Similarity Solution of Jet Boundary Layer for the Initial Segment of a Delta

BAI Yuchuan; XIN Weiyan; XU Haijue

doi:10.21656/1000-0887.400364

Volume 41 Issue 9

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BAI Yuchuan, XIN Weiyan, XU Haijue. Similarity Solution of Jet Boundary Layer for the Initial Segment of a Delta[J]. Applied Mathematics and Mechanics, 2020, 41(9): 1011-1025. doi: 10.21656/1000-0887.400364

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Similarity Solution of Jet Boundary Layer for the Initial Segment of a Delta

doi: 10.21656/1000-0887.400364

¹State Key Laboratory of Hydraulic Engineering Simulation and Safety,Tianjin University, Tianjin 300072, P.R.China;²Institute for Sediment on River and Coast Engineering, Tianjin University, Tianjin 300072, P.R.China

Funds: The National Natural Science Foundation of China（51879182）

Received Date: 2019-11-29
Rev Recd Date: 2020-02-20
Publish Date: 2020-09-01

Abstract

Abstract

Sediment is carried by flow to the lake area during the formation process of the initial segment of a delta, which mainly depends on the initial momentum to maintain its own continuous movement. According to the characteristics of this process, the theoretical model for the plane jet boundary layer in the initial segment of the delta was established based on the shallow water equations for muddy water, and the flow field distribution of the initial segment of delta formation was obtained with the similarity solution method. Based on the general mathematical model of river bed evolution, the theoretical expression of the morphological characteristics of the initial segment was derived, and the erosion and deposition of the initial segment were quantitatively analyzed. Through the experimental verification, the theoretical solution can well describe the erosion and deposition trend and morphological characteristics in the early stage of delta formation.
- delta,
- jet boundary layer,
- initial segment,
- erosion and deposition,
- similarity solution

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References(30)

