**1. Introduction**

In wandering river channels under natural conditions, the incoming water, sediment conditions, and boundary conditions are complex and changeable. The riverbed is wide and straight. The sandbars are dotted in the river channel, the branches are crisscrossed vertically and horizontally, and their shapes are different. The positions of the beaches and water often change. Taking the Yellow River as an example, the Baihe Town Gaocun reaches the lower reaches of the Yellow River, which is a typical wandering river. The length of the reach is 299 km, the distance between the embankments on both banks is generally ~10 km, the maximum width is 20 km, and the longitudinal gradient of the river is 1.72–2.65‱. The riverbed section is wide and shallow and the channel width is 1.5–3.5 km. Under natural conditions, the river channel is densely covered with sandbars, scattered water flow, and numerous branching streams, sometimes up to 4–5 strands [1–3]. The river regime changes frequently and the river facies coefficient under flat beach flow is 20–40. Since the 1980s, the wandering section of the lower Yellow River has been regulated. During the

**Citation:** Xu, L.; Jiang, E.; Zhao, L.; Li, J.; Zhao, W.; Zhang, M. Research on the Asymmetry of Cross-Sectional Shape and Water and Sediment Distribution in Wandering Channel. *Water* **2022**, *14*, 1214. https:// doi.org/10.3390/w14081214

Academic Editors: Qiting Zuo, Xiangyi Ding, Guotao Cui and Wei Zhang

Received: 28 February 2022 Accepted: 7 April 2022 Published: 9 April 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

"National Projects of the Eighth Five-Year Plan" period, the Yellow River regulation workers analyzed the laws of the evolution of the wandering river channel in the lower Yellow River and put forward the "slightly curved regulation scheme". After the implementation of the scheme, the swing range of the main stream and boundary of the wandering river channel was significantly reduced and the river regime of most river sections was initially controlled, which protected the embankment's safety and relieved the downstream flood control pressure to a certain extent. Since 2006 especially, the process of river regulation has been accelerated, the density of regulation works has increased significantly, and the "wide, shallow, scattered, and chaotic" channel shape has been significantly improved [4–6]. At present, there are still some challenges in the wandering river regime which require thorough investigation and excellent river regulation engineering measures [7,8]. River regulation works mainly include control, guidance, and dangerous works [9]. Under the action of regulation works, the wandering range of the river regime has been effectively controlled [10] from 5.5 km in 2000 to 3 km in 2006. In recent years, the swinging range of the main slide of some rivers has become smaller, mostly within 0.5 km.

At the same time, a long-term series of studies on the stabilization of the wandering river regime reported many relevant results that provide constructive opinions on improving the stability of the wandering river regime. Yaoxian et al. [11] found that the longitudinal velocity distribution in a bend is related to the incoming water conditions and boundary conditions through a large-scale bend model test and observation. Liu Yan [12] adopted a slightly curved river regulation scheme to study the impact of changes in the regulation engineering conditions on the river regime of the wandering river in the lower reaches of the Yellow River. The author [8] also studied the change in water and sediment conditions after the construction of Xiaolangdi reservoir. The mismatch between the river regulation project and the new water-sediment relationship led to adjustment of the downstream river regime and frequent occurrence of the abnormal river regime. Hongwu et al. [13] studied the influence of the length of the regulation project on the regulation effect of the wandering river section using the natural river model test, analyzed the adaptability of the built regulation project to medium and small water [14], and discussed the variation law of river length in the straight river section [15,16]. Junhua et al. [7] analyzed the role of downstream wandering river regulation in the new period, analyzed the existing problems of wandering river, and proposed several control countermeasures such as improving river regulation engineering measures. Xinjie [17] studied the impact of beach area project on erosion and deposition in the lower Yellow River. The lower Yellow River has a slightly curved river regulation. River regulation works have strong constraints on the river channel; the riverbed deformation is mainly undercut, the channel width depth ratio is reduced, the river cross-section tends to be narrow and deep, and the river regime tends to be stable [18–20]. In the free-developing river bend, the river boundary constraint is weak, the riverbed deformation is mainly widening, the river width depth ratio increases, the river cross-section tends to be broad and shallow, and the river regime changes significantly. The sediment transport capacity of the broad and shallow areas is weaker than that of the narrow and deep areas, which easily aggravates river sedimentation [21,22] and enhances the heterogeneity of riverbed composition, resulting in a continuous change of section shape with water flow and poor stability of the river regime. Following construction of the river regulation project, the evolution of the river regime is limited to a certain extent, the swing range of the central slip of the wandering river channel is significantly reduced, and the river facies relationship changes accordingly [23,24].

