Hydraulic condition varying relative water depth.
Abstract
Many aquatic plants are often observed, and the submerged canopy flow appears in natural rivers. Complex flow patterns such as Karman vortex and related coherent motions are formed behind vegetation. In particular, mass and momentum transfers and the vertical mixing process are promoted significantly between the within‐canopy layer and over‐canopy layer. Therefore, it is very important for river ecosystem to reveal turbulent diffusion in submerged vegetated open‐channel flows. The present study conducted simultaneously PIV and laser‐induced fluorescence (LIF) measurements using a pair of high‐speed cameras to analyze the contribution of coherent vortex to the turbulent diffusion property.
Keywords
- vegetation flows
- turbulence
- diffusion process
1. Introduction
Aquatic vegetation elements yield a complex current structure which consists of the within‐canopy layer and the over‐canopy layer. Streamwise velocity reduces within canopy in a submerged vegetation flows in which the water depth is larger than the vegetation height, and a relevant shear instability is generated in the vertical direction. This induces coherent turbulence events such as ejection and sweep; near a boundary zone includes the vegetation edge between the within‐canopy and the over‐canopy. It is therefore very important for preservation of an aquatic habitat and a river environment to reveal transport mechanisms of heat, mass, sediment concentration, and momentum in the vegetation edge. This chapter focused on fundamental hydrodynamic characteristics and related turbulent diffusion properties in the vegetated open‐channel flows, because the ejections and the sweeps may have significant relationship with the convection and diffusion of nutrition and suspended sediments.
Case | |||||
---|---|---|---|---|---|
5.0 | 5.0 | 10.0 | 0.14 | 0.5 | |
6.25 | 0.13 | 0.63 | |||
7.5 | 0.12 | 0.75 | |||
10.0 | 0.10 | 1.0 | |||
12.5 | 0.09 | 1.25 | |||
15.0 | 0.08 | 1.5 | |||
20.0 | 0.07 | 2.0 |
A turbulence structure in these canopy flows has been studied intensively in the meteorology. Raupach and Thom [1] have revealed velocity profiles and generation properties of turbulence energy by measurements of air tunnel with a roughness wall. Gao et al. [2] have conducted field measurements in deciduous forest and reported that the sweep and ejection motions influence heat transport significantly. Raupach et al. [3] have pointed out an analogy between the canopy‐flow property and mixing‐layer zone.
In contrast, river environmental problems arouse public interest recently, and thus, turbulence structure, mass, and momentum transport and their diffusion property of the vegetated open‐channels have been highlighted. Nepf et al. [4] have proposed a diffusion model of dye concentration on the basis of random walk model, and they applied to the wake region behind an emergent plant model. Furthermore, Nepf [5] has revealed the relation between the turbulence. Sections 2 and 3 introduce turbulence structure in submerged vegetation flows and turbulent diffusion properties, respectively, on the basis of measurement results.
2. Turbulence structure in submerged vegetated flows
Hydrodynamic properties in vegetated canopy rivers, in which velocity distributions are largely changed in the vertical direction, are required to be revealed in hydraulic engineering. Specifically, the submergence depth, that is, the ratio of the water depth
2.1. Experimental method and hydrodynamic condition
The laboratory experiments were conducted in 10 m long and 40 cm wide tilting flume as shown in Figure 1. The plant models were composed of non‐flexible strip plates and attached vertically on the bottom. The present plant model 50 mm height, 8 mm width, and 1 mm thickness.
2.2. Mean flow structure
The whole depth region could be classified into two or three sublayers on the basis of the vertical profiles of mean streamwise velocity and Reynolds stress (see Poggi et al. [6]; Ghisalberti and Nepf [7]). Our research divides the vegetated open‐channel flow into three sublayers as shown in Figure 2. The lowest layer within the canopy is termed the “wake zone (emergent zone),” as defined by Nepf and Vivoni [8] and Ghisalberti and Nepf [7]. They defined the penetration depth
in which,
Figure 5 shows the vertical profiles of Reynolds stress
in which,
2.3. Space–time analysis
Contours of space–time correlation between the streamwise velocity components,
in which, the subscript
In the result of τ =1.2s, a trajectory line of the maximum correlation position was also shown at every 0.3 s. The vertical movement of the coherent motion is much smaller than the longitudinal one, and the coherent lump structure is moved in parallel to the horizontal canopy plane. The convection velocity of mean eddies was evaluated from the distance between the maximum two‐point correlation positions.
