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Turbulence structure and flow field of shallow water with a submerged eel grass patch
Ecological Engineering 69 (2014) 201–205
Contents lists available at ScienceDirect
Ecological Engineering journal homepage: www.elsevier.com/locate/ecoleng
Short communication
Turbulence structure and flow field of shallow water with a submerged eel grass patch Cui-chao Pang a,b,c,∗ , Di Wu a,d , Xi-jun Lai a , Shi-qiang Wu c , Fang-fang Wang c a
State Key Laboratory of Lake Science and Environment, Nanjing Institute of Geography & Limnology, CAS, Nanjing 210008, PR China Changjiang Institute of Survey, Planning, Design and Research, Shanghai Department, Shanghai 200439, PR China c Hydraulic Engineering Department, Nanjing Hydraulic Research Institute, Nanjing 210029, PR China d Hohai University, Nanjing 210098>, PR China b
a r t i c l e
i n f o
Article history: Received 14 September 2013 Received in revised form 9 February 2014 Accepted 31 March 2014 Keywords: Shallow lake Plant patch Eel grass Time-averaged velocity Turbulent intensity Turbulent shear stress
a b s t r a c t A flume experiment was conducted to investigate the effect of the aquatic herbaceous plant patch on the turbulent structure and flow field of shallow water. The eel grass that is widely distributed in the shallow lakes in China was chosen as the targeted plant. The plants were settled in patch form with three groups of densities and flow velocities. The three-dimensional instantaneous velocities were measured using an Audio Doppler Velocitimeter (ADV). The results indicate that the vertical velocity profile in the plant patch exhibits an S-shape from the canopy to the root of the eel grass. A secondary maximum in the vertical profile of velocity near the plant root is observed. The turbulent intensity increases from the water surface to the canopy, then decreases to the plant root; there is an inflection point around canopy, where the turbulent intensity deceases from the inner region to the side boundary of the patch. The vertical profiles of the eel grass resistance coefficient CP have different forms at different positions in the patch in general, but the forms of the CP profiles are similar along the boundary of the patch, and the forms of the CP profiles are similar in the inner part of the patch. In the patch area, the turbulent flow corresponds to the Quadrant 2 event (ejection event) above the canopy, the turbulent flow corresponds to the Quadrant 4 event (sweep event) below the canopy, but near the bed the Quadrant 1 event (outward interaction), the Quadrant 2 event and the Quadrant 4 event coexist. In the lateral boundary area of the patch the Quadrant 2 event and the Quadrant 3 event (inward interaction event) coexist due to presence of a strong shear layer. © 2014 Elsevier B.V. All rights reserved.
1. Introduction In large water bodies with dense herbaceous plants, water is usually clear and low, and a concentration of suspended sediment is observed. The nutrients are apparently lower in the area with dense herbaceous plants than in the surrounding water area without vegetation. The eutrophication degree of water in the herbaceous type lake is found to be lower than that in the non-herbaceous type lake in general. The mechanism of this specific environmental and ecological effect of the aquatic herbaceous plant patch of the lake has not been explained thoroughly. Therefore, it is necessary to promote the study of the effect of natural aquatic herbaceous plants
∗ Corresponding author at: Nanjing Institute of Geography & Limnology, State Key Laboratory of Lake Science and Environment, No.225, Beijing Donglu Road, Nanjing 210008, PR China. Tel.: +86 15850589312. E-mail address: [email protected] (C.-c. Pang). http://dx.doi.org/10.1016/j.ecoleng.2014.03.075 0925-8574/© 2014 Elsevier B.V. All rights reserved.