The study discussed how the construction of the river regulation project improved and controlled the river regime, resulting in a new river bed shape, especially in the river section where the river regulation works are relatively perfect and the river section is relatively close to the mainstream. The impact on the river cross-section after the construction project and the change in water and sediment transport and riverbed deformation caused by the adjustment of river cross-section were also investigated. The riverbed evolution differs from the natural river channel. The bend circulation in natural rivers causes a prominent

asymmetry in the distribution of river sections and water and sediment factors. At present, research on changing the shape of river sections after construction of the river regulation project mostly remains at the level of qualitative description, and quantitative calculation is rarely involved. This paper proposed an asymmetry index and calculation method to characterize the river section shape and water and sediment factors. Using the formula for the river section and water and sediment factors along with the transverse distribution, this study quantitatively calculated the asymmetry of section shape and water and sediment factors along with the transverse distribution of the typical reach of the wandering section of the lower Yellow River before and after the construction project. This revealed the reasons for the improvement in river sediment transport capacity after the construction project. lation method to characterize the river section shape and water and sediment factors. Using the formula for the river section and water and sediment factors along with the transverse distribution, this study quantitatively calculated the asymmetry of section shape and water and sediment factors along with the transverse distribution of the typical reach of the wandering section of the lower Yellow River before and after the construction project. This revealed the reasons for the improvement in river sediment transport capacity after the construction project. **2. Materials and Methods** 

caused by the adjustment of river cross-section were also investigated. The riverbed evolution differs from the natural river channel. The bend circulation in natural rivers causes a prominent asymmetry in the distribution of river sections and water and sediment factors. At present, research on changing the shape of river sections after construction of the river regulation project mostly remains at the level of qualitative description, and quantitative calculation is rarely involved. This paper proposed an asymmetry index and calcu-

#### **2. Materials and Methods** *2.1. Construction of River Regulation Project in the Lower Yellow River*

#### *2.1. Construction of River Regulation Project in the Lower Yellow River* With the enhancement of river development and utilization in the last decade, ac-

*Water* **2022**, *14*, x FOR PEER REVIEW 3 of 18

With the enhancement of river development and utilization in the last decade, according to the laws of evolution of a wandering natural river channel, some river regulation projects have been built alternately on the concave bank of the river channel which can transport flood and sediment during large floods and maintain the stability of the river regime in small and medium floods (Figure 1). cording to the laws of evolution of a wandering natural river channel, some river regulation projects have been built alternately on the concave bank of the river channel which can transport flood and sediment during large floods and maintain the stability of the river regime in small and medium floods (Figure 1).

(**a**) (**b**)

**Figure 1.** River channel with a finite control boundary: (**a**) Local reach in the lower Yellow River; (**b**) river regulation project in the lower Yellow River. **Figure 1.** River channel with a finite control boundary: (**a**) Local reach in the lower Yellow River; (**b**) river regulation project in the lower Yellow River.

In order to reflect the construction of wandering river channel project, the density of a river regulation project was defined as the ratio of the total length of the river regime control project in the wandering river channel to the length of river channel. This index indirectly reflects the restraint ability of river regulation project to the river regime. The construction of the Baihe–Gaocun river regulation project of the wandering river in the lower Yellow River was collected and river regulation project density from 1960 to 2014 was drawn, as shown in Figure 2. The river regulation project here only included the control project that restricted the river regime, excluding dangerous projects. As can be seen from Figure 2, as of 2014, the density of the wandering river regime control project has In order to reflect the construction of wandering river channel project, the density of a river regulation project was defined as the ratio of the total length of the river regime control project in the wandering river channel to the length of river channel. This index indirectly reflects the restraint ability of river regulation project to the river regime. The construction of the Baihe–Gaocun river regulation project of the wandering river in the lower Yellow River was collected and river regulation project density from 1960 to 2014 was drawn, as shown in Figure 2. The river regulation project here only included the control project that restricted the river regime, excluding dangerous projects. As can be seen from Figure 2, as of 2014, the density of the wandering river regime control project has reached more than 70%.

#### reached more than 70%. *2.2. Quantitative Characteristics of the Asymmetric Index*

In natural rivers, water flow and riverbeds are intrinsically related. Water flow shapes the riverbed, which in turn restricts water flow. Channel evolution occurs and constantly changes its interactions, e.g., vertical evolution and horizontal evolution. The study of lateral evolution involves bend circulation and other problems which are complex. The asymmetry of the river cross-section is caused by bend circulation which affects the transverse distribution of water and sediment factors, resulting in concave scouring and convex siltation under certain water and sediment conditions. All erosion and deposition evolution of the river is related to asymmetry; therefore, study of the river asymmetry is significant.

For the wandering channel, the asymmetry of the section shape and the distribution of water and sediment factors on the section is obvious and there is a strong causal relationship

between them. River regulation works in the wandering reach of the lower Yellow River are arranged according to the asymmetric characteristics of water and sediment movement. The limited engineering boundary is always arranged on one side of the river, and most of the projects on the opposite side are not arranged. Hence, the river boundary condition was termed the limited control boundary condition in this study. Therefore, the limited control boundary is also an asymmetric boundary. After a large number of river regulation projects were built in the lower Yellow River, the distribution of river water and sediment factors in the cross-section has been strongly disturbed, which is bound to change significantly under natural conditions and in turn affects the cross-sectional shape and the adjustment of the river regime. Therefore, it is important to study the asymmetric variation law of the channel cross-sectional shape and transverse distribution of water and sediment factors under limited control boundary conditions. *Water* **2022**, *14*, x FOR PEER REVIEW 4 of 18

**Figure 2.** Density of wandering river regulation works in the lower Yellow River from 1960 to 2014. **Figure 2.** Density of wandering river regulation works in the lower Yellow River from 1960 to 2014.

