G., Meanders, J. Fluid Mech., 554, 271-297, (2006) · Zbl 1091.76021
[43] Seminara, G. & Tubino, M.1989Alternate Bars and Meandering, pp. 267-320. American Geophysical Union.
[44] Seminara, G.; Tubino, M., Weakly nonlinear theory of regular meanders, J. Fluid Mech., 244, 257-288, (1992) · Zbl 0775.76085
[45] Seminara, G.; Zolezzi, G.; Tubino, M.; Zardi, D., Downstream and upstream influence in river meandering. Part 2. Planimetric development, J. Fluid Mech., 438, 213-230, (2001) · Zbl 1034.76017
[46] Talmon, A. M.; Struiksma, N.; Van Mierlo, M. C. L. M., Laboratory measurements of the direction of sediment transport on transverse alluvial-bed slopes, J. Hydraul Res., 33, 4, 495-517, (1995)
[47] Yalin, M. S.1992 River mechanics. Pergamon press.
[48] Zen, S.; Gurnell, A.; Zolezzi, G.; Surian, N., Exploring the role of trees in the evolution of meander bends: the tagliamento river, italy, Water Resour. Res., 53, 7, 5943-5962, (2017)
[49] Zen, S.; Zolezzi, G.; Toffolon, M.; Gurnell, A., Biomorphodynamic modelling of inner bank advance in migrating meander bends, Adv. Water Resour., 93, 166-181, (2016)
[50] Zolezzi, G.2000 River meander morphodynamics. PhD thesis, University of Genova.
[51] Zolezzi, G., Bertoldi, W. & Tubino, M.2012aMorphodynamics of bars in gravel-bed rivers: bridging analytical models and field observations. In Gravel-Bed Rivers: Processes, Tools, Environments, pp. 69-89.
[52] Zolezzi, G.; Guala, M.; Termini, D.; Seminara, G., Experimental observations of upstream overdeepening, J. Fluid Mech., 531, 191-219, (2005) · Zbl 1156.76339
[53] Zolezzi, G.; Luchi, R.; Tubino, M., Morphodynamic regime of gravel bed, single-thread meandering rivers, J. Geophys. Res., 114, F1, F01005, (2009)
[54] Zolezzi, G.; Luchi, R.; Tubino, M., Modeling morphodynamic processes in meandering rivers with spatial width variations, Rev. Geophys., 50, 4, (2012)
[55] Zolezzi, G.; Seminara, G., Downstream and upstream influence in river meandering. Part 1. General theory and application to overdeepening, J. Fluid Mech., 438, 183-211, (2001) · Zbl 1034.76018
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