Loughborough University Institutional Repository Moeling o vegetate rivers or inbank an overbank ows This item was submitte to Loughborough University's Institutional Repository by the/an author. Citation: SHIONO, K.... et al., 01. Moeling o vegetate rivers or inbank an overbank ows. River Flow 01 - Proceeings o the International Conerence on Fluvial Hyraulics, pp. 63-69. Aitional Inormation: This conerence paper was presente at the International Conerence on Fluvial Hyraulics River Flow 01, September 5-7, 01, San Jose, Costa Rica. Metaata Recor: https://space.lboro.ac.uk/134/1179 Version: Accepte or publication Please cite the publishe version.
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Moeling o vegetate rivers or inbank an overbank lows K. Shiono 1 Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK M. Takea Chubu University, Kasugai, Aichi, 487 8501, Japan K. Yang 3 SuichanUniversity, Chengu, Sichuan, 610065, China Y Sugihara 4 Kyushu University, Fukuoka, Japan T. Ishigaki 5 Kansai University, Suita city, Osaka, 564-8680,,Japan ABSTRACT Moel pparameters such as riction actor an ey viscosity in the Shiono & Knight metho (SKM) are consiere through experimental ata obtaine rom a vegetate open channel. The experiment was conucte in a rectangular open channel with cylinrical ros as vegetation. Velocity, Reynols stresses an bounary shear stress were measure with Acoustic Doppler Velocimetry (ADV) an a Preston tube respectively. Both riction actor an ey viscosity were calculate using the measure ata an oun to be not constant in the shear layer generate by ros. The analytical solutions o SKM to preict velocity an bounary shear stress currently in use were base on the constant assumption o these parameters. In this paper a new analytical solution was erive by taking into a variation o these parameters account an was also veriie with the experimental ata. This solution was also applie to low in compoun channel with vegetation. The new solution gives a goo preiction o the lateral istribution o epth-average velocity an bounary shear stress in vegetate channels, an it preicts the bounary shear stress better than that o the original solution without consiering the seconary low term in particular. 1. INTRODUCTION Flooing is the most common cause o loss o lie, human suering an wiesprea amage to builings, crops an inrastructure. However, looing is a natural an necessary process or the maintenance o the ecology o a river, promoting the exchange o material an organisms amongst a mosaic o habitats. The inluence o riparian vegetation on both ecological an hyraulic processes has thereore become increasingly recognize as an integral component o river management. Vegetation such as trees an bushes commonly occurs along the banks o rivers an the eges o looplains (see Fig.1), both naturally an by esign or erosion prevention, habitat creation an lanscape. Despite this, there is little known o the eect o such marginal vegetation on loo hyraulic processes, mass exchanges, seiment transport, an pollutant ispersion uring river loo. This is thus a key weakness in the application o numerical moels in loo risk management an river rehabilitation stuies. This paper thereore particularly ocuses on the impact o trees an bushes on the key topics o velocity an bounary shear stress. Fig. 1 One line trees at the ege o Flooplain o looing river. Most rivers an man-mae channels have looplains that exten laterally away rom the river, orming so-calle compoun channels. Funamental research on compoun channel hyroynamics was carrie out in 1990 th an reveale the presence o high levels o turbulence, seconary lows an large horizontal eies at the junction be-
tween the looplain an the main channel. The results o this work le to the creation o the Shiono an Knight Metho (SKM) or analysis o overbank lows (Shiono & Knight, 1988, 1991). This SKM cannot separate the inluence o the rag riction o riparian vegetation rom the bounary riction, an Rameshwaran & Shiono, (007) emonstrate signiicant over-preiction o bounary shear stress or an emergent vegetation case an then introuce the rag orce term in SKM. As a result, the preiction o bounary shear stress was great improvement. In experimental stuies, Sun an Shiono, (009) emonstrate that low resistance cause by rag orce ue to such vegetation in a small aspect ratio o open channel is signiicant. The vegetal rag orce thus aects loo water levels an consequently loo hazar maps in a relative small aspect ratio o rivers. The exchange o momentum is the key to control low resistance in the vicinity o vegetate areas. Most