The most challenging issues in rivers include sediment management, outer bank erosion, intake choking, channel bed shoaling, and river meandering. This paper provides a concise review of the newly developed sediment and flow control technique known as the Iowa vane or submerged vane. Submerged vanes are small flow training structures designed to redistribute flow and sediment within the channel cross-section. The structural stability and economic feasibility of submerged vanes, which distinguish them from conventional methods such as dikes and groins, have inspired many researchers to study their use and efficiency in river management over many decades. Various hydrodynamic characteristics, such as flow structure, sediment motion, vortex generation, and scouring around submerged vanes and arrays of vanes, have been reviewed. Additionally, various vane parameters that influence these characteristics are also explained. This paper also underscores current limitations in understanding the flow and sediment behavior around submerged vanes, while also providing recommendations for future research in the field.

  • This paper aims to provide a thorough overview of the use of submerged vanes in river management.

  • Several indices, such as flow hydrodynamics, vane dimensions and sediment motion, have been discussed.

  • The literature review identified limitations in existing studies and provided directions for future research.

CD, CL

drag and lift coefficients

d

flow depth

b

width of the section

f

Darcy–Weisbach friction factor

FD

drag force

FL

vane lift force

g

acceleration due to gravity

H

height of vane

L

vane length

m

resistance coefficient

r

the radius of curvature

ri, ro

innermost and outermost radius of curvature

S

bed slope

s

stream-wise component

Tc

centrifugal force torque

Tv

vane-induced torque

u

point velocity at height z

U

average velocity

u*

shear velocity

ua

approach flow velocity

depth-averaged mean velocity

strength of circulation

θ

sweep angle at leading edge

d0

initial pre-vane water depth

dv

water depth at the river bank after installation of the vane

swept ratio

λ

interaction coefficient

λt

taper ratio

ρ

mass density of water

angle of attack

von Karman constant (≈0.40 for clear water)

K

equivalent sand roughness

CL,p

potential flow lift

CL,v

vortex lift

transverse bed shear stress

longitudal bed shear stress

δn

transverse vane spacing

δs

spacing between vane array

Sediment diversion structures on the riverbed are widely utilized in river engineering projects, aiming to prevent bank erosion along the river curves, intake choking, shoaling of the channel bed, and river meandering. Additionally, vanes contribute to protecting the bridge pier and foundation. Despite the employment of various sediment control structures, such as groins and dikes, their usage has been limited due to structural instability and economic unfeasibility. At the Iowa Institute of Hydraulic Research in Iowa (Odgaard & Spoljaric 1986; Odgaard & Mosconi 1987; Odgaard & Wang 1991a; Wang & Odgaard 1993) designed low-height, high-length structures known as Iowa vanes or submerged vanes. These structures were intended to modify the near-bed flow pattern and bed-sediment motion in the transverse direction of rivers. Recent studies on submerged vanes have demonstrated their successful use in increasing flow depth and reducing sediment diversion at water intakes (Barkdoll et al. 1999; Baltazar et al. 2021; Bor 2022; Gumgum & Cardoso 2022), protecting bridge pier and foundations (Zarei et al. 2019; Safaripour et al. 2020; Vaghefi et al. 2023; Hamidi et al. 2024), and preventing stream bank erosion (Odgaard & Kennedy 1983; Odgaard & Mosconi 1987; Wang & Odgaard 1993; Bhuiyan et al. 2010; Tasar et al. 2023). The advantage of submerged vanes over traditional sediment diversion structures, such as dikes, spurs, and groins, lies in their efficient flow redistribution with lower resistance, facilitating easy installation and economic viability. Unlike groins and dikes, which redirect flow perpendicularly through basic continuity, submerged vanes achieve redistribution through vorticity by aligning with the flow, leading to comparatively lower drag forces (Wang & Odgaard 1993). As per Odgaard & Wang (1991a), the oblique orientation of the vane angle results in a pressure differential between its two sides, inducing an upward flow component on the pressure side and a downward flow component on the suction side. The vane produces a tip vortex that propagates downstream, consequently altering the shear stress field. The longitudinal, horizontally helical flow pattern effectively diverts sediment downstream, preventing sediment ingress into the intake canal (Barkdoll et al. 1999). Recent field tests (Rodriguez 2020) have demonstrated the remarkable potential of submerged vanes in effectively mitigating erosion at river curves and providing erosion protection in a bend of the East Nishnabotna River, Iowa (Odgaard & Mosconi 1987) shown in Figure 1(a). In modern river engineering projects, submerged vanes are widely employed for sediment control. In Figure 1(b), submerged vanes are being installed at the water intake to mitigate the entrainment of sediment from the intake on Kosi River, Nepal. Another study by Lake et al. (2021) aimed to divert sediment away from existing infiltration routes and enhance riverbed depth within the matrices by implementing submerged vanes in an Australian river.
Figure 1

(a) Submerged vanes in East Nishnabotna River, Iowa, protecting stream bank against erosion (Odgaard 2009) and (b) submerged vanes being installed at water intake on Kosi River, Nepal (Odgaard 2009).

Figure 1

(a) Submerged vanes in East Nishnabotna River, Iowa, protecting stream bank against erosion (Odgaard 2009) and (b) submerged vanes being installed at water intake on Kosi River, Nepal (Odgaard 2009).

Close modal
Submerged vane is a river training structure designed to manage sediment and control water flow in a river channel. Many researchers (Odgaard & Kennedy 1983; Odgaard & Spoljaric 1986; Odgaard & Mosconi 1987; Odgaard & Wang 1991a) investigated the physics of fluid flow and sediment motion around the submerged vane and provided theorem on it. Figure 2 illustrates the alignment of the submerged vane with the incoming flow and types of vortex by the submerged vane. Wang & Odgaard (1993) and Klovsky & Kozlov (2019) referred to submerged vanes as artificial vortex generators as they are known for inducing vorticity. Here, two different types of vortex are created by the submerged. They are mainly the horseshoe vortex (its axis perpendicular to the submerged vane) and primary vortex (its axis parallel to the submerged vane, also called as tip vortex). The vane's leading edge is the primary factor contributing to the horseshoe vortex, which created an intense scour hole near the origin point of the vortex and was dismissed after some distance. Due to the pressure difference between the two sides of the vane, the primary vortex is generated. The primary vortex is the main reason for a scour channel downstream of the submerged vane (Figure 2).
Figure 2

A schematic diagram showing the vortex flow and bed morphology around the vane.

Figure 2

A schematic diagram showing the vortex flow and bed morphology around the vane.