References

[1]	JOSHI P B. Hydromechanics of tidal jets[J]. Journal of the Waterway, Port, Coastal and Ocean Division,1982,108(3): 239-253.
[2]	ORTEGA-SNCHEZ M, LOSADA M A, BAQUERIZO A. A global model of a tidal jet including the effects of friction and bottom slope[J]. Journal of Hydraulic Research,2008,46(1): 80-86.
[3]	KIM M, JEROLMACK D J. The pulse of calm fan deltas[J]. The Journal of Geology,2008,116(4): 315-330.
[4]	HOYAL D C J D, SHEETS B A. Morphodynamic evolution of experimental cohesive deltas[J]. Journal of Geophysical Research Atmospheres,2009,114(F2). DOI: 10.1029/2007JF000882.
[5]	XIN W Y, BAI Y C, XU H J. Experimental study on evolution of lacustrine shallow-water delta[J]. Catena,2019,182: 1-10.
[6]	WHIPPLE K X, PARKER G, PAOLA C, et al. Channel dynamics, sediment transport, and the slope of alluvial fans: experimental study[J]. The Journal of Geology,1998,106(6): 677-694.
[7]	SCHEIDEGGER A E. Hydraulic effects in geodynamics[J]. Geologie und Bauwesen,1959,25: 3-49.
[8]	CULLING W E H. Analytical theory of erosion[J]. The Journal of Geology,1960,68(3): 336-344.
[9]	PRICE W E. Simulation of alluvial fan deposition by a random walk model[J]. Water Resources Research,1974,10(2): 263-274.
[10]	韩其为. 论水库的三角洲淤积(一)[J]. 湖泊科学, 1995,7(2): 107-118.(HAN Qiwei. Study on the deposition of reservoir delta (1)[J]. Journal of Lake Sciences,1995,7(2): 107-118.(in Chinese))
[11]	韩其为. 论水库的三角洲淤积(二)[J]. 湖泊科学, 1995,7(3): 213-225.(HAN Qiwei. Study on the deposition of reservoir delta (2)[J]. Journal of Lake Sciences,1995,7(3): 213-225.(in Chinese))
[12]	SWENSON J B, VOLLER V R, PAOLA C, et al. Fluviodeltaic sedimentation: a generalized Stefan problem[J]. European Journal of Applied Mathematics,2000,11: 433-452.
[13]	CAPART H, BELLAL M, YOUNG D L. Self-similar evolution of semi-infinite alluvial channels with moving boundaries[J]. Journal of Sedimentary Research,2007,77: 13-22.
[14]	RAJEEV, KUSHWAHA M S, KUMAR A. An approximate solution to a moving boundary problem with space-time fractional derivative in fluvio-deltaic sedimentation process[J]. Ain Shams Engineering Journal,2013,4(4): 889-895.
[15]	LORENZO-TRUEBA J, VOLLER V R, PAOLA C. A geometric model for the dynamics of a fluvially dominated deltaic system under base-level change[J]. Computers & Geosciences,2013,53: 39-47.
[16]	WANG F C. The dynamics of a river-bay delta system[J]. Journal of Geophysical Research: Oceans,1984,89(C5): 8054-8060.
[17]	FALCINI F, JEROLMACK D J. A potential vorticity theory for the formation of elongate channels in river deltas and lakes[J]. Journal of Geophysical Research Atmospheres,2010,115(F4). DOI: 10.1029/2010JF001802.
[18]	NARDIN W, MARIOTTI G, EDMONDS D A, et al. Growth of river mouth bars in sheltered bays in the presence of frontal waves[J]. Journal of Geophysical Research: Earth Surface,2013,118(2): 872-886.
[19]	LEONARDI N, CANESTRELLI A, SUN T, et al. Effect of tides on mouth bar morphology and hydrodynamics[J]. Journal of Geophysical Research: Oceans,2013,118(9): 4169-4183.
[20]	SCHLICHTING H, GERSTEN K. Boundary-Layer Theory [M]. Berlin: Springer Verlag, 1968.
[21]	RAJARATNAM N, STALKER M J. Circular wall jets in coflowing streams[J]. Journal of the Hydraulics Division,1982,108(2): 187-198.
[22]	MUTO T, STEEL R J. Retreat of the front in a prograding delta[J]. Geology,1992,20(11): 967-970.
[23]	PARKER G, MUTO T. 1D numerical model of delta response to rising sea level[C]// 〖STBX〗3rd IAHR Symposium, River, Coastal and Estuarine Morphodynamics. Barcelona, Spain, 2003.
[24]	EDMONDS D A, SHAW J B, MOHRIG D. Topset-dominated deltas: a new model for river delta stratigraphy[J]. Geology,2011,39(12): 1175-1178.
[25]	谢鉴衡. 河流模拟[M]. 北京: 水利电力出版社, 1990.(XIE Jianheng. The Simulation of River [M]. Beijing: Water Conservancy and Electric Power Press, 1990.(in Chinese))
[26]	BARENBLATT G I, ISAAKOVICH B G. Scaling, Self-Similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics [M]. Cambridge: Cambridge University Press, 1996.
[27]	四川大学水力学与山区河流开发保护国家重点实验室. 水力学[M]. 北京: 高等教育出版社, 2016: 210-217.(State Key Laboratory of Hydraulics and Mountain River Engineering of Sichuan University. Hydraulics [M]. Beijing: Higher Education Press, 2016: 210-217.(in Chinese))
[28]	余常昭. 环境流体力学导论[M]. 北京: 清华大学出版社, 1992: 202-206.(YU Changzhao. Introduction to Environmental Hydrodynamics [M]. Beijing: Tsinghua University Press, 1992: 202-206.(in Chinese))
[29]	钱宁, 万兆惠. 泥沙运动力学[M]. 北京: 科学出版社, 1983.(QIAN Ning, WAN Zhaohui. Mechanics of Sediment Movement [M]. Beijing: Science Press, 1983.(in Chinese))
[30]	白玉川, 胡晓, 徐海珏. 入湖浅水三角洲形成过程实验模拟分析[J]. 水利学报, 2018,49(5): 549-560.(BAI Yuchuan, HU Xiao, XU Haijue. Experimental analysis of the formation process of lacustrine shallow-water delta[J]. Journal of Hydraulic Engineering,2018,49(5): 549-560.(in Chinese))