on the turbulent flow structure to explain the environmental and ecological effects of aquatic herbaceous plants and to understand the relevant mechanism of the formation of clean water in the plant patch area and surrounding water. The experimental study on the effect of aquatic plants on the flow from the resistance aspect began in the 1950s (Abood et al., 2006; Chen, 1976; Chow, 1959; Fathi-Maghadam and Kouwen, 1997; Kris Bal et al., 2013; Kouwen et al., 1981; Larsen et al., 2009; Lee et al., 2004; López and Garcia, 1997; Nepf, 1999; Temple et al., 1987; Velasco et al., 2001; Wang, 2009; Wang and Wang, 2010), which involved the analysis of the effect on the resistance coefficient CD , the Manning roughness coefficient n, and the Darcy–Weisbach roughness coefficient f. The Manning roughness coefficient n is commonly used in ecological systems and has been studied most thoroughly. The researchers normally thought that the factors affecting the resistance are the shape, flexibility, spatial distribution and density, relative submergence of the plants and Reynolds number of the flow. Chow (1959) indicated that plants
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C.-c. Pang et al. / Ecological Engineering 69 (2014) 201–205
have a significant effect on the flow only if the water depth is smaller than a certain value and that the value of n would approach a constant value if the water is of sufficient depth. López and Garcia (2001) found that resistance to flow increases with the increase of the plant density. Chen (1976) studied the resistance in the shallow water flow with natural grass cover on the bed; in this study, Kentucky Blue grass and Bermuda grass were used in the experiments. Chen (1976) obtained a curve relating the Darcy–Weisbach roughness coefficient with the Reynolds number f–Re, which revealed that f is directly proportional to the bed slope to the power 0.662 and is inversely proportional to the Reynolds number. With the development of measuring instruments, the fine structure of the turbulent flow containing aquatic plants can now be measured. With the data from such measurements, the influences of aquatic plants on the flow field, turbulent structure and substance transportation could be analysed. The analysis results provide the basis for further study of the environmental and ecological changes due to the presence of aquatic plants (Nepf, 1999; Ikeda and Kanazawa, 1996; Kouwen and Li, 1980; Leonard and Croft, 2006; López and Garcia, 2001; Nepf and Vivoni, 2000; Nezu and Onitsuka, 2001; Wang and Wang, 2010; Wilson et al., 2003; Yang and Choi, 2009). Yang and Choi (2009) analysed the characteristics of the flow structure from the aspects of the time-averaged velocity, turbulent intensity and shear stress in the presence of aquatic plants. In the most of previous research studies, the artificial metal or plastic rigid bar or flexible plastic plant models were used as test aquatic plants in the experiments. Of course, the results from such research do not accurately reflect the effects of natural flexible plants on the flow. The present research involves an experiment to determine the effects of submerged herbaceous plants on the turbulent structure and flow field in shallow water, such as Lake Taihu, in a relatively wide flume. The eel grass that is commonly found in Lake Taihu and other shallow lakes in China was chosen as the test plants. Three main factors were taken into account in the experiment. The first factor is the density of the plants; the second factor is the distribution form of the eel grass, with the patch form being selected; the third factor is the flow velocity. Three plant densities and flow velocities were chosen according to an on-site survey in Lake Taihu performed in 2012. The objective of this study is to determine the specific characteristics of the mean and turbulent structure of the flow influenced by an eel grass patch, i.e., the quantitative resistance coefficient of eel grass, to explain the mechanism of the low turbidity and small pollutant concentration that appears in natural herbaceous plant patches and to provide the basic data for relevant numerical modelling research.
2. Experimental facility and experimental conditions 2.1. Test flume and test plant material The test flume has a length of 12.0 m, width of 2.0 m and bed slope of 3‰. The test flume has a self-contained water circulation system. The eel grass was selected as the test plant. The physical properties of eel grass are as follows: the length of the eel grass is 32–35 cm; there are eight groups of foliage per plant, which grow directly from the root, and the average width of the foliage is approximately 0.8 cm. The test eel grass was replaced every day for each run to keep the eel grass fresh and to ensure the physical properties are consistent among all of the runs. The eel grass was fixed onto a wire net of size of 4 m × 2 m. The eel grass was arranged in quincunx form. The three plant densities used are 172 plants/m2 (A layout), 86 plants/m2 (B layout) and 43 plants/m2 (C layout).