Close modal

Forces around the vane

The flow structure around a submerged vane can vary depending on various factors, such as the forces around the vane, flow characteristics, and vane properties. Researchers have experimentally and analytically studied the effects of these characteristics on a submerged vane (Odgaard & Kennedy 1983; Odgaard & Spoljaric 1986; Odgaard & Wang 1991a; Tan et al. 2005). The bends of a river are typically its most unstable sections, where bank erosion commonly occurs. This erosion is often driven by centrifugally generated secondary currents, known as transverse circulations or helical motion, which emerge due to variations in centrifugal acceleration along a vertical line in the flow. This phenomenon arises from the non-uniformity of the vertical velocity profile and the interaction between vertical velocity gradients. Fast-moving surface currents are compelled to migrate toward the curved bend, while slow-moving near-bed currents are compelled to move toward the center of the river, resulting in large depths and velocities near the outer banks. The difference in centrifugal force between the faster-moving fluid near the free surface and the slower-moving near-bed fluid leads to the erosion of the river bend. By applying a torque on the flow that counterbalances the centrifugally induced torque, a submerged vane can effectively suppress the secondary flow and its associated effects, which are responsible for the erosion of the river bend (Odgaard & Mosconi 1987), as shown in Figure 3. Also, submerged vane structures equalize water depth between the inner and outer banks in open channel flows, consequently decreasing flow velocity by redirecting water depth and velocity from the outer bank to the inner bank (Tasar et al. 2023). In Figure 3, Tc represents the centrifugal force torque, Tv denotes the vane-induced torque, FL indicates the vane-induced lift force, r is the radius of curvature, ri and ro are the innermost and outermost section radius, b is the width of the section, α is the angle of attack, d is the flow depth, L is the vane length, U is the average velocity, and ρ is the mass density of water. Odgaard & Mosconi (1987) derived the formula for centrifugal torque about the centroid of the vane acting on a volume element with the included angle , given as follows:
formula
(1)
Figure 3

A schematic representation of the torque induced by centrifugal acceleration (Section B-B) and the secondary flow caused by vanes (Section A-A) (Odgaard & Mosconi 1987).

Figure 3

A schematic representation of the torque induced by centrifugal acceleration (Section B-B) and the secondary flow caused by vanes (Section A-A) (Odgaard & Mosconi 1987).

Close modal
Here, is the depth-averaged mean velocity. The velocity profile exponent, m, is related to the Darcy–Weisbach friction factor, f, as , where is the von Karman constant (approximately 0.40 for clear water). The friction factor f is given by , where is the shear velocity. Since the radial-pressure-gradient force remains relatively constant across the depth and does not produce any moment around the centroid, Tc is primarily responsible for the secondary flow (Odgaard & Mosconi 1987). Submerged vanes are installed to counter the secondary currents generated by Tc. FL exerted by each vane on the flow generates the Tv. The equation for Tv produced by N independent vanes about the section centroid is given by (Odgaard & Mosconi 1987).
formula
(2)
Here, H represents the height of the vane, and CL is the lift coefficient. In order to neutralize the secondary flow, the torque exerted by the vane, denoted as Tv, must balance with the Tc (Odgaard & Mosconi 1987).To calculate the vane lift force (FL) and drag force (FD), Odgaard & Wang (1991a) derived the equations are given in Equations (3) and (4), respectively.
formula
(3)
Also,
formula
(4)
Here, CD is the drag coefficient. Based on the assumption that the distribution of the vertical circulation around the vane follows an elliptical pattern, with maximum values at the bed and zero at the top of the vane, the lift coefficient and corresponding drag coefficient can be calculated using Equations (5) and (6), respectively (Odgaard & Mosconi 1987).
formula
(5)
And,
formula
(6)

Sediment diversion

Odgaard & Spoljaric (1986, 1989) proposed an analytical technique for designing a system of submerged vanes to regulate depth in alluvial rivers. They concluded that flow separation becomes significant and causes excessive scour around the vane when angles exceed 15°. The employment of vanes alters the secondary flow at bends, which causes the sediment to be redistributed within the channel cross-section and reduces scour at river bends (Odgaard & Kennedy 1983; Odgaard & Mosconi 1987). As per the results of a laboratory experiment conducted in a large meandering mobile-bed channel, the bank-attached vane positioned at a 30° angle efficiently redirects the thalweg toward the center of the channel and fills the scour hole near the outer bank (Bhuiyan et al. 2010). Biswas & Barbhuiya (2018) demonstrate the impact of submerged vanes on three-dimensional flow patterns and riverbed morphology in a meandering river bend, resulting in a reduction of scour depths by as much as 40% at the outer bank of the bend. Aware et al. (2005) experimentally observed that sediment gets deposited toward the outer bank due to the vortex leaving the trailing edge of the vane. Because of the vane alignment, the vortex travels toward the outer bank in the direction of the flow, and sediment deposition at the outer bend mitigates scour and leads to a more uniform flow depth, contrasting with the condition where no vanes are present. Additionally, the pressure difference between the two sides of the vane induces a secondary flow, resulting reducing sediment entry into intake canals and diversion sediment away from the intake (Bor 2022; Gumgum & Cardoso 2022). The vanes prevented the formation of the diversion vortex in the main channel and reduction of sediment divesion by 26% (Baltazar et al. 2021).

On a mobile bed, higher shear stresses on the suction side will increase sediment movement in that location, whereas lower shear stresses on the pressure side will decrease sediment movement (Wang & Odgaard 1993). In order to quantify the transverse bed shear stress necessary to mitigate the presence of secondary currents in fully developed bend flows, Odgaard & Wang (1991a) derived the equation, which is given as follows:
formula
(7)

Tan et al. (2005) conducted an extensive investigation into the flow structures and bed load particle motion within the four distinct zones surrounding the submerged vane. They identified four distinct spatial zones around the vane: the left and right head zones, the immediate frontal zone, and the lee zone. Each zone exhibited a different flow structure. The flow skewed toward the center top of the vane due to lateral diffusion of flow, with a helical vortex generated at a location on the frontal face of the vane. Near-bed fluid flowed around the vane at the left head zone and then along the vane's lee zone toward the center. The study observed that upper fluid dived over the vane and into the bed, increasing near-bed velocity and the rate of bed scour, resulting in a significant scour hole in the vane's lee zone. Their results indicated that the submerged vane offered the best sediment diversion when the vane height was one-fifth of the approach flow depth.

