An Open Channel Flow Experimental and Theoretical Study of Resistance and Turbulent Characterization over Flexible Vegetated Linings

Transcription

1 Flow, Turbulence and Combustion 70: 69 88, Kluwer Academic Publishers. Printed in the Netherlands. 69 An Open Channel Flow Experimental and Theoretical Study of Resistance and Turbulent Characterization over Flexible Vegetated Linings DAVID VELASCO 1, ALLEN BATEMAN 1, JOSE M. REDONDO 2 and VICENTE DEMEDINA 1 1 Hydraulic and Hydrological Section, 2 Applied Physics Department, Polytechnic University of Catalonia UPC, E Barcelona, Spain Received 6 December 2001; accepted in revised form 4 May 2003 Abstract. Hydraulic engineers and scientists working on river restoration recognize the need for a deeper understanding of natural streams as a complex and dynamic system, which involves not only abiotic elements (flow, sediments) but also biotic or biological components. From this point of view, the role played by riverine vegetation in river dynamics and flow conditions becomes essential. Hydro-mechanic interaction between flow and flexible plants covering a river bed is studied in this paper and some previous works are discussed. Experimental tests and measurements of turbulence on the flow in an open channel were performed using plastic plants seeded in a gravel bed. Characterization of flow resistance (friction factors) due to vegetation flexible roughness for different plant densities was attained; furthermore, measuring detailed turbulent velocity profiles within and above submerged and flexed stems allowed us to distinguish different turbulent regimes. Some interesting relationships were obtained between the velocity field and the deflected height of the plants, such as a linear fit between the non-dimensional flexural parameter and the relative deflection of the plants. Turbulent stresses were measured showing two different regions: above and inside the vegetation domain. The spectral interaction between the plant oscillations, their wakes and the turbulence at different heights, forces strongly anisotropic Reynolds tensors and in order to clarify turbulent processes and their complex structure, theoretical concepts (Taylor, Kolmogorov s K41) and several data analysis (autocorrelation functions, integral scales) were applied. Key words: canopy flows, plant turbulence. Nomenclature a B d D 50 E f h h p = interplant length = channel witdh = average plant diameter = percentile 50 in soil particle distribution = stiffness modulus = Darcy Weisbach friction factor = uniform water depth = penetration point Presented at the Fluxes and Structures in Fluids Conference 2001, Moscow, Russia.

2 70 D. VELASCO ET AL. h I k k K κ L M Q q Re Rh T U U V W u,v,w U k ρ υ τ xz, τ xy, τ yz τ = non-bending plant height = second order geometrical momentum = deflected height of plant = wavenumber = turbulent kinectic energy = von Kármán turbulent diffusion constant = integral scale = density of vegetation = discharge = unit discharge = Q/B = Reynolds number = hydraulic radius = turbulent intensity = longitudinal mean velocity = bed shear velocity = transversal mean velocity = vertical mean velocity = longitudinal, transversal and vertical velocity fluctuation, respectively = slip velocity = water density = kinematic viscosity of water = Reynolds stresses = bed shear stress 1. Introduction Several studies have examined the influence on and the global hydraulic relationship between flexible roughness due to plants and the consequent flow conditions. Hydraulic design of grassed irrigation channels lead to the first experimental tests [18], where a reduction in friction factors above natural vegetative linings for higher flow rates was reported. The most important contribution was made by Kouwen s studies [7 9]. Dimensional analysis led him to create a simple model to evaluate resistance to flow depending on the geometric and mechanical properties of submerged plants (density, elasticity) and flow conditions. Momentum transfer mechanics are responsive to vortex organization and flow configuration, as well as heat and dissolved substances exchange and diffusion between bottom and surface regions. Specific models were required to accurately solve the basic fluid mechanics interactions between flexible plants in a similar way as with compilant surfaces. Important works on numerical (k e turbulent schemes) and experimental turbulent characterization over vegetation have been carried out [4, 13]. Good adjustments of the results were obtained from rigid and isolated stem covers, but it is clear that stem flexibility and the heterogeneity of leave density are critical properties needed to correctly estimate drag forces [11]. Likewise, biological and environmental processes in natural rivers related to the presence of vegetation (nutrient transport, oxygen rate) and the fact that plankton and larvae growth in the ocean often take place within Poseidonia fields were of major interest in some stud-