A total of 21 measuring vertical lines were arranged, each of which had 17 measuring points. An ADV (Vectrino+, version 1.03 Beta 4, NORTEK, Norway) was used to measuring the three dimensional instantaneous velocities; the sampling frequency was 25 Hz, and the measuring time was 2 min. 2.2. Experimental conditions The water depth of flume was 40 cm. The experimental conditions are listed in Table 1. 3. Results and discussions 3.1. Mean flow field Here, the data from run 8 are discussed as a representative example. The variations of the vertical profiles of u, (u is timeaverage velocity in x-direction) in the x-direction are shown in Fig. 1a. In the figure, the meaning of label ‘10B1#2’ is as follows: ‘10’ indicates that the test velocity is 10 cm/s; ‘B’ indicates that the plant density is that of the B layout; ‘1’ indicates the first measuring cross-section; ‘#2’ indicates the second measuring vertical line on the first measuring cross-section. ‘KB’ in ‘10KB1#2’ indicates that the measurement was performed in a run without a plant patch in the water. Fig. 1a shows that the plants begin to influence the flow at the upstream facet edge of the plant patch (10B1#2) when the flow enters the plant patch: the velocity of the upper water layer above the plant canopy increases and the velocity of lower water layer below plant canopy decreases. Further into the plant patch, the velocity of the lower water layer below the plant canopy reduces sharply and also further decreases along the way downstream (10B2#2, 10B3#2, 10B4#2); the vertical velocity profiles do not recover to the normal pattern because the influence of the plants remains for a certain distance from the downstream edge of the plant patch (10B5#2, 0.5 m from the downstream edge of the plant patch). 3.2. Turbulent structures Only the results of turbulent intensity are presented here. The turbulent intensity in the plant patch, here denoted as the rela-
¯ is discussed. u¯ is the cross-section tive turbulent intensity, u 2 /u, averaged value of u. The variations of vertical profiles of the relative turbulent intensity along the x-direction are shown in Fig. 1b. In general, the turbulent intensity initially increases from the water surface to the plant canopy, then decreases from the plant canopy to the plant root. There is a turning point at the canopy. The turbulent intensity is the strongest around the canopy, as the magnitude of the foliage swinging is the largest and most furious, and the strongest shearing occurs there. The plant density has no effect on the turning point. At the water surface, the turbulent intensity is weak if there are no disturbances from the outside; hence, there are no additional turbulence productions. Near the plant stem base, there is little production of turbulence because the plant stem is fixed there and because the fixed stem base has an apparent inhibition effect on the turbulence transferred from the canopy, with the dissipation of turbulence being greatly strengthened at the plant stem base; hence, the value of the turbulent intensity is even less than the values of the non-plant cases, as seen in comparing the two curves labelled ‘10B3#2’ and ‘10KB3#2’ in Fig. 1b. The vertical profiles approach more or less normal patterns at the location of the outer portion of upstream boundary of the patch (10B1#2) and the place outside of the downstream boundary of the patch (10B5#2),
C.-c. Pang et al. / Ecological Engineering 69 (2014) 201–205
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Table 1 Experimental conditions. Run
1
2
3
4
5
6
7
8
9
10
11
12
Velocity (cm/s) Density of plants Reynolds number Froude number
3 A 7892 0.018
3 B 7892 0.018
3 C 7892 0.018
5 A 13,153 0.03
5 B 13,153 0.03
5 C 13,153 0.03
10 A 20,307 0.06
10 B 20,307 0.06
10 C 20,307 0.06
3 – 7892 0.018
5 – 13,153 0.03
10 – 20,307 0.06
u 2 /u¯ along the x-direction, (z is the height of the measuring point, h is the bending height of the eel grass in the
Fig. 1. Variations of the vertical profiles of (a) u and (b) flow).
but the profiles are irregular, which indicates the influence of the plants. 3.3. Resistance coefficient of the plants The resistance to water flow caused by aquatic plants is an important factor in open channel flow. It is difficult to measure the resistance coefficient CP directly when the plants exist in the water. Normally, CP is determined indirectly through the measured water level slope, turbulent shear stress and time-averaged velocity. Using a method similar to that of reference Nepf and Vivoni (2000) and the data from experimental condition 8 as an example, the resistance coefficients of the plants for nine measuring lines in the patch area are calculated, with their the average resistance coefficient presented in Fig. 2. The present results are different than the results of references (Nezu and Michio, 2008; Nepf and Vivoni, 2000) because the physical properties of the plants used in the tests are different. The general shapes of the CP profiles at the nine measuring lines are similar. The value of CP increases more rapidly from the canopy towards the root, and a local maximum appears at z/h of approximately 0.4.
2.5 2.0
3.4. Quadrant analysis of the turbulent structure As mentioned in previous studies (Hopkinson, 2012; Nepf, 1999; Nezu and Sanjou, 2008; Velasco et al., 2001), coherent eddies may occur along the canopy due to strong shear instability. To discuss the patterns of coherent eddies, a quadrant analysis method for analysing turbulent stress, u w is used in this study (López and Garcia, 1998; Lu and Willmarth, 1973; Wallace et al., 1972). A program was written according to the quadrant analysis theory. The turbulent events for each measuring point of all 21 measuring vertical lines of experimental condition 8 are analysed using the program. One of the interesting results involves the spatial distribution of the events in a longitudinal section through plant patch centre, as shown in Fig. 3. In the figure, the region encircled by the green rectangle is part of the flume, the region encircled by the red rectangle is the plant patch region, and the region encircled by the violet rectangle is the region where the measurement was conducted. At the longitudinal section through plant patch centre, as shown in Fig. 3, the Q2 event (ejection) dominates in the region above the canopy, the Q4 event (sweep) dominates below the canopy, the Q1 event (outward interactions) and the Q2 event (inward interactions) appear in some areas near the bed. The Q4 event still dominates in the region downstream of the plant patch; this distribution pattern may be formed by the turbulence pattern in the patch by the process of advection and diffusion.
z/h
1.5 1.0 0.5 0.0
0
2
4 CP
6
Fig. 2. Average resistance coefficient CP curve.