Table 1

Summary of the experimental setup and range of different parameters used by various investigators

S .No.Author (s)Discharge (m3/s)Depth of flow (m)Sediment size (mm)Vane parameters
Height (m)Length (m)No. of vanes (Nos)Angle of attack
1. Odgaard & Kennedy (1983)  0.154 0.064–0.253 0.30 0.048 0.12 36–52 15° 
2. Odgaard & Spoljaric (1986)  0.021 0.152 0.3–1.5 0.076 0.213 5–20° 
3. Odgaard & Wang (1991)a)  0.088–0.15 0.178–0.182 0.41 0.074 0.152 4 vanes in 3–4 rows 15–25° 
4. Wang & Odgaard (1993)  0.033–0.133 0.152–0.16 0.41,4 0.076 0.152 Single and multiple rows 15–30° 
5. Marelius & Sinha (1998)  — 0.4 0.9 0.12 0.24 25–57° 
6. Barkdoll et al. (1999)  0.104 0.152 0.9 0.032 0.10 3 vanes in each 7 rows 20° 
7. (Gupta et al. 2006a, 2006b, 2007, 2010— 0.14–0.18 0.225–0.405 0.06 0.18 30–50° 
8. Tan et al. (2005)  0.4 0.2–0.6 10–20 0.05–0.15 1–4 30° 
9. Aware et al. (2005)  — — 0.3 0.03–0.10 0.07–0.17 Single and double array 30° 
10. Bejestan & Azizi (2012)  — 0.25 0.5 0.25 0.075 20° 
11. Biswas & Bharbhuiya (2018)  0.05 0.288 0.28 0.075 0.27 18–36 15° 
12. Sharma & Ahmad (2020)  0.024–0.052 0.09–0.1241 — 0.05–0.12 0.02–0.06 28–76 vanes in four rows 30° 
13. Azizipour et al. (2020)  — 0.14 1.5 0.14 — 23–60° 
14. Safaripour et al. (2020)  0.07 0.18 1.5 0.075 — 25° 
15. Baltazar et al. (2021)  0.029 0.1 0.86 0.1 0.03 7 vane in two row 20° 
16. Gumgum & Cardoso (2022)  0.029 0.1 0.86 0.1 0.02–0.04 3,6 in a row 10–50° 
17. Bor (2022)  0.045 0.12 0.85 0.09 0.03 3 vane in single column 20° 
18. Sarlak et al. (2023)  0.024, 0.05 0.16 0.48 0.08 0.16 10–35° 
19. Vaghefi et al. (2023)  0.07 0.18 1.5 — 0.05–0.1 2–4 15–35° 
20. Tasar et al. (2023)  0.025 0.095 — 0.1 0.1 3 vane in three row — 
21. Hamidi et al. (2024)  0.0014–0.0042 0.02–0.05 0.82 0.1 0.1 10–90° 
S .No.Author (s)Discharge (m3/s)Depth of flow (m)Sediment size (mm)Vane parameters
Height (m)Length (m)No. of vanes (Nos)Angle of attack
1. Odgaard & Kennedy (1983)  0.154 0.064–0.253 0.30 0.048 0.12 36–52 15° 
2. Odgaard & Spoljaric (1986)  0.021 0.152 0.3–1.5 0.076 0.213 5–20° 
3. Odgaard & Wang (1991)a)  0.088–0.15 0.178–0.182 0.41 0.074 0.152 4 vanes in 3–4 rows 15–25° 
4. Wang & Odgaard (1993)  0.033–0.133 0.152–0.16 0.41,4 0.076 0.152 Single and multiple rows 15–30° 
5. Marelius & Sinha (1998)  — 0.4 0.9 0.12 0.24 25–57° 
6. Barkdoll et al. (1999)  0.104 0.152 0.9 0.032 0.10 3 vanes in each 7 rows 20° 
7. (Gupta et al. 2006a, 2006b, 2007, 2010— 0.14–0.18 0.225–0.405 0.06 0.18 30–50° 
8. Tan et al. (2005)  0.4 0.2–0.6 10–20 0.05–0.15 1–4 30° 
9. Aware et al. (2005)  — — 0.3 0.03–0.10 0.07–0.17 Single and double array 30° 
10. Bejestan & Azizi (2012)  — 0.25 0.5 0.25 0.075 20° 
11. Biswas & Bharbhuiya (2018)  0.05 0.288 0.28 0.075 0.27 18–36 15° 
12. Sharma & Ahmad (2020)  0.024–0.052 0.09–0.1241 — 0.05–0.12 0.02–0.06 28–76 vanes in four rows 30° 
13. Azizipour et al. (2020)  — 0.14 1.5 0.14 — 23–60° 
14. Safaripour et al. (2020)  0.07 0.18 1.5 0.075 — 25° 
15. Baltazar et al. (2021)  0.029 0.1 0.86 0.1 0.03 7 vane in two row 20° 
16. Gumgum & Cardoso (2022)  0.029 0.1 0.86 0.1 0.02–0.04 3,6 in a row 10–50° 
17. Bor (2022)  0.045 0.12 0.85 0.09 0.03 3 vane in single column 20° 
18. Sarlak et al. (2023)  0.024, 0.05 0.16 0.48 0.08 0.16 10–35° 
19. Vaghefi et al. (2023)  0.07 0.18 1.5 — 0.05–0.1 2–4 15–35° 
20. Tasar et al. (2023)  0.025 0.095 — 0.1 0.1 3 vane in three row — 
21. Hamidi et al. (2024)  0.0014–0.0042 0.02–0.05 0.82 0.1 0.1 10–90° 

Flow interaction

Several vanes must be installed to generate a larger coherent vortex that propagates the flow structure over a wider area of the river cross-section. Each vane creates a unique vortex, and the resulting circulation is roughly equivalent to that caused by a single isolated vane. However, the aim of using several vanes is not achieved if the vortices do not mix to produce a combined vortex. When the transverse vane spacing (δn) is very small, the contact between the vanes increases, and the vortex created by one vane interacts with the vortex created by another. As the flow traverses the vane system, the circulation induced by each vane generates a velocity field that interacts with the vortex generated by the others. Consequently, the effective circulation induced by each vane within the system is smaller than that of an individual vane under identical flow conditions. The optimal spacing between vanes, ensuring the formation of a coherent vortex without compromising the effectiveness of individual vanes, has been determined by previous studies conducted by Wang & Odgaard (1993), Ouyang et al. (2008), and Odgaard & Wang (1991a).