popular expression o momentum exchange is velocity graient with ey viscosity. For SKM, the ey viscosity is expresse with the be an ro generate turbulence (Shiono et al 009), an non imensional ey viscosity within the analytical solutions o SKM is assume to be constant, however the measure non imensional ey viscosity (White an Nep, 008) in open channel low with the vegetation tens to show ierent behaviour to that assume in the analytical solutions or SKM. The riction actor or SKM is also the key actor an is assume to be constant. The riction actor however appears to be also not constant in the shear layer region occurre by vegetal rag as shown in Xin an Shiono (009). Thereore the ey viscosity an riction actor nee to be reine in such region in SKM. In this paper, a new analytical solution is erive base on having a variation o riction actor an non imensional ey viscosity. This analytical solution is valiate with the measure velocity an bounary shear stress in an open channel with one line vegetation.. EXPERIMENT SETUP Experiments were conucte in a 9m long an 0.915m wie rectangular channel in Loughborough University (LU). A honeycomb was place at the inlet o the channel to remove large unulations o water surace. A single line o vegetation was mae rom a series o 9mm iameter wooen ros. These were hel in place at y=0.455m (centre o the channel) with a series o wooen cross members spanning the with o the channel. The centre to centre spacing between the ros was taken as 160mm, which thereore implies a ro spacing ratio L/D o 17.8, (L=ro spacing an D=ro iameter). This is base on the average tree spacing along a reach o the River Thames, Terrier, et al (010). The be slope, S 0 was set to 0.001, an the water epth was at 0.3m in the measurement area between 4.7m an 5.3m ownstream. Because the channel was not long enough or uniorm low to be establishe, the energy slope was thereore estimate by balancing the orces such as the Reynols shear orce at the ro an bounary shear orce an the weight component an was 0.00016. This value is use as the energy slope in this paper. Data collections were perorme using ADV or velocity an a Preston tube or bounary shear stress. For ADV, measurements were carrie out at 9 hal cross sections over 0.7m length along the channel as shown in Fig.. The measurements were taken place at 4 vertical istances with 6 traverse locations or each the hal cross section. Fig. Measurement locations in the channel The ata recoring each point was 3 minutes an the sample ata rate was 100Hz. For the Preston tube, the measurements were carrie out at the same transverse an longituinal locations as with the ADV measurements. The ata recoring length or each location was also 3 minutes. 3. EXPERIMENTAL RESULTS A typical velocity istribution in the hal cross section between ros at 5.m ownstream rom the inlet is shown in Fig. 3, (U=longituinal velocity, z= vertical istance an y=lateral istance). There is a tenency to have slower velocity near the ro an the maximum velocity aroun the hal water epth, which emonstrates a istinct velocity ip as happene in a narrow channel. It can be seen rom the igure that there has a tenency o bulging low in the shear layer near water surace even the velocity
was measure below 0.4m rom the water surace. This suggests that the rag orce cause by the ros is signiicant in the water surace area. The transverse component o the Reynols stress cause by the vertical plane shearing is also shown in Fig. 3, ( uv =Reynols stress). A large Reynols stress occurs near the ro area aroun y=0.45~0.55m ue to the rag orce o the ros. It was notice that the magnitue o the vertical component o the Reynols stress cause by the horizontal plan shearing in most area was consierably smaller than transverse component one. There was a tenency o the vertical component to have its largest near be, which inicates the ominance o be generate turbulence, however the transverse component is ominate over the water epth near the ro area. It is notice that the location o zero o the Reynols stress is not corresponing to the location o the maximum velocity. They shoul be coincie but not in this experiment. This may be ue to a lack o measurement points. z(m) U( m / s) Fig. 4 Depth average velocity an Reynols stress an Bounary shear stress, an y(m) z(m) uv ( N / m ) Fig. 5 Friction actor an ey viscosity/(uh). y(m) Fig. 3 Velocity an Reynols stress istributions Depth average velocities in the measurement sections were estimate using available ata an are shown in Fig. 4 incluing the transverse component o the epth average Reynols stress