Long-term river meandering as a part of chaotic dynamics? A contribution from mathematical modelling

Earth Surface Processes and Landforms

Volumn 35, Issue 7, 2010, Pages 791-802

  Frascati, Alessandro ^a   Lanzoni, Stefano ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

Chaos; Cutoff processes; Nonlinearity; River meandering

Indexed keywords

CHAOS; CHAOTIC BEHAVIOUR; CHAOTIC DYNAMICS; LOCAL CURVATURE; MATHEMATICAL MODELLING; NON-LINEARITY; PHYSICS-BASED SIMULATION; RIVER MEANDERING DYNAMICS; SELF-ORGANIZED CRITICALITY; TEMPORAL DISTRIBUTION;

COMPUTER SIMULATION; CRITICALITY (NUCLEAR FISSION); RIVERS; TIME SERIES;

TIME SERIES ANALYSIS;

CHAOTIC DYNAMICS; COMPUTER SIMULATION; CURVATURE; FLOW MODELING; LONG-TERM CHANGE; MEANDER; NONLINEARITY; NUMERICAL MODEL; RIVER CHANNEL; SELF ORGANIZATION; TIME SERIES ANALYSIS;

EID: 77953156449     PISSN: 01979337     EISSN: 10969837     Source Type: Journal    
DOI: 10.1002/esp.1974     Document Type: Article

References (56)