3 TURBULENT CHARACTERIZATION OVER FLEXIBLE VEGETATED LININGS 71 Figure 1. Longitudinal flume scheme and transversal section. Photograph of a plastic plant. ies concerning turbulent and contaminant diffusion over submerged and emergent vegetation [14, 15]. Vegetation induces biological depuration processes, so it is a very effective environmental measure for reducing nitrates and phosphates poured into rivers. Moreover, most rivers in populated areas have supported a great antrophic stress during the last decades, so they have become totally degradated. Revegetation techniques must be introduced and public opinion demands effective restoration proceedings, as well as new forms of flood control. As a consequence, a deeper knowledge of hydromechanics over vegetation is obviously required to guarantee appropriate and safe hydraulic designs. In the present study, some experimental tests were conducted under controlled conditions. In order to simplify the inherent complexity of vegetation properties, scaled plastic strips were used to model plants. Different plant densities were tested as well as different flow conditions such as the flow and the ratio of the plant height to the water depth. The velocity field was measured directly in the experimental flume with a Acoustic-Doppler sensor (ADV) which is described in Section 2. The results from the velocity measurements are presented in Sections 3 and 4 and show a reduction in friction factors due to plant bending for an increasing Reynolds number as expected. The characteristics of the turbulent flow and the turbulent velocity profiles as a function of the plant/flow characteristics and an introduction to the analysis of turbulent structures that may explain some of the turbulent velocity data, including autocorrelations, integral length-scale distributions and spectra is included in the discussion and, finally, conclusions are drawn. 2. Experimental Setup The experiments were performed in the hydraulic laboratory of the Polytechnical University of Catalonia (UPC) in Barcelona. A 20 m long concrete flume was used. The cross-section was rectangular, 1 m wide and 0.9 m deep. The gravel bed was extended in a constant slope of 0.64 (D 50 = 2.05 cm). Gravel particles define a friction factor of Manning Strickler n = 0.025, which reproduces the

4 72 D. VELASCO ET AL. Table I. Experimental test conditions. Density M Discharge (l/s) Velocity (m/s) Water depth Plant deflected Submergence Re Bed roughness (plants/m 2 ) h (m) height k (m) h/k E5 1.4E4 Gravel (D = 2cm) E5 1.4E4 Gravel (D = 2 cm) E5 1.5E4 Gravel (D = 2 cm) E5 1.4E4 Gravel (D = 2 cm) E5 1.9E4 Gravel (D = 2 cm) E5 1.4E4 Gravel (D = 2 cm) E4 1.8E4 Sand (D = 0.1 cm)

5 TURBULENT CHARACTERIZATION OVER FLEXIBLE VEGETATED LININGS 73 natural roughness of many local rivers. In Table I the basic flow and geometrical parameters related to the plant models are described for the seven different configurations used. The ranges used for each relevant parameter are indicated. Only one set of experiments (with a plant density of 25 plants per square meter) used sand to generate a much smaller bed roughness. Figure 2 describes the overall conditions of the experimental flume and also shows an example of the plastic plant model used. One of the most important features in the investigation was the realistic physical modelization of natural plant species through plastic, artificial strips. These were designed to reproduce the mechanical behavior of real local river plants. A PVC plastic bunch made of 0.15 m long (h = 0.15 m), thin strips approximates some autochthonous macrophytes shapes (Phragmites Australis-Common Reed), where aerial parts of the plant are concentrated with an average of 20 leaves per plant. Also, it was confirmed from independent tests that the stiffness modulus of plastic (E = Nm 2 ) was adequate to the used hydraulic regimes and flow actions. Kouwen s dimensionless analysis shows that a so-called MEI parameter can be considered as being mainly responsible for the vegetation behavior and thus to exhibit resistance to flow conditions. The MEI factor (after M = density of plants per unit area, E = stiffness modulus and I = inertia momentum) represents the global mechanical and geometrical properties of a group of plants, so we can modify individual stiffness modulus and inertia or the global plant density to achieve similar roughness effects. A simulated vegetated zone was set in a 7 m central zone along the channel and plastic plants were directly fixed on the gravel bed. Initially, three different densities of plants were studied (M = 156, 100 and 70 plants/m 2 ). Another parameter that defines the density of plants is a, an averaged interplant distance, so Ma 2 = 1. According to previous densities, a = 0.08, 0.10 and 0.12 m, respectively. Later three intermediate new densities were tested (M = 170, 130 and 85 plants/m 2 with a = 0.076, and m, respectively). Additionally, a sand bed channel (2.5 m width) was used in some tests. Sand was very uniform (D 50 = 1 mm) and a very low density of plants was set (25 plants/m 2, a = 0.20 m). Spatial distribution of obstacles has a great influence on friction factors (preferable streamlines and velocity gradients) and a staggered plantation pattern was used (natural distribution), but the plant seeding was performed as uniform as possible. A pumping system into the channel set up unitary discharge flows q ranging from to m 2 /s and submergences of plant h/k from 1 to 5.75, where h is the normal average water depth and k is the deflected plant height. Obviously the higher the flow Q = qb, the smaller the deflected plant height. A movable weir located downstream the channel was used to obtain uniform regime conditions along the vegetated zone. Measurement equipment included graduated rubbers and mechanic limnimeters of high precision to register water depths and the deflection of plants. Image analysis of video tapes of some experiments were also useful in detecting