an the bounary shear stress. The transverse component o the epth average Reynols stress in the measurement sections inclue in Fig. 4 was calculate using those values o 9 cross sections along the channel. It can be seen rom the igure that there is a maximum velocity at a istance o 1/3 with rom the channel wall (y=0.9m) an the Reynols stress apparently varies linearly within the hal cross section in the channel. This suggests that the rag orce cause by the ros is almost times the wall shear orce. The istribution o bounary shear stress (Tb) has a tren similar to that o the epth average velocity as shown in Fig. 4. The bounary shear stress is proportional to velocity square near the be, an as can be seen in Fig. 3, there is a tenency o the istribution o velocity near the be similar to the bounary shear stress istribution. The Darcy an Weisbach riction actor () that is one o key parameters in SKM was worke out using the epth average velocity an bounary shear stress, an are plotte on Fig. 5. The riction actor appears to be constant rom the wall (y=0.9m) to y=0.7m an then linearly increases to the ro. It seems to have the linear variation o the riction actor in the shear layer generate by the ros (y=0.45m). This ientiication o the linear an constant variations is important when we revisit SKM consiering riction actor. The analytical solution o SKM currently assumes a constant riction actor, which means that the linear variation o the riction actor in the shear layer inuce by the ros oes not support the analytical so-
lution. Thus the assumption o riction actor or the analytical solution o SKM nees to be reconsiere. The epth average ey viscosity which is also one o the key parameters in SKM was calculate using the epth average Reynols stress an the epth average velocity graient. The epth average velocity graient was obtaine by itting the thir orer polynomial on the epth average velocity. As mentione in the previous section that the Reynols stress is not zero at the velocity graient equal to zero (i.e. at the maximum velocity aroun 0.77), the ey viscosity becomes ininity at the maximum velocity. We avoie at aroun y=0.77m to work out the ey viscosity an only calculate it in the shear layer rom the ro to near the maximum velocity. The ey viscosity was ivie by UH (U=epth average velocity an H=water epth) an then was plotte in Fig. 5. The ivision o UH is irectly relate to the SKM analogy, which will be escribe in next section. The maximum value o nonimensional ey viscosity, ey/ u*h, was 0.164 which is much larger than that o be generate turbulence, a typical value o ey/ u*h is 0.07. u* is the riction velocity. The ey viscosity increases rom y=0.6m towars the ro in the shear layer, which means that it oes not support the constant assumption o the ey viscosity in SKM. This parameter in SKM nees to be also reconsiere. 4. DERIVATION OF ANALYTICAL SOLU- TIONS Lateral istribution methos to preict epth average velocity an bounary shear stress in open channel low have been propose, or example, by Shiono an Knight (1988, 1991), van Prooijen et al, (005). The moel consiere in this paper is the Shiono an Knight Metho (SKM) evelope by Shiono an Knight (1991). SKM incluing rag orce inuce by vegetation is given by Rameshwaran an Shiono (007) an Shiono et. al. (009). This solves the secon orer ierential equation or uniorm low: H UV y H y yx F D gs H where x, y are the longituinal, an lateral irections respectively, U an V is the epth-average velocities in the x an y irections respectively, is the ensity o water, g is the gravitational acceleration, b (1) S is the energy slope an F D is the source term; b is the be shear stress, H is the local water epth. The be shear stress b an the epth-average Reynols shear stress yx can be etermine rom the ollowing Equation : 8 b U 1 t tb UH 8 ghs U y U 8 H UV A e 1 y A e U yx t y y () where is the local riction actor, t is the epthaverage ey viscosity, an tb is the epthaverage imensionless ey viscosity. For no ro area, the source term F D is zero. For the ro area as vegetation, the source term F D is rag orce per unit area an given by: 1 FD NCDSF DHU (3) N = the total ro number/unit area, D=ro iameter, S F =shaing actor an C =rag coeicient. Substituting equation () in equation (1) gives H y y 1 NC DH 8 H 8 8 1 U y gs0h (1 ) 1 NC DH 8 (5) 1/ gs 0 H F H (UV) y (6) D (4) Assuming that, an avection term are constant in a constant water epth omain, Shiono et.al (009) erive an analytical solution to equation (4) as where Rameshwaran an Shiono (007) solve equation (4) numerically, rather than analytically.