1. Abarbanel HDI. 1996. Analysis of Observed Chaotic Data. Springer: New York.
2. Bak P, Tang C, Wiesenfeld K. 1987. Self-organised criticality: An explanation of 1/f noise. Physics Review Letters 59: 381-384.
3. Blondeaux P, Seminara G. 1985. A unified bar-bend theory of river meanders. Journal of Fluid Mechanics 157: 449-470.
4. Brice JC. 1973. Meandering pattern of the White River in Indiana: An analysis. In Fluvial Geomorphology. Morisawa M. (ed.) University of New York: Binghampton.
5. Camporeale C, Perona P, Porporato A, Ridolfi L. 2005. On the long-term behavior of meandering rivers. Water Resources Research 41: W12403, doi: 10.1029/2005WR004109.
6. Camporeale C, Perona P, Porporato A, Ridolfi L. 2007. Hierarchy of models for meandering rivers and related morphodynamic processes. Reviews of Geophysics 45: RG1001, doi: 10.1029/2005RG000185.
7. Camporeale C, Perucca E, Ridolfi L. 2008. Signifiance of cutoff in meandering rivers dynamics. Journal of Geophysical Research 113: F01001, doi: 10.1029/2006JF000694.
8. Cao L. 1997. Practical method for determining the minimum embedding dimension of a scalar time series. Physica D; Nonlinear phenomena 110: 43-50.
9. Darby SE. 1998. Modelling width adjustment in straight alluvial channels. Hydrological Processes 12: 1299-1321.
10. Darby SE, Thorne CR. 1986. Development and testing of riverbank stability analysis. Journal of Hydraulic Engineering 122(8): 443-454.
11. Darby SE, Alabyan AM, Van de Wiel MJ. 2002. Numerical simulation of bank erosion and channel migration in meandering rivers. Water Resources Research 38(9): 1163, doi: 10.1029/2001WR000602.
12. Eckmann JP, Ruelle D. 1985. Ergodic theory of chaos and strange attractors. Reviews of Modern Physics 57: 617.
13. Erskine W, McFadden C, Bishop P. 1992. Alluvial cutoffs as indicators of former channel conditions. Earth Surface Processes and Landforms 17: 2337.
14. Fonstad M, Marcus WA. 2003. Self-organized criticality in riverbank systems. Annals of the Association of American Geographers 93(2): 281-296.
15. Frascati A, Lanzoni S. 2009. Morphodynamic regime and long-term evolution of meandering rivers. Journal of Geophysical Research 114: F02002, doi: 10.1029/2008JF001101.
16. Fraser AM, Swinney HL. 1986. Independent coordinates for strange attractors from mutual information. Physics Review A 33: 1134.
17. Friedkin JF. 1945. A laboratory study of the meandering of alluvial rivers. US Army Engineer Waterways Experiment Station: Vicksburg, Mississippi, USA.
18. Gautier E, Brunstein D, Vauchel P, Roulet M, Fuertes O, Guyot JL, Darozzes J, Bourrel L. 2007. Temporal relations between meander deformation, water discharge and sediment fluxes in the floodplain of the Rio Beni (Bolivian Amazonia). Earth Surface Processes and Landforms 32: 230-248.
19. Grassberger P, Procaccia I. 1983a. Characterization of strange attractors. Physics Review Letters 50: 346-349.
20. Grassberger P, Procaccia I. 1983b. Measuring the strangeness of strange attractors. Physica D 9: 189-208.
21. Hodskinson A, Ferguson RI. 1998. Numerical modelling of separated flow in river bends: Model testing and experimental investigation of geometric controls on the extent of flow separation at the concave bank. Hydrological Processes 12(8): 1323-1338.
22. Hooke JM. 2004. Cutoffs galore! Occurrence and causes of multiple cutoffs on a meandering river. Geomorphology 61: 225-238.
23. Hooke JM. 2007. Complexity, self-organisation and variation in behaviour in meandering rivers. Geomorphology 91: 236-258.
24. Howard A, Knutson TR. 1984. Sufficient conditions for river meandering: A simulation approach. Water Resources Research 20(11): 1659-1667.
25. Ikeda S, Parker G, Sawai K. 1981. Bend theory of river meanders. Part 1. Linear development. Journal of Fluid Mechanics 112: 363-377.
26. Johannesson H, Parker G. 1985. Computer simulated migration of meandering rivers in Minnesota. Project Report 242, St. Anthony Falls Hydraulic Laboratory: University of Minnesota.
27. Johanneson H, Parker G. 1989. Linear theory of river meanders. In River Meandering, Water Resources Monograph Series 12, Ikeda S, Parker G. (eds.) AGU: Washington DC. 181-214.
28. Kantz H, Schreiber T. 1997. Nonlinear Time Series Analysis. Cambridge University Press: Cambridge, UK.
29. Kennel MB, Brown R, Abarbanel HDI. 1992. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Physics Review A 45: 3403.
30. Lanzoni S, Siviglia A, Frascati A, Seminara G. 2006. Long waves in erodible channels and morphodynamic influence. Water Resources Research 42: W06D17, doi: 10.1029/2006WR004916.
31. Lanzoni S, Seminara G. 2006. On the nature of meander instability. Journal of Geophysical Research 111: F04006, doi: 10.1029/2005JF000416.
32. Leys KF, Werritty A. 1999. River channel planform change: Software for historical analysis. Geomorphology 29: 107-120.
33. Lin J. 1991. Divergence measures based on the Shannon entropy. IEEE Trans. Inf. Theory 37(1): 145-151.
34. Montgomery K. 1993. Nonlinear dynamics and river meandering. Area 25(2): 97-108.
35. Mosley MP. 1975. Channel changes on the River Bollin, Cheshire, 1872-1973. East Midlands Geographer 6: 185-199.
36. Perucca E, Camporeale C, Ridolfi L. 2005. Nonlinear analysis of the geometry of meandering rivers. Geophysics Research Letters 32: L03402, doi: 10.1029/2004GL021966.
37. Phillips JD. 1992. Nonlinear dynamical systems in geomorphology: Revolution or evolution? Geomorphology 5: 219-229.
38. Phillips JD. 1995. Self-organization and landscape evolution. Progress in Physical Geography 19: 309-321.
39. Pizzuto J, Meckelnburg T. 1989. Evaluation of a linear bank erosion equation. Water Resources Research 25: 1005-1013.
40. Provenzale A, Smith LA, Vio R, Murante G. 1992. Distinguishing between low-dimensional dynamics and randomness in measured time series. Physica D 58: 31-49.
41. Rodriguez-Iturbe I, Rinaldo A. 1997. Fractal River Basins: Chance and Self-Organization. Cambridge Univ. Press: New York.
42. Rosenstein MT, Collins JJ, De Luca CJ. 1993. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 65: 117-134.
43. Sapozhnikov V, Foufoula-Georgiou E. 1997. Experimental evidence of dynamic scaling and indications of self-organized criticality in braided rivers. Water Resources Research 33(8): 1983-1991.
44. Schreiber T, Schmitz A. 1996. Improved surrogate data for nonlinearity tests. Physics Review Letters 77: 635-638.
45. Schumm SA. 1973. Geomorphic thresholds and complex response of drainage systems. In Fluvial Geomorphology. Morisawa M. (ed.) University of New York: Binghamton, 301-310.
46. Seminara G. 2006. Meanders. Journal of Fluid Mechanics 554: 271-297.
47. Seminara G, Zolezzi G, Tubino M, Zardi D. 2001. Downstream and upstream influence in river meandering. Part 2. Planimetric development. Journal of Fluid Mechanics 438: 213-230.
48. Shannon C. 1948. A mathematical theory of communication. Bell System Technical Journal 27: 379-423, 623-656.
49. Sprott JC. 2003. Chaos and Time Series Analysis. Oxford University Press: New York.
50. Stolum HH. 1996. River meandering as a self-organized process. Science 271: 1710-1713.
51. Sun T, Meakin P, Jøssang T, Schwarz K. 1996. A simulation model for meandering rivers. Water Resources Research 32(9): 2937-2954.
52. Sun T, Meakin P, Jøssang T. 2001. A computer model for meandering rivers with multiple bed load sediment size: 2. Computer simulations. Water Resources Research 37: 2243-2258.
53. Takens F. 1985. On the numerical determination of the dimension of an attractor. In Lecture Notes in Mathematics 1125: Dynamical systems and bifurcations. Springer: Berlin.
54. Theiler J. 1988. Lacunarity in a best estimator of fractal dimension. Physics Letters A 133: 195-200.
55. Theiler J. 1990. Estimating fractal dimension. Journal of the Optical Society of America A 7: 1055-1073.
56. Zolezzi G, Seminara G. 2001. Downstream and upstream influence in river meandering. Part 1. General theory and application to overdeepening. Journal of Fluid Mechanics 438: 183-211.