8 Fig. 3. Spatial distribution of the events in a longitudinal section through the patch centre. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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C.-c. Pang et al. / Ecological Engineering 69 (2014) 201–205
In summary, the spatial distribution of the turbulent event has certain regular patterns in the plant patch area. The Q4 event dominates the region below the canopy, and the Q2 event dominates the region above the canopy. This result is basically consistent with the results of previous works (Hopkinson, 2012; Nezu and Sanjou, 2008; Poggi et al., 2004). However, it is found in this study that the turbulent events Q1 and Q2 occur near the bed, as shown in Fig. 3. The ejection or outward events interact with the sweep event, which involves the high speed fluid brought by sweep motion from around the canopy mixing with the low speed fluid transported from the near bed region by ejection motion or by outward interaction motion. This mixing process would reduce the flow momentum and energy, which in turn affects the transportation of sediment and pollutants. This specific turbulent pattern may be attributed to the irregular motions of the foliage of the eel grass, which affect the turbulent flow in a different manner compared to that of artificial rigid or flexible plants. 4. Conclusions An experiment was conducted to study the turbulent flow structure of the water flow with the existence of eel grass patch in the water. The test data were analysed from the three aspects: time-average velocity, turbulent intensity and shear stress. The conclusions are as follows. (1) The time-average velocity u profile assumes an S-shape from the canopy to the plant root. There is a secondary peak value near the plant root. This result is basically consistent with previous works. However, the velocity profiles are more irregular due to the very soft nature of eel grass, which enables the foliage floating in the water to sway with the flowing water, thereby affecting the flow in a more complex manner than that of artificial plants. (2) Inside the plant patch, the turbulent intensity is the highest at the canopy because the foliage swaying is the most prominent there. The turbulence intensity increases from the water surface to the canopy, then decreases from the canopy to the plant root, with a turning point located at the canopy. The position of the turning point of the turbulent intensity profile is affected by the flow velocity; it moves upward when the flow velocity is low. (3) The value and pattern of the vertical profile of the resistance coefficient of the submerged eel grass is different at different positions in the patch. However, the general patterns of the CP profiles are similar in the boundary area of the patch, and those in the internal area of the patch are similar; the pattern of the CP profile in the downstream boundary is different from the others, which may due to the increased overlap of the eel grasses at that position. (4) The results from the quadrant analysis of −u w indicate that the distribution of the turbulent events in the regions below and above the canopy has certain regular pattern in the spatialaveraged sense, even though the motion of the foliage is so irregular. Basically, the Q4 event is dominant in the flow below the canopy and the Q2 event is dominant in the flow above the canopy. The Q1, Q2 and Q4 events were also found to coexist in the region near bed. The Q4 sweep event brings a high speed water parcel down to the bed, where it meets the low speed water ejected from the flow layer near the bed by the Q2 ejection event or by the Q1 outward interaction motion; the momentum and energy of the water parcel would be reduced, and as a result, the transportation capacity of the water flow would also be reduced. At the side boundaries and adjacent
water area, the dominance of the turbulent event is not so obvious.
Acknowledgements This work is supported by the National Natural Science Foundation of China (no. 41071021), the National Key Basic Research Program of China (973 Program) (2012CB417000), the Ministry of Science and Technology of the People’s Republic of China (2011GB23320010) and the National Science and Technology major projects (2012ZX07506-003-04). The authors also thank the anonymous reviewers for their constructive comments.
References Abood, M.M., Yusuf, B., Mohammed, T.A., Ghazali, A.H., 2006. Manning roughness coefficient for grass-lined channel. Suranaree J. Sci. Technol. 13 (4), 317–330. Chen, C.L., 1976. Flow resistance in broad shallow grassed channels. J. Hydraul. Div. J. 102 (HY3), 307–322. Chow, V.T., 1959. Open-Channel Hydraulies. McGraw-Hill, New York, NY. Fathi-Maghadam, M., Kouwen, N., 1997. Nonrigid nonsubmerged vegetative roughness on flood plains. J. Hydraul. Eng. 123, 51–57. Hopkinson, L.C.,2012. Flow through vegetation patches with multiple layers: a quadrant analysis. In: World Environmental and Water Resources Congress: Crossing Boundaries. ASCE, pp. 1406–1415. Ikeda, S., Kanazawa, M., 1996. Three-dimensional organized vortices above flexible water plants. J. Hydraul. Eng. 122 (11), 634–640. Kris, B., Eric, S., Hans, V., Peter, V., Doncker, D., de Deckere, L., Mostaert, E., Meire, F., Patrick, M., 2013. How do macrophyte distribution patterns affect hydraulic resistances? J. Ecol. Eng. 37 (3), 529–533. Kouwen, N., Li, R.M., Simons, D.B., 1981. Flow resistance in vegetated waterways. J. Trans. ASABE 24 (3), 684–698. Kouwen, N., Li, R.M., 1980. Biomechanics of vegetative channel linings. J. Hydraul. Div. ASCE 106 (HY6), 1085–1103. Larsen, L.G., Harvey, J.W., Crimaldi, J.P., 2009. Predicting bed shear