As can be seen in Fig. 5 that the riction actor an the ey viscosity are not constant in the shear layer, the above analytical solution cannot be use to solve epth average velocity an bounary shear stress in the shear layer region or this experiment case. Because the riction actor appears to vary linearly, it is thereore propose that the riction actor within the shear layer varies linearly as a irst approximation in orer to obtain an analytical solution o SKM. where 0 1 1 1 8D 0 1 1 8D 0 J H 1 D 8 max J 1 l 0 The coeicients o A 3 an A 4 can be solve with bounary conitions 5. SOLVING MODEL SOLUTIONS Fig. 6 Sketch o shear layer with ro The riction actor is now set in the orm: (notations are shown in Fig.6) where, U 0 y y 1 l t 0 1 0 3 HU 8 max 0 0 1 3 1 ghs A A4 (1 ) 0 D 8 (7) l is shear layer with, y 0, is at the outsie o the shear layer, 0, is at y=y 0, max. is at the ro, y R =y 0 +l. This gives a maximum value, max at the ro an ecreases linearly towar the riction actor 0 at the outsie o the shear layer. Now let us consier the ey viscosity term in equation (4) with the linear variation o the riction actor. In orer to have an analytical solution o equation (4) the ey viscosity term shoul have U times the cubic eine as (8) One can then obtain the ollowing analytical solution or constant water epth. (9) Equations (5) an (9) give the lateral istributions o epth average velocity an bounary shear stress (via equation ()) in no shear layer region an shear layer region respectively. In this experimental open channel case, the hal channel cross section was ivie into two subsections consisting o the shear layer inuce by the ros an the outsie o this shear layer. This leas 4 unknown coeicients, A1, A, A3 an A4 in equations 5 an 9. In orer to solve these coeicients, a system o equation is irst mae by the bounary conitions assuming the continuity o U an U /y at the joint o the subsections, an it becomes a 4 x 4 system o equation. Microsot Excel can be use to solve a 4 x 4 system o equation rom which all the coeicients A s are calculate, hence the velocity an bounary shear stress istributions can be worke out by equations (5) an (9). Let s now consier the riction actor that is require to solve SKM as one o input parameters. Fig. 5 shows that the riction actor in the outsie shear layer tens to be constant. In an area o a constant riction actor, Rameshwaran an Shiono (007) suggeste to use the moiie Colebrook White equation as given by Equation 10. log 3.0 k s 3 18gH S 1. 30H where is the kinematic viscosity o water. (10) This equation was use to estimate a constant riction actor in the outsie o the shear layer in this case. The measure ata were use to calibrate the roughness height k s which was oun to be 0.01m. This gives 0. In the shear layer, the riction actor is set to a linear variation as with the experimental ata as shown in Fig. 5 an is matching the constant riction actor 0 at the joint between the shear layer an its outsie. The maximum riction actor was estimate rom the experimental ata. The istribution o riction actor using equation (7) an the ata are shown in Fig. 7 an both agree reasonably well.
Let s consier another parameter, the ey viscosity, require in SKM. The ey viscosity is expresse with equation (8) in the shear layer. Through the calibration o unertaken using the ata, was oun to be 0.1 in the shear layer an 0.03 in the outsie o shear layer. The istribution o the ey viscosity o equation (8) ivie by UH, is shown in Fig. 8. The ata an equation (8) are reasonably in agreement in the shear layer region. Fig. 7 Distribution o riction actor o velocity istribution near the wall an to accurately preict velocity near the wall, the velocity at near the wall or the bounary conition can be assume to be an appropriate value using either the log-law or the 7 th power law. In this case, the velocity at the wall was estimate using the mean bounary shear stress proportion to the wall shear stress with the Darcy riction equation U =0.75RgS 0 /(/8). For the other bounary conition at the ro, the velocity was similarly estimate using the mean bounary shear stress proportional to the rag orce/unit area, in this case, U =RgS 0 /(0.5C NHD) was use, where C =1. or the ro. It is note that these bounary conitions at the wall an ro were only calibrate by the experimental ata an an appropriate metho is thereore require or establishing bounary conitions at the wall an ro with a variety o ata. With using above the input parameters, namely riction actor an ey viscosity, an the bounary conitions the preictions o velocity an bounary shear stress were perorme with the mathematical solutions (5) an (9) an are shown in Figs. 9 an 10 together with the measure ata an the SKM with constant the riction actor an ey viscosity. It is note that the seconary low term was set to zero. Fig. 8 Distribution o ey viscosity/uh Fig. 9 Preicte an measure velocity. 6. BOUNDARY CONDITIONS To solve the analytical solutions in two regions, namely shear layer region an the outsie region o the shear layer, the bounary conitions are require at the wall o the channel, the joint o two regions an the ro. At the joint between two regions, conventional the bounary conitions, the continuity an graient o velocity were use as mentione in the previous section. For the bounary conition at the wall, the velocity is usually set to zero. However, this oes not give an accurate velocity istribution near the wall, especially in narrow channels. This channel is classiie as a narrow channel, an the velocity istribution near the wall using the velocity being set to zero is shown in Fig. 9 as emonstration. To avoi a sharp change Fig. 10 Preicte an measure bounary shear stress. The original an new solutions or velocity agree well with the measure ata whereas the solutions or the bounary shear stress are quite ierent in the shear layer. The original SKM solution is uner