The determination of the effective circulation induced by each vane, considering the influence of vane interaction, is based on the work of Milne-Thomson (1966) and is provided in Equation (8).
formula
(8)
where subscript i is 1, ……. ,N, and N denotes the number of the vane, ua is the approach flow velocity, vi is the transverse velocity components at vane i.
Milne-Thomson (1966) provided an equation for the induced circulation of a single vane, which is as follows:
formula
(9)
Odgaard & Mosconi (1987) also derived the same finding for a single vane. To investigate the effectiveness of the vanes, an interaction coefficient λi is defined as the ratio of the effective circulation to the undisturbed circulation and is given as:
formula
(10)
where is the effective circulation for ith no of vane under the effect of vane interactions, is the undisturbed circulation for ith no of the vane. Odgaard & Wang (1991a) observed that having more than one vane in an array increases the width of the affected area of the flow field but reduces the effectiveness of circulations due to the interaction of their vortices. Wang & Odgaard (1993) found that an effective coherent structure can be generated with an interaction coefficient (λ) of approximately 0.9 by maintaining the vane spacing within 2–3 times the vane height. They also observed that if the vane spacing exceeds 2–3 times the vane height, the vane array will generate individual vortices and be less efficient. Furthermore, they concluded that vortices generated by neighboring vanes interfere, resulting in a circulation per vane that is less than that generated by an isolated vane, along with downwash along the flow. Figure 4 shows the values of the vane interaction coefficient λ for various aspect ratios, showing an increase in this coefficient as the aspect ratio decreases (Odgaard & Wang 1991a). To maintain a specifically induced circulation and induced bed shear stress downstream, the vane array must be repeated at regular intervals. In a vane array characterized by vanes of uniform size and spacing, the area-averaged induced bed shear stresses are as follows:
formula
(11)
Figure 4

Calculated values of interaction coefficient λ, with different aspect ratios (Odgaard & Wang 1991a).

Figure 4

Calculated values of interaction coefficient λ, with different aspect ratios (Odgaard & Wang 1991a).

Close modal
Also,
formula
(12)
where is the longitudal bed shear stress, Av is equal to (δn. δs), δs is the longitudinal vane spacing and and are the factors arising from the area-averaging process (Wang 1990).

Ouyang et al. (2008) modeled the vane-induced flow field by considering each vane inducing a bound vortex and a tip vortex. They investigated a row of three vanes constituting the vane system and showed that if the vane spacing is smaller than the inner vane within the three-vane system, it serves no purpose and may be removed without significantly affecting the vane system. According to the λ calculated by Ouyang et al. (2008), the acceptable working range for the lateral spacing between the vanes is approximately 0.6–1.5 times the vane lengths. If the spacing exceeds 1.5 times the vane length, all interaction coefficients of the vanes tend to unity. In a three-vane arrangement, Ouyang & Lu (2016) found that the ratio of interaction parameters between the second and first vanes was less than 1 for small values of relative lateral spacing (ratio of lateral spacing with a depth of water) and the value exceeds 1 as the relative lateral spacing increases, indicating that the first tapered vane influenced the flow for smaller relative lateral spacing and the second one dominated the flow for larger relative lateral spacing. In rivers, the longitudinal spacing typically falls within the range of 10–30 times the vane height, while the lateral spacing is typically set at three times the vane height (Odgaard 2009).

This chapter focuses on how the effectiveness of submerged vanes is influenced by their dimensions and orientation. In this context, the focus is limited to vane structures that aim to achieve design goals related to inducing bed shear stresses by creating a secondary circulation in the flow downstream rather than using alternatives such as deflecting walls. The efficiency of a submerged vane is determined by vane parameters such as vane angle, height, length, and spacing, among others.

Angle of attack and aspect ratio of vanes

Adjusting the angle of attack makes it possible to control the lift and drag forces generated by the vane. At low angles of attack, the lift force is generally small, and the drag force is relatively low, while at higher angles of attack, the lift force increases, but so does the drag force. At first, Odgaard & Kennedy (1983) examined the effectiveness of vanes in diminishing near-bank velocity and near-bank depth by adjusting the angles of attack of the vanes. Their findings indicated that when the vanes were positioned at angles of attack greater than 20°, the scour holes were generated at the upstream edges of each vane due to separation of flow. The study further revealed that reducing the angle of attack decreased the size of the scour holes. According to Odgaard & Spoljaric (1986), the flow separation causes the lift coefficient to drop when the angle of attack increases above 20°. As the angle of attack increases, lift decreases while flow separation and resulting drag become more pronounced. Therefore, the optimal range is typically between 15 and 20°.

The aspect ratio, defined as the ratio of the vane height to vane length, significantly influences vane efficiency by affecting the generation and distribution of vortices in the fluid flow. Generally, a higher aspect ratio leads to a more efficient vane, promoting the formation of longer and narrower vortices that produce less drag. Conversely, as the aspect ratio decreases, the flow at the suction side becomes increasingly dominated by tip flow, resulting in the enlargement of the primary vortex. Odgaard & Spoljaric (1986) recommend an aspect ratio in the range of 0.1–0.5. During the design stage, they suggest a vane height to flow depth (H/d) ratio of approximately 0.4–0.5, while Odgaard & Mosconi (1987) propose a range of 0.2–0.5 suitable for all flow stages that can cause erosion. In field applications, the length of the vane varies between 0.9 and 7 m, while the height ranges from 0.9 to 5.5 m (Odgaard 2009). Table 1 presents the range of various parameters utilized by previous researchers.

Shape of the vanes

Most investigations have focused on rectangular vanes due to the simplicity of the theory, building upon earlier research on submerged vanes. While Spoljaric (1988) and Ouyang (2009) delved into the connection between vane form and flow training effects, their findings only pertain to single vanes. According to Bertin & Smith (1979), wings with non-rectangular geometries, such as tapered or delta wings, can provide more significant lift than rectangular shapes. The shape of a submerged vane has been widely recognized as a crucial factor influencing its performance improvement, as noted by several researchers (Gupta et al. 2006a, 2007; Ouyang 2009; Ouyang & Lin 2016; Azizipour et al. 2020). Thus, investigating the flow pattern around non-rectangular submerged vanes is essential to produce stronger secondary currents. The leading edge of a submerged vane significantly influences the vortex, with non-linear effects being more significant for vanes with sharp edges due to flow separation and vortex creation. Therefore, the shape of the leading edge is crucial, while the shape of the top edge may be less significant.

