Theoretical analyses on bed topography responses in large depth-to-width ratio river bends with constant curvatures

doi:10.1007/s10483-018-2324-6

Abstract

Abstract:

Bed morphology is the result of a dynamic response to a complex meandering river system. It is an important factor for the further development of river. Based on the meandering river characterized by a large depth-to-width ratio, a theoretical model is established with the coupling of Navier-Stokes (N-S), sediment transport, and bed deformation equations. The flow characteristics and bed response of river are obtained with the perturbation method. The research results show that, under the effect of twodimensional flow disturbance, the bars and pools present the regular response. For a given sinuousness, the amplitude of the bed response can be used as a criterion to judge the bedform stability. The effects of the Reynolds number, disturbance wavenumber, sinuousness, and bed morphology gradient on the bed response development are described.

Key words: singular boundary value problems, nonlinear, positive solution, existence, bed response, meandering river, large depth-to-width ratio channel, disturbance wave

2010 MSC Number:

76E20
34C60

Shuxian GAO, Haijue XU, Yuchuan BAI. Theoretical analyses on bed topography responses in large depth-to-width ratio river bends with constant curvatures. Applied Mathematics and Mechanics (English Edition), 2018, 39(5): 747-766.

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References

[1] Yalin, M. S. Mechanics of Sediment Transport, Pergamon Press, Oxford, 100-114(1972)
[2] Johannesson, H. Flow Field and Bed Topography in River Meanders, Ph. D. dissertation, University of Minnesota, Twin Cities, 684-689(1988)
[3] Johannesson, H. and Parker, G. Linear Theory of River Meanders, American Geophysical Union, Washington, D. C. (1989)
[4] Bai, Y. C. and Luo, J. S. The loss of stability of laminar flow in open channel and the mechanism of sand ripple formation. Applied Mathematics and Mechanics (English Edition), 23(3), 276-293(2002) https://doi.org/10.1007/BF02438335
[5] Seminara, G. Meanders. Journal Fluid Mechanics, 554, 271-297(2006)
[6] Pittaluga, M. B., Nobile, G., and Seminara, G. A nonlinear model for river meandering. Water Resource Research, 45, 1-22(2009)
[7] Martin, R. L. and Jerolmack, D. J. Origin of hysteresis in bed form response to unsteady flows. Water Resource Research, 49, 1314-1333(2013)
[8] Nelson, A. and Dube, K. Channel response to an extreme flood and sediment pulse in a mixed bedrock and gravel-bed river. Earth Surface Processes and Landforms, 41, 178-195(2016)
[9] Xu, H. J. and Bai, Y. C. The nonlinear theory for sediment ripple dynamic process of straight river. Science China Technological Sciences, 55, 753-771(2012)
[10] Xu, H. J. and Bai, Y. C. Theoretical analyses on hydrodynamic instability in narrow deep river with variable curvature. Applied Mathematics and Mechanics (English Edition), 36(9), 1147-1168(2015) https://doi.org/10.1007/s10483-015-1971-6
[11] Xu, D., Bai, Y. C., and Tan, Y. Experiment on characteristics of flow and sediment movement in sine-generated meandering channels with movable bed (in Chinese). Journal of Tianjin University (Natural Science Edition), 43, 762-770(2010)
[12] Bai, Y. C., Ji, Z. Q., Liu, X. X., Xu, H. J., Yang, S. Q., and Yang, Y. H. Instability of laminar flow in narrow and deep meander channel with constant curvature (in Chinese). Scientic Sinica:Physica, Mechanica and Astronomica, 42, 162-171(2012)
[13] Bai, Y. C., Ji, Z. Q., and Xu, H. J. Stability and self-adaption character of turbulence coherent structure in narrow-deep river bend. Science China:Technological Sciences, 55, 2990-2999(2012)
[14] Qian, N. and Wan, Z. H. Mechanics of Sediment Transport, Science Press, Beijing(2003)
[15] Zhou, H., Lu, C. G., and Luo, J. S. Modeling of individual coherent structures in wall region of a turbulent boundary layer. Science in China (Series A):Methematics, 42, 366-372(1999)
[16] Zhang, D. M., Luo, J. S., and Zhou, H. Dynamic model of coherent structure in the wall region of a turbulent boundary layer. Science in China (Series G):Physica, Mechanica and Astronomica. 46, 291-299(2003)
[17] Bai, Y. C. and Yang, Y. H. The dynamic stability of the flow in a meander channel. Science China Technological Sciences, 54, 931-940(2011)
[18] Parker, G. Discussion of "Lateral bed load transport on side slopes" by Syunsuke Ikeda. American Society of Civil Engineers, 110, 197-199(1984)
[19] Kikkawa, H., Ikeda, S., and Kitagawa, A. Flow and bed topography in curved open channels. American Society of Civil Engineers, 102, 1327-1342(1976)
[20] Zimmermann, C. and Kennedy, J. F. Transverse bed slopes in curved alluvial channels. American Society of Civil Engineers, 104, 33-48(1978)