stress and its role in sediment dynamics and restoration potential of the Everglades and other vegetated flow systems. J. Ecol. Eng. 35 (12), 1773–1785. Lee, J.K., Roig, L.C., Jenter, H.L., Visser, H.M., 2004. Drag coefficients for modeling flow through emergent vegetation in the Florida Everglades. J. Ecol. Eng. 22, 237–248. Leonard, L.A., Croft, A.L., 2006. The effect of standing biomass on flow velocity and turbulence in Spartina alterniflora canopies. J. Estuarine Coastal Shelf Sci. 69, 325–336. López, F., Garcia, M., 1997. Open-channel flow through simulated vegetation: turbulence modeling and sediment transport. In: Wetlands Research Program Technical Report: WRP-CP-10, U.S. Army Corps of Engineers Waterways Experiment Station, Vicksburg, MS, pp. 56–77. López, F., Garcia, M., 1998. Open-channel flow through simulated vegetation: suspended sediment transport modeling. Water Resour. Res. 34 (9), 2341– 2352. López, F., Garcia, M.H., 2001. Mean flow and turbulence structure of openchannel flow through non-emergent vegetation. J. Hydraul. Eng. 127, 392–402. Lu, S.S., Willmarth, W.W., 1973. Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J. Fluid Mech. 60 (part 3), 481–511. Nepf, H.M., 1999. Drag, turbulence, and diffusion in flow through emergent vegetation. J. Water Resour. Res. 35 (2), 479–489. Nepf, H.M., Vivoni, E.R., 2000. Flow structure in depth limited, vegetated flow. J. Geophys. Res. 105 (C12), 28547–28557. Nezu, I., Michio, S.J., 2008. Turburence structure and coherent motion in vegetated canopy open-channel flows. J. Hydro-environ. Res. 2, 62–90. Nezu, I., Onitsuka, K., 2001. Turbulent Structures in partly vegetated open channel flows with LDA and PIV measurements. J. Hydraul. Res. 39 (6), 629–642. Nezu, I., Sanjou, M., 2008. Turbulence structure and coherent motion in vegetated canopy open-channel flows. J. Hydro-environ. Res. 2, 62–90. Poggi, D., Porporato, A., Ridolfi, L., Albertson, J.D., Katul, G.G., 2004. The effect of vegetation density on canopy sub-layer turbulence. Boundary Layer Meteorol. 111, 565–587. Temple, D.M., Robinson, K.M., Ahring, R.M., Davis, A.G., 1987. Stability design of grass-lined open channels. In: Agriculture Handbook 667. Agricultural Research Service, U.S. Department of Agriculture, Washington, DC. Velasco, D., Bateman, A., Redondo, J.M., et al., 2001. An Open Channel Flow Experimental and theoretical Study of Resistance and Turbulent Characterization Over Flexible Vegetated Linings. Technical University Catalonia (UPC) (November 15).
C.-c. Pang et al. / Ecological Engineering 69 (2014) 201–205 Wang, C., 2009. Flow structure of partly vegetated open-channel flows with eel grass. J. Hydrodyn. 21 (3), 301–307. Wallace, J.M., Eckelmann, H., Brodkey, R.S., 1972. The wall region in turbulent shear flow. J. Fluid Mech. 54 (part 1), 39–48. Wang, P.F., Wang, C., 2010. Hydraulic resistance of submerged vegetation related to effective height. J. Hydrodyn. 22 (2), 265–273.
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Contents lists available at ScienceDirect
Ecological Engineering journal homepage: www.elsevier.com/locate/ecoleng
Short communication
Turbulence structure and flow field of shallow water with a submerged eel grass patch Cui-chao Pang a,b,c,∗ , Di Wu a,d , Xi-jun Lai a , Shi-qiang Wu c , Fang-fang Wang c a
State Key Laboratory of Lake Science and Environment, Nanjing Institute of Geography & Limnology, CAS, Nanjing 210008, PR China Changjiang Institute of Survey, Planning, Design and Research, Shanghai Department, Shanghai 200439, PR China c Hydraulic Engineering Department, Nanjing Hydraulic Research Institute, Nanjing 210029, PR China d Hohai University, Nanjing 210098>, PR China b
a r t i c l e
i n f o
Article history: Received 14 September 2013 Received in revised form 9 February 2014 Accepted 31 March 2014 Keywords: Shallow lake Plant patch Eel grass Time-averaged velocity Turbulent intensity Turbulent shear stress
a b s t r a c t A flume experiment was conducted to investigate the effect of the aquatic herbaceous plant patch on the turbulent structure and flow field of shallow water. The eel grass that is widely distributed in the shallow lakes in China was chosen as the targeted plant. The plants were settled in patch form with three groups of densities and flow velocities. The three-dimensional instantaneous velocities were measured using an Audio Doppler Velocitimeter (ADV). The results indicate that the vertical velocity profile in the plant patch exhibits an S-shape from the canopy to the root of the eel grass. A secondary maximum in the vertical profile of velocity near the plant root is observed. The turbulent intensity increases from the water surface to the canopy, then decreases to the plant root; there is an inflection point around canopy, where the turbulent intensity deceases from the inner region to the side boundary of the patch. The vertical profiles of the eel grass resistance coefficient CP have different forms at different positions in the patch in general, but the forms of the CP profiles are similar along the boundary of the patch, and the forms of the CP profiles are similar in the inner part of the patch. In the patch area, the turbulent flow corresponds to the Quadrant 2 event (ejection event) above the canopy, the turbulent flow corresponds to the Quadrant 4 event (sweep event) below the canopy, but near the bed the Quadrant 1 event (outward interaction), the Quadrant 2 event and the Quadrant 4 event coexist. In the lateral boundary area of the patch the Quadrant 2 event and the Quadrant 3 event (inward interaction event) coexist due to presence of a strong shear layer. © 2014 Elsevier B.V. All rights reserved.