preicte an this is cause by using the constant riction actor an ey viscosity in the shear layer albeit both increases towars the ro. It is notice that there is a slightly ip at the joint between two subsections or the new solution. This is cause by ierent rates o change o riction actor an velocity as well ey viscosity. The new solution is now valiate with the ata. 7. COMPOUND CHANNEL The new solution was also applie to the compoun channel ata (Shiono et. al. 009) an the results are shown in Figs. 11 an 1. epth average velocity is mathematically iscontinuous at the interace between the main channel an looplain, the preiction was separately unertaken in the main channel an looplain. The bounary conitions at the main channel an looplain walls were use as with the simple open channel low case mentione above. For looplain the bounary conitions are U =0.75RgS 0 /(/8) at the looplain wall an U =RgS 0 /(0.5C NHD) at the square blocks. R=hyraulic raius o looplain. For the main channel, the bounary conitions are U =0.75RgS 0 /(/8) at the main channel wall an U =R gs 0 /(0.5C NHD)+0.5R gs 0 /(/8)(h/H) which inclues the eects o the ro rag orce/unit area an the wall shear stress, R =hyraulic raius o the main channel. It is note that the constant 0.5 o the wall riction is smaller than a regular value o 0.75 use or the other walls. The shear layer with was estimate rom the ata in this preiction since there have been no metho which etermines with o shear layer in the literature except van Prooijen et al, (005) who introuce shear layer with etermine by the concept o percentile o the maximum velocity. In orer to establish the metho how to etermine shear layer with, more ata rom ierent channel conigurations with ierent vegetation cases are require. Fig. 11 Measure an Preicte Velocity Fig. 1 Measure an preicte bounary shear stress The compoun channel has a series o square ros along the ege o the looplain an the etails o the experimental set up can be oun in Shiono et. al. (009). The SKM in the igures inclue the seconary low term =0.56, similar to values or cylinrical ros on the looplain (Rameshwaran an Shiono, 007, an Xin an Shiono 008). This is signiicant high compare with other values (0.15~0.5) or no ro case (Shiono an Knight (1991). Again the new solution gives a better preiction or the bounary shear stress without the seconary low term. It shoul be note that since the 8. CONCLUSIONS The experiment was conucte in a single open channel with a series o cylinrical ros, as vegetation, along the centre o the channel. Velocity an Reynols stress were measure with ADV an bounary shear stress was measure with a Preston tube. The measure velocity, Reynols stress an bounary shear stress were use to estimate riction actor an ey viscosity an both were oun to be not constant in the shear layer inuce by the ros. Base on the experimental ata, the variations o riction actor an ey viscosity in SKM were introuce an a new analytical solution was erive. These variations were a linear unction or riction actor an a cubic unction or the ey viscosity in the shear layer. The valiation o the new analytical solution was unertaken using two experimental ata o the single an two stage channels. With the new analytical solution the preictions o velocity an bounary shear stress are better than those given by the original solution o SKM, an in particular, the preiction o bounary shear stress is much better. The original solution o SKM requires a large value o the seconary low coeicient, but the new solution oes not nee to have the seconary low coeicient because the variation o riction accounts or the seconary low term. The new solution o SKM can be thereore use to estimate
stage-ischarge rating curve an to investigate spacing o trees an bushes or river management. REFERENCES van Prooijen, B.C., Battjes, J.A. an Uijttewaal, W.S.J. (005). Momentum Exchange in Straight Uniorm Compoun Channel Flow. J. Hyraul. Engrg. 131, 175 183. Rameshwaran, P. an Shiono, K. (007), Quasi two imensional moel or straight overbank lows through emergent vegetation on looplains, JHR, Vol. 45, No. 3, pp. 30-315. Shiono, K. an Knight, D.W., (1988), Two imensional analytical solution or a compoun channel, Proc. 3 Int. Symp. on Reine Flow Moelling an Turbulence Measurements, (Eitors: Y. Iwasa, N. Tamai an A. Waa), Universal Acaemy Press, pp.591-599. Shiono K. an Knight, D.W. (1991), Turbulent open channel lows with variable epth across the channel, JFM, vol., pp.617-646. Shiono, K. Ishigaki, T., Kawanaka, R. an Heatlie, F. (009), Inluence o one line vegetation on stageischarge rating curves in compoun channel, 33 r IAHR Congress, Water Engineering or a sustainable Environment, PP1475-148. Sun, X. an K Shiono, K. (008), Moelling o velocity an bounary shear stress or one-line vegetation along the ege o looplain in compoun channel, ICHE 008, Nagoya, Sept. Sun, X. an Shiono, K. (009), Flow resistance o One-line Emergent Vegetation along the looplain ege o a Compoun Open Channel, AWR, vol. 3, pp. 430-438. Terrier, B, Ronbinson, S. an Shiono, K, (010), Inluence o vegetation to bounary shear stress in open channel or overbank low, Proc. Riverlow010 conerence, Bruansweig, Germany, Vol. 1, pp.85-9. White, B.L. an Nep, H. (008), Vortex-base moel o velocity an shear stress in a partially vegetate shallow channel, WRR, vol. 44, pp.1-15.