To explain the non-linear lift behavior of delta wings at high angles of attack, Polhamus (1966) introduced the leading edge suction analogy, which provided rise to the concept of vortex lift. According to this analogy, if flow reattachment occurs on the top surface, the total lift can be estimated as the sum of potential flow lift and the lift associated with separated leading edge spiral vortices. The lift coefficient (CL) combines both vortex lift, which depends on flow, and lift from potential flow, which depends on the form or shape of the aerofoil. Polhamus (1966) and Gupta et al. (2007) assumed that the total lift coefficient could be determined as the sum of potential flow lift (CL,p) and lift from separated leading edge spiral vortices (CL,v). The potential flow lift coefficient for the zero-leading edge suction condition is given as (Gupta et al. 2007):
formula
(13)
Here, Kp (∂CL/∂α) represents the slope of the normal force, as derived from the small disturbance potential flow lifting surface theory. Additionally, the derived equation of vortex lift is given as follows (Gupta et al. 2007):
formula
(14)
Here,
formula
(15)
Here, θ represents the sweep angle at the leading edge, and is defined as the derivative of drag coefficient with respect to the square of lift coefficient, i.e., . Equations (14) and (15) suggest that as the θ increases, KV will also increase, consequently leading to an increase in CL. According to Gupta et al. (2007), a delta wing with a greater θ is capable of generating higher axial vorticity values at the same angle of attack compared to a wing with a smaller sweep. With the aim of producing secondary currents with the greatest possible strength, Gupta et al. (2006a) conducted an experimental study to determine the ideal characteristics of double curve and J-type vanes. While regulating sediment erosion in fluvial channels, the results show that double curve and J-type vanes performed less effectively than rectangular vanes with the same aspect ratio. In another experiment, Gupta et al. (2007) investigated the ideal tapering angle of a tapered vane to produce the strongest secondary currents possible. They calculated the ideal tapering angle using the moment of momentum approach and found it to fall between 33 and 45°. Ouyang (2009) measured the performance of the vane by (d0dv)/d0 with different α where d0 is the initial pre-vane water depth; dv is the water depth at the river bank after installation of the vane, λt is the taper ratio, and is the swept ratio (η/L, is defined to measure the degree that the top of the vane is swept; where η = displacement of the vane's quarter-length line on the top of the vane) shown in Figure 5. The finding explored the use of tapering vanes to regulate silt in alluvial channels and observed that a lower tapering ratio (defined as the ratio of a tapered vane's top width, LT, to its base width, Lb) improved the vane's efficacy as a sediment-managing device for a given constant surface area and height (Figure 5). Additionally, results for the swept vane indicate that it performs better than the baseline rectangular vane when its top is swept forward only to the oncoming flow. Ouyang & Lin (2016) conducted a numerical analysis of the performance of a row of rectangular, swept, and tapered vanes. They discovered that rectangular and sweeping vanes both elevated the bank bed level by 16 and 17%, respectively, while tapered vanes increased the bed level by 19%. Shafai Bejestan & Azizi (2012) analyzed the effectiveness of rectangular and triangular vanes and found that the triangular vane outperforms rectangular vanes in reducing local scour at the leading edge of the submerged vane. They also concluded that the largest chamfer at the leading edge of the vanes resulted in the highest reduction in scour depth. Teronpi & Misra (2015) suggested that among rectangular, curved, and trapezoidal submerged vanes, the maximum scour depth occurs specifically with rectangular vanes. Azizipour et al. (2020) introduced slotted vanes attached to the bank as a method to mitigate local scour at the apex of the triangular submerged vane. The findings indicate that the slotted vanes are more effective than traditional vanes in safeguarding a bank against erosion by minimizing the maximum scour depth. Since rectangular vanes are primarily installed in rivers. Therefore, further investigations are needed to explore approaches aimed at minimizing local scour depth around the tip of submerged vanes by utilizing non-rectangular vane shapes.
Figure 5

Near-bank bed level change induced by a taper and swept vane (Ouyang 2009).

Figure 5

Near-bank bed level change induced by a taper and swept vane (Ouyang 2009).

Close modal

The use of submerged vanes for river training and sediment deflection can be formulated empirically by incorporating kinetic parameters, as outlined in the following sections. This section provides a review of how previous researchers have expressed various flow parameters, including vorticity, velocity distribution, bed shear stress, and moment of momentum, in their studies.

Vane-induced vorticity

Vorticity holds significance in fluid dynamics, where it plays a crucial role in comprehending the behavior of turbulence, boundary layers, and other intricate flows. When a fluid flows past a submerged vane, it can generate vorticity due to changes in flow direction caused by the vane's orientation with the flow. Vorticity emerges at the edges of the vane and moves downstream with the fluid flow. Essentially, the angle of attack of the vanes significantly influences the vorticity. Marelius & Sinha (1998) identified that continuously evolving flow fields and topographical features in the field may result in vanes at higher angles of attack. They observed that at a 40° angle of attack, a horseshoe vortex was present on the pressure side of the vane. However, there has been a lack of experimental studies focusing on developing a dimensionless parameter for assessing the strength of secondary circulation induced by submerged vanes. The development of such a dimensionless parameter necessitates experimental research to establish an empirical correlation between the damping function of vortex strength (Gupta et al. 2006a, 2006b). It noted that the decay of vane-induced strength does not follow a consistent trend and appears to be influenced by factors such as the location of the vortex center, Froude number, and other variables.

Velocity distribution and vane-induced bed shear stresses

When a fluid flows over a submerged vane, it undergoes changes in velocity distribution, leading to the generation of bed shear stresses. The velocity profile for a submerged vane can be modeled using different equations, such as the logarithmic law or the power law. The power law velocity distribution is given as:
formula
(16)
Here, u is the point velocity at height z. As the velocity profile changes, the submerged vane also generates bed shear stresses, whose magnitude depends on the velocity of the fluid and the roughness of the bed surface. The tip vortex exhibits similarities to a Rankine vortex but degrades with distance downstream of the vane due to viscous diffusion. The tangential velocity perpendicular to the core axis in an unbounded flow field is defined as (Odgaard & Wang 1991a):
formula
(17)
where is the strength of circulation, r is the radius of local curvature, K is the equivalent sand roughness, ε is eddy viscosity, and s is the stream-wise component. In the open channel, the presence of the channel bed and the free surface distorts the vortex. The method of images can be employed to incorporate the influence of boundaries on tangential velocity analytically. Here, the transverse component of the tangential velocity near the bed is given as:
formula
(18)
where ri and ro are the innermost and outermost radius of curvature of depth-averaged turbulence, respectively, i and j are the influence functions, and z is the vertical coordinate. Calculations and experimental data by Wang & Odgaard (1993) have shown that the core of the vortex is located approximately 0.2 times the vane height below the top elevation of the vane.