1. Introduction In large water bodies with dense herbaceous plants, water is usually clear and low, and a concentration of suspended sediment is observed. The nutrients are apparently lower in the area with dense herbaceous plants than in the surrounding water area without vegetation. The eutrophication degree of water in the herbaceous type lake is found to be lower than that in the non-herbaceous type lake in general. The mechanism of this specific environmental and ecological effect of the aquatic herbaceous plant patch of the lake has not been explained thoroughly. Therefore, it is necessary to promote the study of the effect of natural aquatic herbaceous plants
∗ Corresponding author at: Nanjing Institute of Geography & Limnology, State Key Laboratory of Lake Science and Environment, No.225, Beijing Donglu Road, Nanjing 210008, PR China. Tel.: +86 15850589312. E-mail address: [email protected] (C.-c. Pang). http://dx.doi.org/10.1016/j.ecoleng.2014.03.075 0925-8574/© 2014 Elsevier B.V. All rights reserved.
on the turbulent flow structure to explain the environmental and ecological effects of aquatic herbaceous plants and to understand the relevant mechanism of the formation of clean water in the plant patch area and surrounding water. The experimental study on the effect of aquatic plants on the flow from the resistance aspect began in the 1950s (Abood et al., 2006; Chen, 1976; Chow, 1959; Fathi-Maghadam and Kouwen, 1997; Kris Bal et al., 2013; Kouwen et al., 1981; Larsen et al., 2009; Lee et al., 2004; López and Garcia, 1997; Nepf, 1999; Temple et al., 1987; Velasco et al., 2001; Wang, 2009; Wang and Wang, 2010), which involved the analysis of the effect on the resistance coefficient CD , the Manning roughness coefficient n, and the Darcy–Weisbach roughness coefficient f. The Manning roughness coefficient n is commonly used in ecological systems and has been studied most thoroughly. The researchers normally thought that the factors affecting the resistance are the shape, flexibility, spatial distribution and density, relative submergence of the plants and Reynolds number of the flow. Chow (1959) indicated that plants
202
C.-c. Pang et al. / Ecological Engineering 69 (2014) 201–205
have a significant effect on the flow only if the water depth is smaller than a certain value and that the value of n would approach a constant value if the water is of sufficient depth. López and Garcia (2001) found that resistance to flow increases with the increase of the plant density. Chen (1976) studied the resistance in the shallow water flow with natural grass cover on the bed; in this study, Kentucky Blue grass and Bermuda grass were used in the experiments. Chen (1976) obtained a curve relating the Darcy–Weisbach roughness coefficient with the Reynolds number f–Re, which revealed that f is directly proportional to the bed slope to the power 0.662 and is inversely proportional to the Reynolds number. With the development of measuring instruments, the fine structure of the turbulent flow containing aquatic plants can now be measured. With the data from such measurements, the influences of aquatic plants on the flow field, turbulent structure and substance transportation could be analysed. The analysis results provide the basis for further study of the environmental and ecological changes due to the presence of aquatic plants (Nepf, 1999; Ikeda and Kanazawa, 1996; Kouwen and Li, 1980; Leonard and Croft, 2006; López and Garcia, 2001; Nepf and Vivoni, 2000; Nezu and Onitsuka, 2001; Wang and Wang, 2010; Wilson et al., 2003; Yang and Choi, 2009). Yang and Choi (2009) analysed the characteristics of the flow structure from the aspects of the time-averaged velocity, turbulent intensity and shear stress in the presence of aquatic plants. In the most of previous research studies, the artificial metal or plastic rigid bar or flexible plastic plant models were used as test aquatic plants in the experiments. Of course, the results from such research do not accurately reflect the effects of natural flexible plants on the flow. The present research involves an experiment to determine the effects of submerged herbaceous plants on the turbulent structure and flow field in shallow water, such as Lake Taihu, in a relatively wide flume. The eel grass that is commonly found in Lake Taihu and other shallow lakes in China was chosen as the test plants. Three main factors were taken into account in the experiment. The first factor is the density of the plants; the second factor is the distribution form of the eel grass, with the patch form being selected; the third factor is the flow velocity. Three plant densities and flow velocities were chosen according to an on-site survey in Lake Taihu performed in 2012. The objective of this study is to determine the specific characteristics of the mean and turbulent structure of the flow influenced by an eel grass patch, i.e., the quantitative resistance coefficient of eel grass, to explain the mechanism of the low turbidity and small pollutant concentration that appears in natural herbaceous plant patches and to provide the basic data for relevant numerical modelling research.