2.4. Visualization of coherent structure
Figure 9 shows time variation of the distributions of the instantaneous Reynolds stress
Periods of the sweeps and ejections,
2.5. Detection of spanwise vortices
PIV measurements in turbulent boundary layers conducted by Adrian et al. [12] allow us to understand a packet structure of hairpin vortices. Figure 12 shows same time‐series of the instantaneous velocity vectors subtracted by a vortex convection velocity
Consequently, the ejections and sweeps form the organized coherent eddies. These coherent eddies are convected downstream at
A length scale of the coherent eddy was evaluated accurately from the present PIV measured data in the following ways:
, in which
3. Turbulent diffusion in submerged vegetated canopy open‐channel flows
Environmental problems in river basin have been recently highlighted as public interest, and thus, many researchers tried to reveal mass and momentum transfers associated with the wind waves, turbulence diffusion, and coherent vortex. Komori et al. [13] have revealed that wind waves promote gas transfer beneath air–water interface. There exists experimental works focused on the diffusion process in the vegetated canopies. Nepf et al. [4] have proposed a diffusion model of dye concentration on the basis of random walk model, and they applied it to the wake region behind an emergent plant model.
Furthermore, Nepf [5] has revealed the relation between the turbulence diffusion and the transport mechanism of dye concentration. However, there are many uncertainties about turbulent diffusion mechanism, because it is hard to measure the velocity fluctuations and the concentration simultaneously. In consideration of this subject, our group tried to conduct some simultaneous measurements of PIV and the laser‐induced fluorescence (LIF) using a pair of high‐speed cameras, and evaluated the relation between the turbulent diffusion property and the coherent motions reasonably.
3.1. Experimental method
A schematic depiction of the turbulent diffusion in vegetated open‐channel flows is shown in Figure 15. The shear instability occurs due to the velocity inflection point between the within‐canopy and the over‐canopy in the submergence condition as mentioned above. This instability causes the sweeps and ejections near the canopy edge, and these coherent motions have significant effects on mass and momentum exchanges between the within‐ and over‐canopies. Concentration of sediment and nutrition are comparably large near the bottom bed in natural rivers, and these convection and diffusion processes are related significantly with activities of aquatic ecosystem. It is thus important to reveal the diffusion properties of turbulence in vegetated open‐channel flows in order to promote such an environmental subject intensively.
The PIV‐LIF measurement is introduced in this section. The contribution of turbulence structure to the diffusion process of the dye concentration is investigated by injecting dye near the flume bottom. Experiments were conducted in a 10 m long and 40 cm wide glass‐wall flume. Figure 16 shows the experimental setup and coordinate system.
These vegetation models were placed vertically on the flume bed with a square grid allocation of
Table 2 shows the hydraulic condition.
Case | |||||||
---|---|---|---|---|---|---|---|
3.0 | 10.0 | 15 | 15,000 | 0.08 | 5.0 | 0.39 | |
0.9 | 4.2 | 4.5 | 1890 | 0.06 |
3.2. Basic characteristics of flow structure
Figure 17a, b shows the vertical profiles of time‐averaged primary velocity
In the emergent case,
3.3. Time‐averaged dye concentration
The distribution of time‐averaged concentration
Figure 19b shows some comparisons between the submerged and the emergent cases. The concentration is larger within the canopy at
3.4. Evaluation of turbulent diffusivity
Reynolds stress and the correlation
in which
4. Conclusions
The Section 2 explained the PIV turbulence measurements and their results in the vegetated open‐channel flows. Particularly, mean‐flow properties, turbulence structure, and coherent motions were revealed as follows;
In the larger submergence depth condition, the momentum transfer of Reynolds stress toward the within canopy layer is promoted significantly. Consequently, the penetration depth is evaluated reasonably from the Reynolds stress distributions. On the basis of mean velocity profiles and the eddy periodicity, it was found that there is a significant analogy between the canopy shear layer and the mixing shear layer.
The coherent eddy has a significant relation with generations of the sweeps and the ejections, and the trajectory of the vortex core is driven by these coherent motions. The length scales of coherent eddies were evaluated from PIV images, and it was found that the large‐scale eddies appear in large submergence depth.
The Section 3 introduced PIV and LIF simultaneous measurement technique with two sets of high‐speed cameras, which could evaluate the relation between the turbulent diffusion property and coherent motions. The main findings obtained here are as follows;
Two components of the instantaneous velocity vectors and the dye concentration were measured simultaneously using the combination of PIV and LIF methods. The dye concentration is lifted up to the over‐canopy by the ejection motions, and returned to the within‐canopy by the sweep motion.
The contribution of the sweep motion to the transport of the dye concentration is larger than that of the ejection motions near the vegetation edge, and it was found from the simultaneous measurements of the velocity and concentration that the turbulent diffusivity is in the same order of magnitude as the eddy viscosity.
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