6 74 D. VELASCO ET AL. Figure 2. Variability of friction factor f versus Re. variations in the flow and in the model plant canopy. The discharges were controlled in an upstream triangular weir. Two different types of velocity sensors were used to measure temporal series of velocity in different positions. A 2D electromagnetic velocimeter took data of average velocity along a cross-section. In the detailed study of turbulent structures, a 2D and a 3D acoustic Doppler velocimeter (SONTEK-ADV) were used after extensive calibration. Analysis of the range of turbulent length scales (until viscous micro-scales) requires a high resolution and measurement frequency. Temporal series of 5000 data were taken per point, with a 25 Hz measurement frequency. Higher measurement frequencies up to 75 Hz were also tested but they did not produce more accurate data, due to spatial non-homogeneities in the seeding of the sampling volume, typically 2 10 cubic milimeters. Some vertical profiles in the center streamline of the channel were registered, in order to recognize vertical distribution of velocities, but, because of the geometry of the sensors, only the experiments with deepest flows were analyzed. The relative position of the sensor inside the vegetation pattern is critical because of the structures of the wakes of the plants, the local effects of stems in the surrounding velocity field, pressure gradients, interaction of the turbulent wakes, and other sources of coherent structures that had to be treated in an statistical way. In order to reduce local effects, one or two plants were removed to create a spatialy uniform flow area, where the sensor was located. We consider that this does not affect the statistical turbulent properties of the flow.

7 TURBULENT CHARACTERIZATION OVER FLEXIBLE VEGETATED LININGS 75 Figure 3. Comparison of friction factors between our data and Kouwen s artificial roughness data (extract from [7]). 3. Results 3.1. VARIABILITY ON FRICTION FACTORS One of the main objectives of this work is to evaluate the global resistance to flow under different conditions of flow and density of plants. The estimation of these friction factors, depending on bed roughness, is a very critical point in open hydraulic flumes. The flexible properties of plants cause a rapidly reduction of relative roughness (k/h) for increasing Reynolds numbers or hydraulic power (U.R h ). This fact is clearly observed in the retardance curves shown in Figure 2, where the friction factor (Darcy Weisbach f ) falls progressively. These kind of curves were first plotted by Ree and Palmer [18], who used a wide range of natural grasses in their tests. In our study, a minimal value of f is obtained for totally deflected plants (prone condition where the relative deflection of plant k/h = ) and this value is very similar to the non-vegetated friction factor (f gravel = 0.15) also measured. In consequence, the influence of flexible vegetation is attenuated in high velocity fields, such as in a natural river flooding. Also it may be observed that the variation of plant density is a factor that becomes minimized for increasing velocities. In Figure 3, our data is compared with Kouwen s retardance curves for