2. Experimental facility and experimental conditions 2.1. Test flume and test plant material The test flume has a length of 12.0 m, width of 2.0 m and bed slope of 3‰. The test flume has a self-contained water circulation system. The eel grass was selected as the test plant. The physical properties of eel grass are as follows: the length of the eel grass is 32–35 cm; there are eight groups of foliage per plant, which grow directly from the root, and the average width of the foliage is approximately 0.8 cm. The test eel grass was replaced every day for each run to keep the eel grass fresh and to ensure the physical properties are consistent among all of the runs. The eel grass was fixed onto a wire net of size of 4 m × 2 m. The eel grass was arranged in quincunx form. The three plant densities used are 172 plants/m2 (A layout), 86 plants/m2 (B layout) and 43 plants/m2 (C layout).
A total of 21 measuring vertical lines were arranged, each of which had 17 measuring points. An ADV (Vectrino+, version 1.03 Beta 4, NORTEK, Norway) was used to measuring the three dimensional instantaneous velocities; the sampling frequency was 25 Hz, and the measuring time was 2 min. 2.2. Experimental conditions The water depth of flume was 40 cm. The experimental conditions are listed in Table 1. 3. Results and discussions 3.1. Mean flow field Here, the data from run 8 are discussed as a representative example. The variations of the vertical profiles of u, (u is timeaverage velocity in x-direction) in the x-direction are shown in Fig. 1a. In the figure, the meaning of label ‘10B1#2’ is as follows: ‘10’ indicates that the test velocity is 10 cm/s; ‘B’ indicates that the plant density is that of the B layout; ‘1’ indicates the first measuring cross-section; ‘#2’ indicates the second measuring vertical line on the first measuring cross-section. ‘KB’ in ‘10KB1#2’ indicates that the measurement was performed in a run without a plant patch in the water. Fig. 1a shows that the plants begin to influence the flow at the upstream facet edge of the plant patch (10B1#2) when the flow enters the plant patch: the velocity of the upper water layer above the plant canopy increases and the velocity of lower water layer below plant canopy decreases. Further into the plant patch, the velocity of the lower water layer below the plant canopy reduces sharply and also further decreases along the way downstream (10B2#2, 10B3#2, 10B4#2); the vertical velocity profiles do not recover to the normal pattern because the influence of the plants remains for a certain distance from the downstream edge of the plant patch (10B5#2, 0.5 m from the downstream edge of the plant patch). 3.2. Turbulent structures Only the results of turbulent intensity are presented here. The turbulent intensity in the plant patch, here denoted as the rela-
¯ is discussed. u¯ is the cross-section tive turbulent intensity, u 2 /u, averaged value of u. The variations of vertical profiles of the relative turbulent intensity along the x-direction are shown in Fig. 1b. In general, the turbulent intensity initially increases from the water surface to the plant canopy, then decreases from the plant canopy to the plant root. There is a turning point at the canopy. The turbulent intensity is the strongest around the canopy, as the magnitude of the foliage swinging is the largest and most furious, and the strongest shearing occurs there. The plant density has no effect on the turning point. At the water surface, the turbulent intensity is weak if there are no disturbances from the outside; hence, there are no additional turbulence productions. Near the plant stem base, there is little production of turbulence because the plant stem is fixed there and because the fixed stem base has an apparent inhibition effect on the turbulence transferred from the canopy, with the dissipation of turbulence being greatly strengthened at the plant stem base; hence, the value of the turbulent intensity is even less than the values of the non-plant cases, as seen in comparing the two curves labelled ‘10B3#2’ and ‘10KB3#2’ in Fig. 1b. The vertical profiles approach more or less normal patterns at the location of the outer portion of upstream boundary of the patch (10B1#2) and the place outside of the downstream boundary of the patch (10B5#2),
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Table 1 Experimental conditions. Run
1
2
3
4
5
6
7
8
9
10
11
12
Velocity (cm/s) Density of plants Reynolds number Froude number
3 A 7892 0.018
3 B 7892 0.018
3 C 7892 0.018
5 A 13,153 0.03
5 B 13,153 0.03
5 C 13,153 0.03
10 A 20,307 0.06
10 B 20,307 0.06
10 C 20,307 0.06
3 – 7892 0.018
5 – 13,153 0.03
10 – 20,307 0.06
u 2 /u¯ along the x-direction, (z is the height of the measuring point, h is the bending height of the eel grass in the
Fig. 1. Variations of the vertical profiles of (a) u and (b) flow).
but the profiles are irregular, which indicates the influence of the plants. 3.3. Resistance coefficient of the plants The resistance to water flow caused by aquatic plants is an important factor in open channel flow. It is difficult to measure the resistance coefficient CP directly when the plants exist in the water. Normally, CP is determined indirectly through the measured water level slope, turbulent shear stress and time-averaged velocity. Using a method similar to that of reference Nepf and Vivoni (2000) and the data from experimental condition 8 as an example, the resistance coefficients of the plants for nine measuring lines in the patch area are calculated, with their the average resistance coefficient presented in Fig. 2. The present results are different than the results of references (Nezu and Michio, 2008; Nepf and Vivoni, 2000) because the physical properties of the plants used in the tests are different. The general shapes of the CP profiles at the nine measuring lines are similar. The value of CP increases more rapidly from the canopy towards the root, and a local maximum appears at z/h of approximately 0.4.
