# An Integrated Review of River Bars for Engineering, Management and Transdisciplinary Research

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Summary of Bar Studies

#### 2.1. Bar Classification and Terminology

#### 2.2. Linear Bar Theories

_{0}, and a deviation from this value, h′, that varies in time and space: $h={h}_{0}+{h}^{\prime}$. The average flow depth corresponds to a flat riverbed without bars. The deviation, or perturbation, corresponds to a superimposed pattern of bars and pools. Suppose that the square of the flow depth, h

^{2}, appears somewhere in the equations. This can then be elaborated as: ${h}^{2}={h}_{0}^{2}+2{h}_{0}{h}^{\prime}+{\left({h}^{\prime}\right)}^{2}$. The key assumption of linearization is that the perturbation is much smaller than the average value, also called “basic state”: h′ << h

_{0}. This justifies neglecting (h′)

^{2}. The remaining ${h}_{0}^{2}+2{h}_{0}{h}^{\prime}$ is then substituted for h

^{2}in the equations, along with similar substitutions for other nonlinear terms. The basic state, however, is already known to be a solution of the set of equations. Subtracting the corresponding basic-state equations for h

_{0}from the perturbed equations results in a set of equations for the perturbation, h′, only. These are the equations that describe the pattern of bars and pools.

#### 2.3. Nonlinear Bar Theories

#### 2.4. Numerical Modelling

#### 2.5. Laboratory Investigations

#### 2.6. Field Observations

## 3. Summary of Insights Gained

- (1)
- Fluvial bars can be divided into forced bars, occurring locally, and periodic bars, occurring as rhythmic sequences of more or less similar bars.
- (2)
- Forced bars are generated by local geometry or discontinuity. Examples are point bars at inner bends, confluence bars at tributary junctions, and eddy bars at locations of flow separation.
- (3)
- Periodic bars result from morphodynamic instability of the riverbed. The influence of physical parameters on their features can be understood from linear and nonlinear theoretical analyses of the fundamental mathematical equations for the motion of water and sediment.
- (4)
- Periodic bars can be divided into free bars, migrating through the river, and hybrid bars, which have fixed positions because at least one of the bars in the sequence is forced locally.
- (5)
- The river pattern can be characterized by the bar mode, which represents the number of bars in cross-sections. Alternate bars are typical of meandering rivers whereas multiple bars characterize braided rivers.
- (6)
- The major parameter governing bar length, bar growth rate, bar migration speed (celerity), and bar mode is the width-to-depth ratio of the flow. Periodic bars do not develop if the width-to-depth ratio is below about 10. Channels become braided at width-to-depth ratios larger than about 50. Forced bars do not depend on morphodynamic instability and can occur at width-to-depth ratios below the critical value for the formation of periodic bars.
- (7)
- The wave lengths of hybrid alternate bars are 10–15 times the channel width. The wave lengths of free bars at the same width-to-depth ratio are two to three times smaller.
- (8)
- The longer the bar, the smaller the migration speed.
- (9)
- Observed bar migration is not necessarily associated with free bars. It can also result from elongation during the development of a pattern of hybrid bars, as observed experimentally [26], numerically [15], and in the field [14]. Bars forced during floods at locations of overbank flows migrate too after the fall of the flood, while being eroded away gradually.
- (10)
- Migrating bars can be distinguished from non-migrating bars by their shape. They present a clear migration front and tend to be triangular (Figure 6).
- (11)
- The intensity of the forcing determines the location of hybrid bars, but it does not alter the bar mode. The type of forcing (symmetric in cross-sectional direction or antisymmetric) can impose the presence of symmetric (such as central bars) or antisymmetric bars (such as alternate bars) for a certain distance and thus locally influence the bar mode. For instance, imposing an asymmetric flow to a central-bar system has been found to force the formation of compound alternate bars [19].