8 76 D. VELASCO ET AL. Figure 4. Linear adjustment between dimensionless flexural parameter and relative deflection of plant k/h. plastic strips and, regarding the differencies in the MEI parameter, the evolution of friction factors becomes really well adjusted. The relationship between the friction factor and the Reynolds number defined in the same way as done by Kouwen [7], also shows that the different plant densities do not have much affect on the overall behavior but there may be differences with a factor of MECHANICAL RESPONSE OF VEGETATION TO THE FLOW Another subject of this study is the deformation response of the flexible element to flow stresses. Thus it was experimentally measured as the progressive decrease of the vertical height of the deflected plants, k, as the higher flows produced increasing bed stresses (τ =ρu 2 ) and forced the submergence of the plants. The elastic behavior of stems is confirmed according to the mechanical and dimensional model proposed by Kouwen, in spite of some experimental data dispersion. Figure 4 shows the relative plant deflection k/h,whereh is the non-bended plant height, versus a non-dimensional parameter, similar but modified slightly with respect to the well-known Kouwen parameter. This modified parameter, which takes into account plant and distribution geometry, mechanical properties and flow conditions, is non-dimensional and may be defined by using k/a instead of M as ( ) (k/a) E I 1/4 1 Ko = ρu 2 h,

9 TURBULENT CHARACTERIZATION OVER FLEXIBLE VEGETATED LININGS 77 where the variables indicate, respectively, k = deflected plant height, a = interplant length, E = stiffness modulus of the plant, I = inertial modulus, U = bed shear velocity and h = non-bending plant height. The k/a ratio that appears in this parameter describes the relationship that exists between the characteristic roughness scales as k represents the vertical roughness of the canopy, whereas the interplant length scale defines a lateral spatial distribution and density of roughness elements. Combination of both scales is important for resistance to flow. An excellent linear fit is observed in Figure 4, where all data was included. Anyway, new tests are necessary to confirm that the substitution of M for k/a in Kouwen s MEI model, produces a better predictive relationship but it is important to remark that all tests were set up under a wide range of submergence conditions and it is assumed that emerging plant conditions do not comply with the law k/h = m Ko + c, with m, c the linear fit constants VELOCITY PROFILES It is known that the longitudinal mean velocity (U) profile differs from the typical boundary-layer model (law of the wall) because of the presence of vertical elements (flexible stems) into the flow. A different momentum diffusion mechanism is developed. As a first macroscopic result, the average velocity U decreases and water depth increases. This effect of longitudinal velocity reduction (retardance) is very important inside the vegetated region, and very low values of U were registered. Figure 5 shows an example of velocity profiles for many submergence conditions of plants. The well-known logarithmic profile (von Kármán s universal law) is no longer valid in this roughness condition. Two different regions can be distinguished in all the profiles; the first is the outer region that spans from the top of the plants until the free-water surface (z >k), and the second region is the inner, deeper zone from the bed to the extreme of the plant, where drag forces are present. Figure 6 shows experimental data as non-dimensional velocity U/U k versus the ln(z/k) for different densities of plants. The slip velocity, U k, is defined as longitudinal velocity just in the top of the canopy, where a boundary layer between the inner and outer region is registered. The slip velocity represents a relevant characteristic velocity and it is responsible of the improved data collapse in Figure 6. In the outer region, the velocity profiles fit well a logarithmic distribution [8, 9], but von Kármán turbulent diffusion constant (κ = 0.41) is not confirmed in our data and lower values were estimated. In the inner region, velocity profiles are complex but they will be commented upon later. Some authors explained this region using a uniform and constant velocity scheme, but some vertical gradients of velocity are registered which are governed by obstruction capability (frontal areas and deformation of stem and leaf). In this sense, it is important to know the relation between vertical biomass distribution and velocity profiles. Also, these

10 78 D. VELASCO ET AL. Figure 5. Variation of U velocity profiles for different density and discharge. Circles indicate deflected plant height. Figure 6. Dimensionless logarithmic velocity profile, where U k = slip velocity. regions correspond to two different energy transfer schemes. Experimental studies by Nepf [14, 15] with semi-rigid plants show that turbulent mechanical production and von Kármán wakes behind obstacles are dominant in the inner region and a constant velocity profile is developed. A logarithmic profile is explained above vegetation domain because of the importance of shear stresses (shear turbulence production). Our data agrees with that of Nepf, but in our gravel bed tests, particle roughness increases vertical momentum diffusion and velocity gradients near the