2.5 2.0
3.4. Quadrant analysis of the turbulent structure As mentioned in previous studies (Hopkinson, 2012; Nepf, 1999; Nezu and Sanjou, 2008; Velasco et al., 2001), coherent eddies may occur along the canopy due to strong shear instability. To discuss the patterns of coherent eddies, a quadrant analysis method for analysing turbulent stress, u w is used in this study (López and Garcia, 1998; Lu and Willmarth, 1973; Wallace et al., 1972). A program was written according to the quadrant analysis theory. The turbulent events for each measuring point of all 21 measuring vertical lines of experimental condition 8 are analysed using the program. One of the interesting results involves the spatial distribution of the events in a longitudinal section through plant patch centre, as shown in Fig. 3. In the figure, the region encircled by the green rectangle is part of the flume, the region encircled by the red rectangle is the plant patch region, and the region encircled by the violet rectangle is the region where the measurement was conducted. At the longitudinal section through plant patch centre, as shown in Fig. 3, the Q2 event (ejection) dominates in the region above the canopy, the Q4 event (sweep) dominates below the canopy, the Q1 event (outward interactions) and the Q2 event (inward interactions) appear in some areas near the bed. The Q4 event still dominates in the region downstream of the plant patch; this distribution pattern may be formed by the turbulence pattern in the patch by the process of advection and diffusion.
z/h
1.5 1.0 0.5 0.0
0
2
4 CP
6
Fig. 2. Average resistance coefficient CP curve.
8 Fig. 3. Spatial distribution of the events in a longitudinal section through the patch centre. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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In summary, the spatial distribution of the turbulent event has certain regular patterns in the plant patch area. The Q4 event dominates the region below the canopy, and the Q2 event dominates the region above the canopy. This result is basically consistent with the results of previous works (Hopkinson, 2012; Nezu and Sanjou, 2008; Poggi et al., 2004). However, it is found in this study that the turbulent events Q1 and Q2 occur near the bed, as shown in Fig. 3. The ejection or outward events interact with the sweep event, which involves the high speed fluid brought by sweep motion from around the canopy mixing with the low speed fluid transported from the near bed region by ejection motion or by outward interaction motion. This mixing process would reduce the flow momentum and energy, which in turn affects the transportation of sediment and pollutants. This specific turbulent pattern may be attributed to the irregular motions of the foliage of the eel grass, which affect the turbulent flow in a different manner compared to that of artificial rigid or flexible plants. 4. Conclusions An experiment was conducted to study the turbulent flow structure of the water flow with the existence of eel grass patch in the water. The test data were analysed from the three aspects: time-average velocity, turbulent intensity and shear stress. The conclusions are as follows. (1) The time-average velocity u profile assumes an S-shape from the canopy to the plant root. There is a secondary peak value near the plant root. This result is basically consistent with previous works. However, the velocity profiles are more irregular due to the very soft nature of eel grass, which enables the foliage floating in the water to sway with the flowing water, thereby affecting the flow in a more complex manner than that of artificial plants. (2) Inside the plant patch, the turbulent intensity is the highest at the canopy because the foliage swaying is the most prominent there. The turbulence intensity increases from the water surface to the canopy, then decreases from the canopy to the plant root, with a turning point located at the canopy. The position of the turning point of the turbulent intensity profile is affected by the flow velocity; it moves upward when the flow velocity is low. (3) The value and pattern of the vertical profile of the resistance coefficient of the submerged eel grass is different at different positions in the patch. However, the general patterns of the CP profiles are similar in the boundary area of the patch, and those in the internal area of the patch are similar; the pattern of the CP profile in the downstream boundary is different from the others, which may due to the increased overlap of the eel grasses at that position. (4) The results from the quadrant analysis of −u w indicate that the distribution of the turbulent events in the regions below and above the canopy has certain regular pattern in the spatialaveraged sense, even though the motion of the foliage is so irregular. Basically, the Q4 event is dominant in the flow below the canopy and the Q2 event is dominant in the flow above the canopy. The Q1, Q2 and Q4 events were also found to coexist in the region near bed. The Q4 sweep event brings a high speed water parcel down to the bed, where it meets the low speed water ejected from the flow layer near the bed by the Q2 ejection event or by the Q1 outward interaction motion; the momentum and energy of the water parcel would be reduced, and as a result, the transportation capacity of the water flow would also be reduced. At the side boundaries and adjacent
water area, the dominance of the turbulent event is not so obvious.
Acknowledgements This work is supported by the National Natural Science Foundation of China (no. 41071021), the National Key Basic Research Program of China (973 Program) (2012CB417000), the Ministry of Science and Technology of the People’s Republic of China (2011GB23320010) and the National Science and Technology major projects (2012ZX07506-003-04). The authors also thank the anonymous reviewers for their constructive comments.
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