The purpose of this research is to investigate the sinuosity of major rivers in the United States and the world, and to compare them to that predicted by the existing theories. It is shown that the average sinuosity of meandering rivers deviates considerably from what has been reported previously as π. Calculations of the mean value of actual sinuosities of major rivers in the United States and in the World show that this average is very close to 2. Exact models as well as a Monte Carlo simulation for meandering rivers that is based on Gaussian probability distribution function are also presented, and the possibility of composite meandering is discussed.
Ikeda, S., Parker, G. and Sawai, K. (1981) Bend Theory of River Meanders. Part 1. Linear Development. Journal of Fluid Mechanics, 112, 363-377. https://doi.org/10.1017/S0022112081000451
[3]
Blondeaux, P. and Seminara, G. (1985) A Unified Bar Bend Theory of River Meanders. Journal of Fluid Mechanics, 157, 449-470. https://doi.org/10.1017/S0022112085002440
[4]
Zolezzi, G. and 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.
[5]
Blanckaert, K. and de Vriend, H.J. (2003) Nonlinear Modeling of Mean Flow Redistribution in Curved Open Channels. Water Resources Research, 39, 1375-1388. https://doi.org/10.1029/2003WR002068
[6]
Chen, D. and Duan, J.D. (2006) Simulating Sine-Generated Meandering Channel Evolution with an Analytical Model. Journal of Hydraulic Research, 44, 363-373. https://doi.org/10.1080/00221686.2006.9521688
[7]
Chen, D. and Duan, J.D. (2006) Modeling Width Adjustment in Meandering Channels. Journal of Hydrology, 321, 59-76. https://doi.org/10.1016/j.jhydrol.2005.07.034
[8]
Blanckaert, K. and de Vriend, H.J. (2010) Meander Dynamics: A Nonlinear Model without Curvature Restrictions for Flow in Open-Channel Bends. Journal of Geophysical Research: Earth Surface, 115, 79-93. https://doi.org/10.1029/2009JF001301
[9]
Ottevanger, W., Blanckaert, K., Uijttewaal, W.S.J. and de Vriend, H.J. (2013) Meander Dynamics: A Reduced-Order Nonlinear Model without Curvature Restrictions for Flow and Bed Morphology. Journal of Geophysical Research: Earth Surface, 118, 1118-1131. https://doi.org/10.1002/jgrf.20080
[10]
Gu, L., Zhang, S., He, L., Chen, D., Blanckaert, K., Ottevanger, W. and Zhang, Y. (2016) Modeling Flow Pattern and Evolution of Meandering Channels with a Nonlinear Model. Water, 8, Article No. 418. https://doi.org/10.3390/w8100418
[11]
Mandelbrot, B.B. (1983) The Fractal Geometry of Nature. Freemen, New York, NY.
[12]
Snow, R.S. (1989) Fractal Sinuosity of Stream Channels. In: Scholz, C.H. and Mandelbrot, B.B., Eds., Fractals in Geophysics. Pure and Applied Geophysics, Birkhäuser, Basel, 99-109. https://doi.org/10.1007/978-3-0348-6389-6_6
[13]
Montgomery, K. (1996) Sinuosity and Fractal Dimension of Meandering Rivers. Area, 28, 491-500.
[14]
Stolum, H.H. (1998) Planform Geometry and Dynamics of Meandering Rivers. Geological Society of America Bulletin, 110, 1485-1498.
Underwood, E. (2017) A New Model for River Meanders. Eos. https://eos.org/research-spotlights/a-new-model-for-river-meanders
[17]
Bogoni, M., Putti, M. and Lanzoni, S. (2017) Modeling Meander Morphodynamics over Self-Formed Heterogeneous Floodplains. Water Resources Research, 53, 5137-5157.
[18]
Stolum, H.H. (1996) River Meandering as a Self-Organization Process. Science, 271, 1710-1713. https://doi.org/10.1126/science.271.5256.1710
[19]
List of Longest Rivers of the United States. Wikipedia. https://en.wikipedia.org/wiki/List_of_longest_rivers_of_the_United_States_(by_main_stem)
[20]
List of Rivers by Length. Wikipedia. https://en.wikipedia.org/wiki/List_of_rivers_by_length
[21]
Rubinstein, R.Y. (1981) Simulation and the Monte Carlo Method. John Wiley & Sons, New York, NY, 6-12. https://doi.org/10.1002/9780470316511