11 TURBULENT CHARACTERIZATION OVER FLEXIBLE VEGETATED LININGS 79 bed. So, in the inner region, both pressure turbulent production and shear turbulent production are strongly present TURBULENT REYNOLDS STRESSES An intensive analysis of local velocity fluctuations (u = U + u ) from temporal series at 25 Hz measuring frequency, led us to calculate second-order statistics in vegetated and non-vegetated tests. Vertical distribution of Reynolds stresses were calculated in order to characterize the momentum diffusion mechanisms. Turbulent intensity T, turbulent kinetic energy K, and Reynolds stresses τ xz, τ xy and τ yz are defined as T = 2 3 K1/2 U with the turbulent kinetic energy K = 1 2 (u 2 + v 2 + w 2 ), τ xz = ρu w, τ xy = ρu v, τ yz = ρv w, where U is the average longitudinal velocity and u, v, w are longitudinal, transversal and vertical velocity fluctuations, respectively. The turbulent intensity represents an isotropic velocity fluctuation average, whereas vertical Reynolds stress (τ xz ) induces longitudinal to vertical momentum exchange and then it shows vertical mixing activity. Horizontal Reynolds stress (τ xy ) conversely defines momentum diffusion in an horizontal plane. The turbulent measurements clearly show that the flow regime is highly anisotropic and that Reynolds stresses are very useful for analyzing the velocity field. Plant deflected height has a great influence on turbulent intensity T. In erected plant conditions, showing no significant deformation, a local maximum of T is registered in the extreme of plants which is more noticeable in higher plant density experiments, but it was shown that the maximum moves downwards for increasing flows and the maximum in turbulent intensity is located near the bed in prone plant conditions. The top of canopies (z = k) locates the highest velocity gradients and turbulent stresses. This zone is a geometrical discontinuity to roughness and supposes a boundary between both very different turbulent production schemes. Transversal Reynolds stresses (τ xy ) confirm this point. In non-vegetated tests (only with a gravel bed), vertical stresses dominate transversal stresses, which are negligible. But in vegetated conditions, the tendency changes and, inside the plants, transversal stresses increase and overcome vertical ones. Development of pressure gradients in the form of turbulent wakes behind obstacles generates this important horizontal diffusion of momentum. Once above top of the canopies, where no obstruction

12 80 D. VELASCO ET AL. Figure 7. Reynolds stresses profiles for (a) vegetated channel, (b) non-vegetated channel. Figure 8. Dimensionless Reynolds stresses profiles for vegetated channel. exists, anisotropy governs and transversal effects gradually become negligible (Figure 7). In Figure 8, we plot two different Reynolds stress profiles which are nondimensional using gravity bed shear stress τ. Measured values are lower than a 2D flow theorical distribution. The answer is the influence upon τ xz of secondary currents in a rectangular flume [16]. In the gravel test, ratio h/b =[ ] is high enough to involve wall shear effects and then large length-scale structures are developed across the channel. They contribute to the gravity shear stress τ absortion. On the other hand, Figure 9 shows an accurate fit between measured Reynolds vertical stresses and gravity shear stress profile in the free zone. These test were carried out in a 2.5 m width flume, so the ratio h/b < 0.1. Secondary currents become very weak and then vertical measurements at the center of the channel are not affected. Apart from secondary currents, it is very important to assume that advection of v and w components in the velocity field and transversal momentum diffusion are not negligible during the presence of vegetation. In addition, highly anisotropic turbulence is generated inside the vegetation domain.

13 TURBULENT CHARACTERIZATION OVER FLEXIBLE VEGETATED LININGS 81 Figure 9. Vertical profiles of three different tests for M = 25 plants/m 2 (sand bed). Dimensionless plots correspond to longitudinal velocity U, Reynolds turbulent stresses and turbulent intensity for each component. As mentioned above, it is very interesting to characterize the amount of stress that is absorbed by a single plant because it represents a basic approach to understand resistance to flow due to these complex elements. A clear relationship exists between the vertical distribution of biomass (frontal area) and longitudinal momentum absorption. Reynolds x-equation in the outer region (above plants, no obstruction) shows turbulent stresses dissipating gravity forces, which are proportional to energy slope. But inside the vegetated zone, flexible stems absorb momentum, and bend. Then drag forces ( vegetative drag forces ) appear in the Reynolds equation. Leaves and stems absorb available gravity stresses (normal and tangential shear stresses to surface), but efficiency depends on vertical biomass structure. Remaining gravity stresses are transformed into turbulent stresses (mainly in transversal stresses) through pressure gradients and vortex streching around obstacles [3, 20]. Nepf [14] observed a characteristic depth inside the canopy where vertical turbulent stresses τ xz becomes zero. Momentum absorbing capability of vegetation and gravity stress (i.e., submergence condition) defines this region near the bed where no vertical momentum is diffused, and the velocity profile is very uniform. In our flume tests, gravel roughness (macroroughness) was responsible for shear stress production near the bed, so that region was never observed. To avoid this matter, a 2.5 m width sand bed flume was used to investigate sediment transport and shear stresses. Figure 9 shows three different tests and velocity, turbulent stresses and turbulent intensity profiles are plotted, respectively.