Moment of momentum

The moment of momentum (MOM) is non-dimensional parameter, also known as angular momentum. It is a physical quantity that describes the amount of rotational motion of an object around an axis. At first, Marelius & Sinha (1998) and Sinha & Marelius (2000) used this non-dimensional parameter (MOM) to present the physics of the flow past a submerged vane at higher angles of attack. Using the MOM concept, Marelius & Sinha (1998) discovered that the angle of attack for generating optimal strength of vortical currents from a submerged vane must be 40° (Figure 6). Furthermore, Gupta et al. (2007) investigate the maximum level of secondary circulation strength generated by vanes of different shapes and determined that maintaining a taper angle of 33.7° could further enhance the MOM for a given optimal angle of attack of 40°.
Figure 6

Moment of Momentum (MOM) with an angle of attack (Marelius & Sinha 1998).

Figure 6

Moment of Momentum (MOM) with an angle of attack (Marelius & Sinha 1998).

Close modal

The primary objective in designing submerged vanes is to induce secondary circulation within the primary flow, alter flow patterns near the riverbed, and divert sediment within the channel cross-section. The author has discussed the theory related to submerged vanes and examined the critical findings and challenges identified by various researchers. Over the past few decades, numerous studies (Odgaard & Kennedy 1983; Odgaard & Spoljaric 1986; Odgaard & Wang 1991a; Ouyang 2009; Gupta et al. 2010; Odgaard 2015; Solanki et al. 2020) on submerged vanes have been conducted, leading to the development of design guidelines for vane systems based on their outcomes. Van Zwol (2004) argue that the Odgaard theory falls short of accurately predicting the lift and drag forces applied to vanes because the existing model fails to fully consider the underlying flow physics associated with the passage of water flow over submerged vanes. The theory of Odgaard is based on the lifting line theory for finite wings, known as Prandtl's lifting theory, which is unsuitable for low aspect ratio wings as well. At a greater angle of attack, the main vortex becomes stronger. The primary vortex appears to originate from the suction side of the vane surface away from the leading edge, which decreases as the angle of attack increases and increases as the initial vane height decreases (Odgaard & Spoljaric 1986). In summary, the angle of attack and aspect ratio are critical factors that must be carefully considered when designing a submerged vane to ensure optimal performance. As lift decreases for lower angles of attack and the drag becomes more noticeable with increasing angle of attack, the ideal range is described as 15–30°, suggested by many researchers (Odgaard & Kennedy 1983; Odgaard & Spoljaric 1986; Odgaard & Wang 1991a). According to Odgaard & Spoljaric (1986), the occurrence of flow separation results in a decrease in the lift coefficient when the angle of attack increases above 15°. At a greater angle of attack, the higher stream-wise velocities are more effectively redistributed toward the bed via vortex motion. According to Odgaard & Mosconi (1987) research, fluctuations in the H/d ratio over the range 0.2 < H/d < 0.5 have little impact on how much torque a vane generates when submerged. At the design stage, a study by Odgaard & Spoljaric (1986) proposed 0.4 < H/d < 0.5, whereas Odgaard & Mosconi (1987) suggested 0.2 < H/d < 0.5 for all flow stages that induce erosion.

The orientation of the flow significantly impacts the local scour depths at submerged vanes. The intensity of the horseshoe vortex along the pressure side is such that it effectively carries material away from the scour hole at angles of attack of 30° and above. As the angle of attack increases, the region of maximum scour migrates along the pressure side of the vane toward the trailing edge (Marelius & Sinha 1998). However, a notable increase in scour depth is observed at an angle of attack of more than 20°, which is not practical for field application (Gupta et al. 2010). The primary disadvantage of utilizing submerged vanes is the potential for structural disintegration due to local scour near their tips. Therefore, there is a need for more research on reducing the local scour depth around the vane's tip, as very few researchers (Bejestan & Azizi 2012; Teronpi & Misra 2015; Azizipour et al. 2020) have attempted to address this aspect. Also, grabion submerged vane can be also the alternative use of the scour reduction around the vane (Sarlak et al. 2023). The horseshoe vortex and potentially additional vortices may introduce unfavorable forces in the system, influencing the transverse movement of sediment. However, this aspect has not yet been thoroughly investigated (Marelius & Sinha 1998). In the case of a vane array, the equilibrium strength of horseshoe vortices may be lower compared to that of a single vane, as the scour holes of nearby vanes might overlap. Additionally, the presence of scour holes could lead to some vortex stretching in the transverse direction, effectively increasing the width of each vane (Odgaard 2009).

Most investigations have prioritized rectangular vanes, primarily due to the simplicity of the underlying theory and in consideration of previous research conducted on submerged vanes. Anderson Jr. (2007) and Bertin & Smith (1979) have established that wings with non-rectangular geometries, such as tapered or delta wings, offer greater lift capabilities compared to wings with a rectangular shape. Some researchers, such as Gupta et al. (2007), Ouyang (2009), and Solanki et al. (2020), have suggested that tapered vanes are more efficient in sediment management than rectangular vanes because tapered vanes introduce a more gradual adverse pressure into the flow. However, there is still a lack of extensive experimental research on the potential flow lift generated by non-rectangular vanes. Hence, further research is imperative to optimize the geometric vane parameters, specifically in terms of their taper angle. Despite significant advancements in submerged vanes over the years, there are still unexplored applications. Only a limited number of studies have delved into the potential of submerged vanes for excavation purposes (Odgaard 2009, 2015), indicating the need for further research in this area. Consequently, the potential of submerged vanes to enhance inland navigation has been partially explored, and the impact of a vane system on induced changes in energy slope remains unclear and requires further research. Harsini et al. (2022) and Bagheri et al. (2023) have investigated the effective utilization of submerged vanes for dissipating the energy of hydraulic jumps downstream of hydraulic structures. The incorporation of submerged vanes can be employed in designing cost-effective hydraulic structures and stilling basins.