- (12)
- Linear theories provide fair predictors of bar mode, bar length, and bar migration (Section 4.1 and Section 4.2). Neither linear nor nonlinear theories, however, provide reliable predictors for bar height and pool depth (Section 4.3). The latter inevitably require numerical modelling or empirical estimates.
- (13)
- Bars may have a simple shape, or a compound shape crossed by smaller channels. Compound bars may arise from discharge variability [53] and from forcing (see point 11).
- (14)
- Fully developed bars assume a lower mode if incipient bars have modes higher than 2. This occurs through a process of merging into larger compound bars. This means that linear theories, strictly speaking valid for incipient bar characteristics, tend to overestimate the bar mode at larger width-to-depth ratios.
- (15)
- The development of an initially straight channel with erodible banks into a meandering alignment can be explained from the formation of non-migrating bars, either hybrid bars [54] or free bars with zero celerity [2]. However, meandering requires accretion of the opposite bank too. Otherwise the bank erosion merely results in a pattern of width expansions and constrictions as in Figure 7.
- (16)
- Discharge variations affect bar characteristics. Tubino [37] finds that bars grow during falling stages of floods, and that bar geometry is controlled by the duration of the active part of flood waves, i.e., the part capable of reworking bed sediment. Hall [55] finds that the mere presence of flow variations can produce non-migrating bars.
- (17)
- Sediment transport in suspension changes bar characteristics if it exhibits significant spatial lags in its adaptation to changing flow conditions [56]. Talmon [57] finds that sediment suspension makes hybrid bars longer and higher. Extending analyses by Bolla Pittaluga and Seminara [58] and Federici and Seminara [59], Bertagni and Camporeale [38] find that suspension has the same effect on free alternate bars. Comparing experimental findings with theoretical and numerical results, Talmon [57] infers that gravity pull along transverse bed slopes affects not only bedload but also part of the suspended load.
- (18)
- Riverbeds composed of mixtures of different grain sizes lead to other bar characteristics than beds composed of uniform sediment. Horizontal and vertical sorting because of bar migration and selective transport interact with the formation and evolution of bars. Free bars are higher and longer for mixed-size sediment than for uniform sediment [21]; hybrid bars, however, are lower [21,24]. Their lengths were shorter compared to bars in uniform sediment in experiments with weakly bimodal mixtures [24] but longer in numerical simulations for more strongly heterogeneous mixtures [21]. Imposed spatial patterns of grain size variations suppress the occurrence of free bars and force the bed into a pattern of steady bars [60]. Sediment heterogeneity appears to influence also river braiding, since higher heterogeneity was found to increase the braiding degree while decreasing the length of braid bars in numerical simulations [20].

## 4. Applications

#### 4.1. Managing Bar Modes

^{2}); b is the degree of non-linearity of the sediment transport law expressed as a function of flow velocity (-), for which Crosato and Mosselman [10] suggest b = 10 for gravel-bed rivers (low sediment mobility) and b = 4 for sand-bed rivers (high sediment mobility). In our experience, b = 10 holds for laboratory experiments with low-mobility sand too. B is the channel width (m); i is the longitudinal bed slope (-); ∆ is the relative submerged mass density of sediment (-); D

_{50}is the median sediment grain size (m); C is the Chézy coefficient for hydraulic resistance (m

^{1/2}/s) and Q

_{W}is the water discharge (m

^{3}/s), suggested as bankfull [10], but in general to be chosen depending on the situation. The Chézy coefficient, C, can be derived from the Manning coefficient, n, and flow depth, h, through C = h

^{1/6}/n.