14 82 D. VELASCO ET AL. The submergence ratio is low, gravity stresses are absorbed efficiently by the plant, which is bending, and vertical turbulent stress comes to zero near the top of the canopy. This position, where τ xz = 0, is called the penetration depth, z = h p.no vertical exchange has been reported inside this region [15], which is called the longitudinal exchange zone (z <h p ). In our experiments, negative vertical turbulent stresses have been measured there, and then negative velocity gradients are developed. Notice the importance of τ xy and τ yz in this region. Vertical distribution of biomass is responsible of the presence of a secondary vortex which locally reverses the longitudinal to vertical momentum exchange mechanism (τ xz < 0). The palm shape or typology of the plastic elements used in our tests accumulates its main absorbing area at the upper zones where the leaves become totally separated. This characteristic distribution of palm shape was registered even for totally prone, bending conditions, quite distinct from the streamlined shapes that are typically observed in natural riverine species. Two instances of coupling between the velocity profiles and the horizontal transport of vertical momentum, reflected by the τ xz profiles are apparent for most of the experiments. The zero values of vertical turbulent stress are also apparent as local maxima or minima on the S-shape velocity profiles. We also observe that at the heights where there is a minima of the τ xz profile, most of the time, at the same height there is an inflection point or change or curvature in the corresponding velocity profile. In consequence, any attempt to numerically fit a velocity profile in the presence of vegetation should take into account turbulent stress distribution, which governs velocity gradients and inflection points. As a result of the budget ot momentum, mean effective bed shear stresses τ are substantially reduced, but an important activity of horseshoe swirls is noticed (but not yet directly measured). Local scour induces load sediment transport, which modifies the geometry around the canopy. 4. Integral Scales The autocorrelation functions Re(τ) were calculated at different depths, according to the expression Re(τ) = u (t).u (t + τ), u 2 where t is a time scale and u the velocity fluctuation in the flow direction x. This normalized parameter represents a correlation factor of a recurrent phenomenon that is acting in the flow at different time scales. Assuming Taylor s frozen whirl hypothesis, l = U. τ, it is possible to find a direct relationship between time τ and space scales l, through the mean longitudinal velocity U, for homogeneous turbulent conditions. It is necessary to note that homogeneous turbulence conditions are not present in our tests, but they are accepted as a first

15 TURBULENT CHARACTERIZATION OVER FLEXIBLE VEGETATED LININGS 83 Figure 10. Definition of geometrical interplant length a. approximation to investigate the general turbulence state, for lack of direct Lagrangian measures in the flume. As a generic concept, these derived spatial scales represent the length or the dimension of turbulent structures (whirls) acting and developing in the streamline direction. Some incoherence could be noticed between a theoretical Re(τ) function and the experimental one, because the tangent at τ = 0 should be horizontal (symmetrical function). Our results do not show this typical shape of function because of an insufficient measurement frequency (25 Hz). Apart from this instrumental limitation, the calculation of integral scales is very interesting and sheds new light on the statistical structure of the turbulent interplant flows. The integral scale Lx is considered to be a characteristic length scale which is able to transfer an equivalent momentum by the local turbulence. This parameter is obtained through integration of Re(τ) as Lx = 0 Re(l) dl. Some interesting relations are obtained from the analysis of integral length scale vertical profiles for vegetated conditions and densities. The data shows a dependence between the geometrical-spatial distribution of roughness (plants) and the turbulent structures. For this purpose, we defined and used a geometrical length scale, a, as the interplant transverse length, see Figure 10. This value represents an average transversal distance between plants in the bed. If a very uniform distribution of canopies is established, a is expressed in terms of the density M as a = 1/M 1/2. Relationships found between the integral scale Lx and length a change from the emergent plant condition to the totally submerged condition. In the first case, when stems are emerging from surface, results show a constant ratio L/a = 0.3 along the vertical profile and then characteristic vortices are very uniform and do not merely develop towards the surface. Horizontal whirls (vertical rotation axis) governs the flow and secondary currents become very important. But, in totally submerged plant conditions (h >k) there is a tendency, a distribution in the L/a ratio, inside and above the vegetation (Figure 11). In spite of dispersion

