The Quasi‐Equilibrium Longitudinal Profile in Backwater Reaches of the Engineered Alluvial River: A Space‐Marching Method
The Quasi‐Equilibrium Longitudinal Profile in Backwater Reaches of the Engineered Alluvial River: A Space‐Marching Method
复制标题
DOI：
10.1029/2019jf005195
复制
发表时间：
2019-11
期刊：
影响因子：
--
通讯作者：
L. Arkesteijn;A. Blom;M. Czapiga;V. Chavarrías;R. Labeur
中科院分区：
文献类型：
--
作者：
L. Arkesteijn;A. Blom;M. Czapiga;V. Chavarrías;R. Labeur
工程冲积河流（即，固定宽度的河道）平面形状受限，但可自由调整河道坡度和河床表面纹理。这些特征受到控制：水文线、泥沙通量和下游基准面。如果控制持续（或相对于信道响应的时间尺度缓慢变化），则信道最终达到平衡（或准平衡）状态。为了简洁起见，我们使用术语“准平衡”作为这两种状态的简写。这种准平衡状态的特征在于准静态和动态分量，其定义了床面动态达到平均值的特征时间尺度。虽然存在准正常流段准平衡河道几何形状的分析模型，但仍然缺乏确定回水主导段准平衡几何形状的快速方法。我们表明，无论其动态如何，回水或准正常流段的河床坡度可以近似为准静态（即，静态斜率近似）。这种近似使我们能够在回水和准正常流段中推导出准平衡渠道几何形状的准静态分量的快速数值空间推进解。空间推进法意味着通过空间步进来找到解，而无需计算瞬态相位。附加的数值时间步进模型描述了准平衡通道几何形状的动态分量。这两个模型对回水-Exner模型的测试证实了它们的有效性。我们的分析验证了先前的研究，表明流量持续时间曲线决定了准静态平衡剖面，而流量序列则决定了动态波动。
An engineered alluvial river (i.e., a fixed‐width channel) has constrained planform but is free to adjust channel slope and bed surface texture. These features are subject to controls: the hydrograph, sediment flux, and downstream base level. If the controls are sustained (or change slowly relative to the timescale of channel response), the channel ultimately achieves an equilibrium (or quasi‐equilibrium) state. For brevity, we use the term “quasi‐equilibrium” as a shorthand for both states. This quasi‐equilibrium state is characterized by quasi‐static and dynamic components, which define the characteristic timescale at which the dynamics of bed level average out. Although analytical models of quasi‐equilibrium channel geometry in quasi‐normal flow segments exist, rapid methods for determining the quasi‐equilibrium geometry in backwater‐dominated segments are still lacking. We show that, irrespective of its dynamics, the bed slope of a backwater or quasi‐normal flow segment can be approximated as quasi‐static (i.e., the static slope approximation). This approximation enables us to derive a rapid numerical space‐marching solution of the quasi‐static component for quasi‐equilibrium channel geometry in both backwater and quasi‐normal flow segments. A space‐marching method means that the solution is found by stepping through space without the necessity of computing the transient phase. An additional numerical time stepping model describes the dynamic component of the quasi‐equilibrium channel geometry. Tests of the two models against a backwater‐Exner model confirm their validity. Our analysis validates previous studies in showing that the flow duration curve determines the quasi‐static equilibrium profile, whereas the flow rate sequence governs the dynamic fluctuations.