In recent times, the employment of submerged vanes has become prevalent across various fields and has prompted a multitude of studies aimed at advancing the formulation of design principles for vane systems throughout the past decades. A theoretical review of the submerged vane on flow control and sediment diversion has been presented. The efficiency of a submerged vane is determined by vane parameters such as vane angle, height, length, shape, and spacing, among others. A lot of attention should be given to the orientation of the vane angle with the mean flow for generating an intense vortex. Also, a much more detailed analysis is required to understand the interaction effect of a system of vanes that depends on vane spacing. The principal drawback associated with the utilization of submerged vanes lies in the susceptibility to structural deterioration caused by localized scour in the vicinity of their tips. Because, the vane's leading edge is the primary factor contributing to the horseshoe vortex, which created an intense scour hole near the origin point of the vortex and was dismissed after some distance. A lack of investigation still exists to minimize the depth of local scour around the submerged vanes. In the future, further study is required to assess the viability of utilizing non-rectangular-shaped vanes in safeguarding against local scour around submerged vanes. Also, the understanding of turbulence associated with submerged vanes is considerably limited compared to analytical endeavors.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors hearby declare that there is no conflict.

Anderson
J. D.
Jr
.
2007
Fundamentals of Aerodynamics
(4th edn).
Tata McGraw-Hill
,
New Delhi, India
.
Aware
R.
,
Ahmad
Z.
&
Asawa
G. L.
2005
Scour control by submerged vanes in a curved channel
.
ISH Journal of Hydraulic Engineering
11
(
3
),
81
90
.
https://doi.org/10.1080/09715010.2005.10514803
.
Azizipour
M.
,
Meymani
F. A.
&
Shooshtari
M. M.
2020
Enhancing scour protection in river bends: A novel slotted bank-attached vane
.
Water Supply
20
,
6
.
doi:10.2166/ws.2020.116
.
Bagheri
H.
,
Heidarpour
M.
&
Noghani
F.
2023
Laboratory investigations on hydraulic jump characteristics using submerged vanes and adverse slope
.
Journal of Hydro-Environment Research
51
,
15
24
.
https://doi.org/10.1016/j.jher.2023.09.002
.
Baltazar
J.
,
Alves
E.
,
Bombar
G.
&
Cardoso
A. H.
2021
Effect of a submerged vane-field on the flow pattern of a movable bed channel with a 90° lateral diversion
.
Water
13
,
828
.
https://doi.org/10.3390/w13060828
.
Barkdoll
B. D.
,
Ettema
R.
&
Odgaard
A. J.
1999
Sediment control at lateral diversions: Limits and enhancements to vane use
.
Journal of Hydraulic Engineering
125
(
8
),
862
870
.
doi:10.1061/(ASCE)0733-9429(1999)125:8(862)
.
Bejestan
M. S.
&
Azizi
R.
2012
Experimental investigation of scour depth at the edge of different submerged vanes shapes
. In:
World Environmental and Water Resources Congress
.
ASCE
,
Reston, VA, USA
,pp.
1376
1385
.
https://doi.org/10.1061/9780784412312.138
.
Bertin
J. J.
&
Smith
M. L.
1979
Aerodynamics for Engineers
(1st edn).
Cambridge University Press, Cambridge, UK
.
Bhuiyan
F.
,
Hey
R. D.
&
Wormleaton
P. R.
2010
Bank attached vanes for bank erosion control and restoration of river meanders
.
Journal of Hydraulic Engineering
136
(
9
),
583
596
.
https://doi.org/10.1061/(ASCE)HY.1943-7900.0000217
.
Biswas
P.
&
Bharbhuiya
A. K.
2018
Effect of submerged vane on three-dimensional flow dynamics and bed morphology in river bend
.
River Research and Applications
35
(
3
),
301–
3312
.
doi:10.1002/rra.3402
.
Gumgum
F.
&
Cardoso
A. H.
2022
Optimizing the desilting efficiency of submerged vane fields at lateral diversions
.
Journal of Hydraulic Engineering
149
(
1
),
04022031
.
doi:10.1061/(ASCE)HY.1943-7900.0002030
.
Gupta
U. P.
,
Ojha
C. S. P.
&
Sharma
N.
2006a
Vorticity with different shapes of submerged vanes
.
ISH Journal of Hydraulic Engineering
12
(
1
),
13
26
.
doi:10.1080/09715010.2006.10514813
.
Gupta
U. P.
,
Ojha
C. S. P.
&
Sharma
N.
2006b
Decay of strength of vortex downstream of submerged vane
.
ISH Journal of Hydraulic Engineering
12
(
2
),
37
48
.
doi:10.1080/09715010.2006.10514830
.
Gupta
U. P.
,
Sharma
N.
&
Ojha
C. S. P.
2007
Performance evaluation of tapered vane
.
Journal of Hydraulic Engineering
45
(
4
),
472
477
.
doi:10.1080/00221686.2007.9521781
.
Gupta
U. P.
,
Ojha
C. S. P.
&
Sharma
N.
2010
Enhancing utility of submerged vanes with collar
.
Journal of Hydraulic Research
136
(
9
),
651
655
.
doi:10.1061/(ASCE)HY.1943-7900.0000212
.
Hamidi
M.
,
Sadeqlu
M.
&
Khalili
A. M.
2024
Investigating the design and arrangement of dual submerged vanes as mitigation countermeasure of bridge pier scour depth using a numerical approach
.
Ocean Engineering
299
,
117270
.
https://doi.org/10.1016/j.oceaneng.2024.117270
.
Harsini
H. S.
,
Aghbolaghi
M. A.
,
Nafchi
R. F.
&
Norouzi
K.
2022
Experimental investigation of the joint effect of flow expansion and submerged vanes on hydraulic jump characteristics
.
Iranian Journal of Science and Technology, Transactions of Civil Engineering
46
,
3283
3293
.
https://doi.org/10.1007/s40996-021-00740-6
.
Klovsky
A. V.
&
Kozlov
D. V.
2019
Generation of artificial transverse circulation in an open channel flow by submerged vanes
.
Journal on Construction and Architecture
14
(
9
),
1158
1166
.
doi:10.22227/1997-0935.2019.9.1158-1166
.
Lake
R. W.
,
Shaeri
S.
&
Senevirathna
S. T. M. L. D.
2021
Design of submerged vane matrices to accompany a river intake in Australia