16 84 D. VELASCO ET AL. Figure 11. Dimensionless plot of the vertical evolution of integral scales for different plant density tests. z/k = 1 denotes the top of the deflected canopy. of experimental data, integral scales increase just inside the vegetation (z <k) as a consequence of high momentum exchange, but ratios L/a are smaller than 1. Above the top of the plant, it is in the outer region (z >k), where L/a are greater than 1, but no distribution has been fitted accurately. These results confirm the idea that the spatial distribution of roughness elements sets a limit and controls development of large-scale turbulent structures in very concise ranges DESCRIPTION OF THE FLOW The top of the deflected plant canopy is seen as the transition point between to different turbulent production mechanisms but inside the plant canopy we may also distinguish the region close to the bed affected by shear. The Reynolds stresses at different heights exhibit a very strong anisotropy, as seen in Figure 9. The different mechanisms, such as the vertical flapping of the very deflected leaves, may also produce some resonance for certain flow parameters. The same is true for resonant coupling of von Kármán vortices among the stems. For example, at the level z/h = 0.6 of Figure 9b) the longitudinal rms velocities u are much larger than v and w and the Reynolds tensors would be very elongated. On the other hand, at heights z/h = the rms turbulent velocities are more isotropic. This is also appreciated, for example, at z/h = 0.3 for experiment (c) where a maximum in U/U is also apparent. Very near the ground the strong vertical shear detected also produces elongated anisotropic Reynolds stresses. The spectra from data at different heights is also

17 TURBULENT CHARACTERIZATION OVER FLEXIBLE VEGETATED LININGS 85 Figure 12. Frequency spectra for three different heights within the plant canopy (h/k = 2.57), corresponding to heights (z/k = 0.12) near the gravel bed, (z/k = 1) at the deflected plant top and (z/k = 1.59) corresponding to a point above the canopy. instructive. For example, in Figure 12 a comparison of the frequency spectra from velocity measurements u at three heights, above the canopy, at the level k,andvery near the ground, show that the turbulence is completely developed. The same data converted to a wavenumber spectra may be compared with the three forcing scales imposed by the dynamic flow geometry; namely: the deflected plant height k, the interplant distance a, and the much smaller stem effective diameter d. The fact that near the ground there is much less energy available for turbulence production in spite of the strong vertical shear is shown by the area below the inertial subrange. At the same time, the higher velocities above the canopy do not produce more turbulence possibly because the lack of the stem flapping. 5. Discussion and Conclusions Reynolds stresses distribution, turbulent production and turbulent integral length scales were calculated for the available data showing very detailed vertical profiles of mean and turbulent relevant parameters. The realization of the strong anisotropy from the ADV measurements and some visual observations of the flow structure shows that there are many possible coupled length scales and coherent structure mechanisms. Thus, a future investigation should also include PIV or flow visualization for a wide range of parameters.

18 86 D. VELASCO ET AL. Figure 13. The same data plotted in Figure 12 for the cited three levels converted to wavenumber spectra. The dashed lines correspond to the wavenumbers due to the deflected plant height K k = 2π/k, to the plant separation K a = 2π/a and due to an average plant diameter K d = 2π/d. The ultimate objective in the future will be to connect this complex hydrodynamic turbulent model with sediment transport phenomena, load or suspended sediment, that takes place inside vegetated regions or wetlands at natural streams. Several authors have reported that the turbulent structures, which are generated inside and above vegetation, induces general sedimentation and reduces local scouring effects. The reduction of resistance to flow in flexible vegetation has been confirmed for increasing flows and low relative roughness (k/h). Under totally prone plant conditions, variations in friction factors for different plant densities are reduced and their values fall to a nearly asymptotic friction factor, equivalent to the nonvegetated one. There is a direct relationship between vegetative effective roughness and local plant deformation (deflected plant height). In that sense, the dimensionless function based on Kouwen s investigations is confirmed. Density, stiffness, and geometric moment of the vegetative model, combined with flow conditions, causes resistance to flow. The use of the average interplant length scale a, and its use in the presented modified Kouwen parameter seems a better predictive indicator. Two different momentum exchange mechanism were analyzed: inside the vegetation, where transversal turbulent stresses dominate vertical components (spatial