*2.2. Quantitative Characteristics of the Asymmetric Index*  In natural rivers, water flow and riverbeds are intrinsically related. Water flow shapes the riverbed, which in turn restricts water flow. Channel evolution occurs and constantly changes its interactions, e.g., vertical evolution and horizontal evolution. The study of lateral evolution involves bend circulation and other problems which are com-Here, we discussed some important characteristics of the asymmetry of water and sediment factors along with the transverse distribution, focusing on the comparative analysis of the overall characteristics of the asymmetry of water and sediment factors on the left and right sides of the river. Taking the centerline of the river cross-section under flat discharge as the axis, it was divided into left and right sides, and the square root of the area ratio of each physical quantity on both sides was used to qualitatively describe the asymmetry. Here, regardless of the left and right sides or the left or the right bank bend, the large side index was used as the numerator and the small side as the denominator. Thus, the asymmetry index *AS*<sup>i</sup> is expressed as

$$AS\_{\rm i} = \sqrt{i\_{\rm max}/i\_{\rm min}} \tag{1}$$

tionship between them. River regulation works in the wandering reach of the lower Yel-

and most of the projects on the opposite side are not arranged. Hence, the river boundary condition was termed the limited control boundary condition in this study. Therefore, the limited control boundary is also an asymmetric boundary. After a large number of river regulation projects were built in the lower Yellow River, the distribution of river water and sediment factors in the cross-section has been strongly disturbed, which is bound to change significantly under natural conditions and in turn affects the cross-sectional shape and the adjustment of the river regime. Therefore, it is important to study the asymmetric variation law of the channel cross-sectional shape and transverse distribution of water

Here, we discussed some important characteristics of the asymmetry of water and

*ASii* i max min = (1)

sediment factors along with the transverse distribution, focusing on the comparative analysis of the overall characteristics of the asymmetry of water and sediment factors on the left and right sides of the river. Taking the centerline of the river cross-section under flat discharge as the axis, it was divided into left and right sides, and the square root of the area ratio of each physical quantity on both sides was used to qualitatively describe the asymmetry. Here, regardless of the left and right sides or the left or the right bank bend, the large side index was used as the numerator and the small side as the denominator.

the transverse distribution of water and sediment factors, resulting in concave scouring and convex siltation under certain water and sediment conditions. All erosion and deposition evolution of the river is related to asymmetry; therefore, study of the river asymwhere *i* is any physical quantity, e.g., river cross-section, cross-sectional velocity, sediment concentration, suspended sediment composition, and sediment-carrying capacity. *AS*<sup>i</sup> > 1, and the greater the *AS*<sup>i</sup> , the stronger the asymmetry. When *AS*<sup>i</sup> = 1, the overall distribution of each physical quantity on both sides of the river section is symmetrical.

metry is significant. For the wandering channel, the asymmetry of the section shape and the distribution of water and sediment factors on the section is obvious and there is a strong causal rela-According to the above definition, we derived a formula for the asymmetry index of the overall distribution of the channel cross-sectional shape as well as water and sediment factors on both sides of the channel cross-section (Equations (2)–(6)), marking the specific contents of each element with the lower corner mark. The asymmetry index of the channel

and sediment factors under limited control boundary conditions.

Thus, the asymmetry index *AS*i is expressed as

cross-sectional shape (*AS*A) as well as those of the overall distributions of velocity (*AS*V), sediment concentration (*AS*S), average suspended sediment size (*AS*dcp), and sediment carrying capacity (*AS*S\*) on both sides of the river cross-section were obtained.

$$AS\_{\rm A} = \sqrt{\frac{A\_{\rm max}}{A\_{\rm min}}} \tag{2}$$

$$AS\_{\rm V} = \sqrt{\frac{V\_{\rm max}}{V\_{\rm min}}} \tag{3}$$

$$AS\_{\rm S} = \sqrt{\frac{S\_{\rm max}}{S\_{\rm min}}} \tag{4}$$

$$AS\_{\rm dcp} = \sqrt{\frac{(d\_{\rm cp})\_{\rm max}}{(d\_{\rm cp})\_{\rm min}}} \tag{5}$$

$$\text{AS}\_{\text{S}\_{\ast}} = \sqrt{\frac{(\text{S}\_{\ast})\_{\text{max}}}{(\text{S}\_{\ast})\_{\text{min}}}} \tag{6}$$

Using the above formula, the asymmetry of the channel cross-sectional shape and the asymmetry of the water and sediment factor distribution caused by the asymmetric adjustment of the channel cross-sectional shape were calculated. The calculation method for the transverse distribution of river water and sediment factors is given below. Using this method, the transverse distribution values of water and sediment factors could be calculated and substituted into Equations (2)–(6) to obtain the quantitative indicators of the asymmetry of the river cross-section and water and sediment factors.