.
Journal of Environmental Engineering and Science
16
(
2
),
58
65
.
doi:10.1680/jenes.19.00037
.
Marelius
F.
&
Sinha
S. K.
1998
Experimental investigation of flow past submerged vanes
.
Journal of Hydraulic Engineering
124
(
5
),
542
545
.
doi:10.1061/(ASCE)0733-9429(1998)124:5(542)
.
Milne-Thomson
L. M.
1966
Theoretical Aerodynamics
.
Dover Publications, Inc
,
New York, NY, USA
.
Odgaard
A. J.
2009
River Training and Sediment Management with Submerged Vanes
.
American Society of Civil Engineers
,
Baltimore, MD, USA
.
Odgaard
A. J.
2015
River channel stabilization with submerged vanes
. In: Yang, C. & Wang, L. (eds)
Advances in Water Resources Engineering
.
Springer
,
Cham
, Switzerland, pp.
107
136
.
https://doi.org/10.1007/978-3-319-11023-3_3
.
Odgaard
A. J.
&
Kennedy
J. F.
1983
River-bend bank protection by submerged vanes
.
Journal of Hydraulic Engineering
109
(
8
),
1161
1173
.
doi:10.1061/(ASCE)0733-9429(1983)109:8(1161)
.
Odgaard
A. J.
&
Spoljaric
A.
1986
Sediment control by submerged vanes
.
Journal of Hydraulic Engineering
112
(
12
),
1164
1181
.
Odgaard
A. J.
&
Mosconi
C. E.
1987
Streambank protection by submerged vanes
.
Journal of Hydraulic Engineering
113
(
4
),
520
536
.
doi:10.1061/ (ASCE)0733-9429(1987)113:4(520)
.
Odgaard
A. J.
&
Spoljaric
A
.
1989
Sediment control by submerged vanes. Design basis
. In: Ikeda, S. & Parker, G. (eds)
Water Resources Monograph No. 12
.
American Geophysical Union
,
Washington, DC, USA
, pp.
127
151
.
Odgaard
A. J.
&
Wang
Y.
1991a
Sediment management with submerged vanes. I: Theory
.
Journal of Hydraulic Engineering
117
(
3
),
267
283
.
doi:10.1061/(ASCE)0733-9429(1991)117:3(267)
.
Ouyang
H. T.
2009
Investigation on the dimensions and shape of a submerged vane for sediment management in alluvial channels
.
Journal of Hydraulic Engineering
135
(
3
),
209
217
.
doi:10.1061/(ASCE)0733-9429(2009)135:3(209)
.
Ouyang
H. T.
&
Lin
C. P.
2016
Characteristics of interactions among a row of submerged vanes in various shapes
.
Journal of Hydro-Environment Research
13
,
14
25
.
doi:10.1016/j.jher.2016.05.003
.
Ouyang
H. T.
&
Lu
C.
2016
Optimizing the spacing of submerged vanes across rivers for stream bank protection at channel bends
.
Journal of Hydraulic Engineering
142
(
12
),
04016062
.
doi:10.1061/(ASCE)HY.1943-7900.0001210
.
Ouyang
H. T.
,
Lai
J. S.
,
Yu
H.
&
Lu
C. H.
2008
Interaction between submerged vanes for sediment management
.
Journal of Hydraulic Research
46
(
5
),
620
627
.
doi:10.3826/jhr.2008.3160
.
Polhamus
E. C.
1966
A Concept of the Vortex Lift of Sharp-Edge Delta-Wings on a Leading-E Suction Analogy
.
TN D-3767, December
.
NASA, Washington, DC, USA
.
Rodriguez-Amaya
C.
,
Duran-Ariza
A.
&
Duarte-Mendez
S.
2020
Submerged vane technology in Colombia: Five representative projects
.
Water
12
(
4
),
984
.
doi:10.3390/w12040984
.
Sarlak
H.
,
Bejestan
M. S.
&
Sajjadi
S. M.
2023
Experimental investigation of the effect of permeability and angle of gabion submerged vane on bed topography
.
Arabian Journal of Geosciences
16
,
288
.
https://doi.org/10.1007/s12517-023-11332-1
.
Sharma
H.
&
Ahmad
Z.
2020
Turbulence characteristics of flow past submerged vanes
.
International Journal of Sediment Research
35
(
1
),
42
56
.
https://doi.org/10.1016/j.ijsrc.2019.07.002
.
Sinha
S. K.
&
Marelius
F.
2000
Analysis of flow past submerged vanes
.
Journal of Hydraulic Research
38
(
1
),
65
71
.
doi:10.1080/00221680009498360
.
Solanki
K.
,
Sharma
H.
&
Joshi
N.
2020
Flow and parameter optimization of tapered vane
.
Journal of Ecohydraulics
1
13
.
doi:10.1080/24705357.2020.1771223
.
Spoljaric
A.
1988
Mechanics of Submerged Vanes on Flat Boundaries
.
Ph.D. Thesis
,
University of Iowa, at Iowa City
,
Iowa
.
Tan
S. K.
,
Yu
G.
,
Lim
S. Y.
&
Ong
M. C.
2005
Flow structure and sediment management around submerged vanes in open channel
.
Journal of Waterway, Port, Coastal and Ocean Engineering
131
(
3
),
132
136
.
doi:10.1061/(ASCE)0733-950X(2005)131:3(132)
.
Tasar
B.
,
Unes
F.
,
Gemici
E.
&
Zelenakova
M.
2023
Experimental and numerical study on flow control using 3-array submerged vane in laboratory channel bend
.
Water
15
,
659
.
https://doi.org/10.3390/w15040659
.
Teronpi
J.
&
Misra
U. K.
2015
Experimental investigation of local scour around submerged vanes
.
International Journal of Innovative Research in Advanced Engineering
2
(
7
),
21
24
.
Vaghefi
M.
,
Zarei
E.
,
Ahmadi
G.
&
Behroozi
A. M.
2023
Experimental analysis of submerged vanes' configuration for mitigating local scour at piers in a sharp bend: Influence of quantity, length, and orientation
.
Ocean Engineering
289
,
116267
.
https://doi.org/10.1016/j.oceaneng.2023.116267
.
Van Zwol
J. A.
2004
Design Aspect of Submerged Vanes
.
Ph.D. Thesis
,
Delft University of Technology
,
Delft, The Netherlands
.
Wang
Y.
1990
Sediment Control with Submerged Vanes
.
Ph.D. Thesis
,
University of Iowa, at Iowa City
,
Iowa
.
Wang
Y.
&
Odgaard
A. J.
1993
Flow control with vorticity
.
Journal of Hydraulic Research
31
(
4
),
549
562
.
doi:10.1080/00221689309498877
.
Zarei
E.
,
Vaghefi
M.
&
Hashemi
S. S.
2019
Bed topography variations in bend by simultaneous installation of submerged vanes and single bridge pier
.
Arabian Journal of Geosciences
12
,
178
,
1–10. doi:10.1007/s12517-019-4342-z
.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY-NC-ND 4.0), which permits copying and redistribution for non-commercial purposes with no derivatives, provided the original work is properly cited (http://creativecommons.org/licenses/by-nc-nd/4.0/).