19 TURBULENT CHARACTERIZATION OVER FLEXIBLE VEGETATED LININGS 87 gradients of pressure in wakes), and above plants, where turbulent production by Reynolds vertical stresses develops a logarithmic velocity profile. The anisotropy of the turbulence is apparent at different heights and due to several different mechanisms. The Reynolds stress ellipsoid is elongated in the u axis both near the bed and near the deflected canopy height. Vegetation geometry (vertical biomass distribution) and deformation capabilities defines absorbed stresses due to plants and reconfigures Reynolds stress tensor. Pressure gradients and secondary currents govern the lowest zone of vegetation domain, reducing the amount of bed shear stress. The calculations of integral length scales clearly show the distribution of vortical structures with height. Large-scale turbulent structures are limited by spatial and geometrical roughness scales and the spectral information at different heights is very helpful. In the future, a more detailed flow visualization of the vortical structures enhanced by the stems and the conditions for resonant interaction will be attempted. Acknowledgements We thank S. Raffaeli for performing some of the experiments and Alexei Platonov for technical assistance. Acknowledgement of the support of the Spanish Ministry of Science and Technology (REN HID) and the Network of Fluid Dynamics and Geophysical Turbulence (XT ) is due. References 1. Ben Mahjoub, O., Non-local dynamics and intermittency in non-homogeneous flows. Ph.D. Thesis, Universidad Politecnica de Catalunya (2000). 2. El-Hakim, O. and Salama, M., Velocity distribution inside and above branched flexible roughness. ASCE, J. Irrigation Drainage Engrg. 118(6) (1992) Finnigan, J., Turbulence in plant canopies. Annual Rev. Fluid Mech. 32 (2000) Ikeda, S. and Kanazawa, M., Three-dimensional organized vortices above flexible water plants. ASCE J. Hydraulic Engrg. 122(11) (1996) Knight, D.W., Boundary Shear in smooth and rough channels. ASCE J. Hydraulics Div. 107(HY7) (1981) Kouwen, N., Unny, T.E. and Hill, H.M., Flow retardance in vegetated channels. ASCE J. Irrigation Drainage Div. 95(IR2) (1969) Kouwen, N. and Unny, T.E., Flexible roughness in open channels. ASCE J. Hydraulics Div. 99(HY5) (1973) Kouwen, N. and Unny, T.E., Flexible roughness in open channels. ASCE J. Hydraulics Div. (HY1) (1975) Kouwen, N. and Li, R., Biomechanics of vegetative channel linings. ASCE J. Hydraulics Div. 106(HY6) (1980) Kouwen, N., Flow resistance in vegetated waterways. ASCE J. Irrigation Drainage Engrg. 5 (1992) Kouwen, N. and Fathi-Moghadam, M., Friction factors for coniferous trees along rivers. ASCE J. Hydraulic Engrg. 126(10) (2000)

20 88 D. VELASCO ET AL. 12. Lopez, F. and Garcia, M.H., Mean Flow and turbulence structure of open-channel flow trough non-emergent vegetation. ASCE J. Hydraulics Div. 127(HY5) (2001) Naot, D., Nezu, I. and Nakagawa, H., Hydrodynamic behaviour of partly vegetated open channels. ASCE J. Hydraulic Engrg. 122(11) (1996) Nepf, H.M., Drag, turbulence and diffusion in flow through emergent vegetation. Water Resources Res. 35(2) (1999) Nepf, H.M. and Vivoni, E., Flow structure in depth-limited,vegetated flow. J. Geophys. Res. 105 (2000) Nezu, I. and Nakagawa, H., Turbul ence i n O pen C hannel F, l Monograph ow s Series IAHR. Balkema, Rotterdam (1993). 17. Raffaelli, S. and Domenichini, F., Reistenza al moto in un alveo vegetato: Indagine sperimentale di laboratorio. In: Proceedings of the 28th Convention on Idraulica e Costruzioni Idrauliche Potenza (2002). 18. Ree, W.O. and Palmer V.J., Flow of water in channels protected by vegetative linings. Soi l Conservation Service, US Department of Agriculture 967 (1949). 19. Rouse, H., Elementary Mechanics of Fluids. Dover Publications, New York (1946). 20. Simpson, R.L., Junction flows. A nnual R ev. F l ui d M ech. 33 (2001)