地理学报 ›› 2020, Vol. 75 ›› Issue (5): 1079-1094.doi: 10.11821/dlxb202005014

• 气候变化与地表过程 • 上一篇    下一篇

河流过程的累积现象和随机模型

景唤1, 钟德钰1,2(), 张红武1, 石旭芳3, 王彦君1   

  1. 1.清华大学水沙科学与水利水电工程国家重点实验室,北京 100084
    2.青海大学省部共建三江源生态与高原农牧业国家重点实验室,西宁 810016
    3.青海大学水利电力学院,西宁 810016
  • 收稿日期:2019-06-25 修回日期:2020-03-12 出版日期:2020-05-25 发布日期:2020-07-25
  • 通讯作者: 钟德钰 E-mail:zhongdy@mail.tsinghua.edu.cn
  • 作者简介:景唤(1993-), 女, 河南虞城人, 博士生, 研究方向为河流动力学。E-mail: jingh16@mails.tsinghua.edu.cn
  • 基金资助:
    国家自然科学基金项目(91547204);国家重点研发计划(2016YFC0402500);国家重点研发计划(2017YFC0404303)

The accumulation phenomenon and stochastic model in fluvial processes

JING Huan1, ZHONG Deyu1,2(), ZHANG Hongwu1, SHI Xufang3, WANG Yanjun1   

  1. 1.State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China
    2.State Key Laboratory of Plateau Ecology and Agriculture, Qinghai University, Xining 810016, China
    3.School of Water Resources and Electric Power, Qinghai University, Xining 810016, China
  • Received:2019-06-25 Revised:2020-03-12 Online:2020-05-25 Published:2020-07-25
  • Contact: ZHONG Deyu E-mail:zhongdy@mail.tsinghua.edu.cn
  • Supported by:
    National Natural Science Foundation of China(91547204);National Key R&D Program of China(2016YFC0402500);National Key R&D Program of China(2017YFC0404303)

摘要:

累积现象普遍存在于河流过程中,准确考虑前期水沙条件的累积影响对冲积河流河床演变规律的研究至关重要。为揭示累积现象的物理实质,本文对国内外多条典型冲积河流上枢纽修建后其上下游河道冲淤实测资料进行了分析。定义水沙条件变化为外部扰动,并假定其发生概率符合泊松分布及单个扰动引发的系统反馈强度随时间呈指数衰减。本文运用统计力学中的随机理论给出了冲积河流外部扰动诱发的内部反馈随时间的累积过程及其时空间演进的数学描述和理论模型,并将其应用于枢纽修建后其上下游河道形态时空调整过程的模拟。结果发现,从时间上看,断面垂向、横向及全河段的冲淤调整速率早期较快,之后迅速减缓,河床累积冲刷深度、河宽及河段累积淤积量随时间不断增大直至平衡,表现出典型的累积特性;从空间上看,坝下河段冲刷强度沿程非线性衰减直至消失,这种空间分布上的不平衡是外部扰动引发的系统反馈在空间传播的同时随时间衰减的综合结果,是河流过程累积特性的另一外在表现。模型应用结果表明,河道垂向、横向、纵向及全河段的时空冲淤调整过程均可用归一化公式来描述,计算值与实测值符合较好,相关系数R 2达0.92、0.93、0.76和0.95。本文模型同时考虑了河流过程的累积特性和系统反馈的空间传播特性,可为定量描述扰动后非平衡态河道的时空调整过程提供理论依据和新的计算方法。

关键词: 累积现象, 河流过程, 累积冲淤量, 累积冲刷深度, 河宽

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