河流过程的累积现象和随机模型

doi:10.11821/dlxb202005014

Abstract

Abstract:

The accumulation phenomenon commonly occurs in fluvial processes. Accurately considering the accumulation effects of previous water and sediment conditions is essential for the study of riverbed evolution. To reveal the physical dynamics of the accumulation phenomenon, herein various geometry observations upstream and downstream of dam on several domestic and overseas typical fluvial rivers were analyzed. To do this, the changes in water and sediment conditions were defined as external disturbances, based on assumptions that the probability of an external disturbance conforms to the Poisson distribution and the feedback intensity induced by an individual disturbance decays exponentially with time. In this paper, a mathematical description of the accumulation processes of internal feedback induced by external disturbances is given, and a corresponding theoretical model is proposed for simulating the spatio-temporal adjustment processes of river characteristic variables on the basis of the stochastic theory in statistical mechanics. Further, the above models were then applied to investigate the spatio-temporal adjustment processes of the upper and lower reaches of dams after their construction. Results revealed two key findings. (i) Temporally, the vertical, lateral, and whole reaches' adjustment rates over time are relatively fast in the early period following disturbances but then slow down rapidly, while the accumulated bed degradation, river width and accumulated sedimentation continuously increase until a new dynamic equilibrium state is attained; these phenomena reflect the representative accumulation characteristics of fluvial processes. (ii) Spatially, the erosion intensity downstream of dams decreases nonlinearly along the channel until it eventually diminishes. In fact, the unbalanced distribution of erosion intensity across space arises from the system feedback caused by external disturbances propagating in space yet decaying over time, which is another external manifestation of an accumulation characteristic in fluvial processes. Model applications indicate that the spatio-temporal adjustment processes of cross sections and channel reaches can be accurately described by the unified theoretical formula derived from equation deforming, since the model predictions show good agreement with observed field data: coefficient of determination (R ²) between them attained values of 0.92, 0.93, 0.76, and 0.95. The proposed theoretical models take both the accumulative characteristics of fluvial processes and the spatial propagation characteristics of system feedback into account synthetically. In demonstrating this approach, this study provides the theoretical basis and new calculation method for quantitatively describing the spatio-temporal adjustment processes of non-equilibrium fluvial channels following disturbances.

Key words: accumulation phenomenon, fluvial process, accumulated erosion and sedimentation, accumulated riverbed degradation, channel width

JING Huan, ZHONG Deyu, ZHANG Hongwu, SHI Xufang, WANG Yanjun. The accumulation phenomenon and stochastic model in fluvial processes[J].Acta Geographica Sinica, 2020, 75(5): 1079-1094.

Figures/Tables 11

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枢纽名称	所在河流	年平均流量(m³/s)		断面(河段) 编号	距坝里程 (km)	河流特征量	测试时段(a)	测量次数
枢纽名称	所在河流	建库前	建库后	断面(河段) 编号	距坝里程 (km)	河流特征量	测试时段(a)	测量次数
胡佛大坝	科罗拉多河	520	400	CHD-1—CHD-3	10~36	累积冲刷深度	1935—1948	15
帕克大坝		230	340	CPD-1—CPD-3	39~95		1938—1975	16
戴维斯大坝		400	340	CDD-1—CDD-2	1~9		1948—1975	28
佩克堡大坝	密苏里河	200	280	MFP-1—MFP-3	9~75	河宽	1936—1973	8
加里森大坝		600	660	MGD-1—MGD-3	32~54		1949—1976	6
加文斯角大坝		930	740	MGP-1—MGP-3	7~48		1955—1974	5
丹江口水库	汉江	1335	1091	黄家港—皇庄	3~270	枯水位降低值	1960—1976	6
三门峡水库	黄河	1522	1412	小浪底—利津	61~678	冲淤量	1961—1984	21
三门峡水库	黄河	1522	1412	四站—潼关(库区)	-		1965—1984	20
小浪底水库	黄河	1266	807	小浪底—利津	61~678		2000—2015	16
三峡水库	长江	14027	12873	宜昌—湖口	30~807		2003—2016	14

垂向调整	衰减系数α	横向调整	衰减系数α	全河段调整	衰减系数α
CHD-1—CHD-3	0.30, 0.40, 0.30	MGP-1—MGP-3	0.40, 0.45, 0.50	三门峡库区四站—潼关	0.40
CPD-1—CPD-3	0.14, 0.22, 0.09	MFP-1—MFP-3	0.18, 0.15, 0.05	黄河全下游(1968—1975年)	0.45
CDD-1—CDD-2	0.17, 0.16	MGD-1—MGD-3	0.60, 0.25, 0.40	黄河全下游(1976—1984年)	0.40

纵向调整	综合衰减系数α/v
黄家港—皇庄段(1965—1975)	0.0160, 0.0120, 0.0090
小浪底—利津段(1961—1964)	0.0065, 0.0060, 0.0042, 0.0038
小浪底—利津段(2003—2015)	0.0100, 0.0050, 0.0050
宜昌—湖口段(2003—2015)	0.0033, 0.0033, 0.0025

The accumulation phenomenon and stochastic model in fluvial processes

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