- (1)
- Equation (1) is a useful tool to assess the new river width as a function of discharge, riverbed slope, sediment characteristics. This formula derived for hybrid bars was found to provide good predictions for migrating free bars too [10]. However, its application should be restricted to channels having width-to-depth ratio smaller than 100. Considering that the channel roughness, represented by Chézy’s coefficient, is a bulk parameter incorporating the effects of many factors on flow and sediment processes, it is advised to use several values of this coefficient, selected within a realistic range, and not a single value to compute the bar mode.
- (2)
- Duró et al. [19] showed that it is sufficient to narrow a river for a distance of about 10 times the channel width to free a location in the center of the narrowed reach from alternate bars.
- (3)
- Equation (1) was successfully applied using the bankfull discharge. However, it can also be used to assess the different bar modes that are likely to appear in a river channel as a result of discharge variations [70]. The relation between bar mode and discharge, Q
_{W}, is inverse: a larger discharge decreases the bar mode, and vice versa. In practice discharge variations produce compound bars that are a combination of different bar modes of which the dominant one pertains to bankfull conditions.

#### 4.2. Managing Bar Length and Migration Rates

_{P}is the m-mode bar wavelength and

_{0}being the reach-averaged water depth and θ

_{0}the reach-averaged Shields parameter. The function for the effect of gravity pull, $f({\theta}_{0})$, can be expressed as [71]:

_{D}, which defines the longitudinal damping of hybrid-bar amplitude:

#### 4.3. Managing Bar Height and Pool Depth

_{0}with θ); $h$ is the local water depth and $R$ is the radius of depth-averaged streamline curvature. Theoretically, for curved channels with uniform width and well away from the banks, $A$ depends on Chézy coefficient, $C$, and Von Kármán coefficient, $\kappa $ (= 0.4), according to

## 5. Conclusions and Recommendations

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Gravel-bars under a bridge, Tagliamento River, Italy (courtesy of Paolo Reggiani); (

**b**) sediment sorting on a bar in the River Adige, at Castelvecchio Bridge, Verona, Italy.

**Figure 2.**(

**a**) Rhine River, the Netherlands. Point bar inside a river bend, forced by channel curvature, hinders navigation. Flow direction from top to bottom. (

**b**) Cauca River, Colombia. Compound central bar forced by a local width expansion. Flow direction from bottom to top.

**Figure 4.**Bar classification after Duró et al. [19].

**Figure 5.**Longitudinal and transverse bed oscillations caused by the presence of alternate and central (periodic) bars. Alternate bars: one row of alternate bars in the channel (m = 1). Central bars: two parallel rows of alternate bars in the channel (m = 2).

**Figure 6.**(

**a**) Free bars migrating in downstream direction in the laboratory. Flow direction from bottom to top (courtesy of Andrés Vargas-Luna). (

**b**) Comparison between the shape and size of free bars migrating in downstream direction (channel above) and of steady hybrid bars (channel below) obtained with identical boundary conditions in a 2D numerical model constructed with the Delft3D code (courtesy of Le Thai Binh). Flow direction from left to right.

Approach | Bar Type | Key Characteristics | Bar Regime | ||
---|---|---|---|---|---|

Sub-Resonant | Resonant | Super-Resonant | |||

Genoa | Uniform free bars | Migrating | Downstream migration | Zero celerity | Upstream migration |

Delft | Hybrid bars long. varying amplitude | Steady | Amplitude damping in downstream direction | No amplitude variation | Amplitude growing in downstream direction |

Applicable to all bar modes | Width-to-depth ratio => |

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**MDPI and ACS Style**

Crosato, A.; Mosselman, E.
An Integrated Review of River Bars for Engineering, Management and Transdisciplinary Research. *Water* **2020**, *12*, 596.
https://doi.org/10.3390/w12020596

**AMA Style**

Crosato A, Mosselman E.
An Integrated Review of River Bars for Engineering, Management and Transdisciplinary Research. *Water*. 2020; 12(2):596.
https://doi.org/10.3390/w12020596

**Chicago/Turabian Style**

Crosato, Alessandra, and Erik Mosselman.
2020. "An Integrated Review of River Bars for Engineering, Management and Transdisciplinary Research" *Water* 12, no. 2: 596.
https://doi.org/10.3390/w12020596