TOWARD INTEGRATED MULTI-SCALE SIMULATIONS OF FLOW AND SEDIMENT TRANSPORT IN RIVERS

TOWARD INTEGRATED MULTI-SCALE SIMULATIONS OF FLOW AND SEDIMENT TRANSPORT IN RIVERS Shoi FUKUOKA and Tatsuhiko UCHIDA Fellow of JSCE, PhD., Dr. of Eng., Professor, Research and Development Initiative, Chuo University (--7 Kasuga, Bunkyo-ku, Tokyo -8, Japan) Memer of JSCE, Dr. of Eng., Associate Professor, Research and Development Initiative, Chuo University (ditto) An integrated multi-scale simulation method of flow and sediment transport in rivers is required for river channel designs and maintenance managements. This paper highlights the need of a new depth integrated model without the assumption of the shallow water flow for integrated simulations of D and D phenomena in rivers, indicating the applicale ranges and limitations of previous depth integrated models. The general Bottom Velocity Computation method without the shallow water assumption is proposed and its applicaility for flows with D structures and ed variations is discussed in this paper. The unified calculation method for integrated multi-scale simulations is presented to elucidate flow and sediment transport in laoratory channel and rivers during flood. Finally, we discuss issues to e solved and the future works toward integrated multi-scale simulations of flow and sediment transport in rivers. Key Words: integrated multi-scale simulation, depth integrated model, shallow water assumption, flood oservation, phenomena scale in river. INTRODUCTION Flows and sediment transport are controlled y two kinds of oundaries confining the river width in the lateral direction and the water depth in the vertical directions. River engineers and researchers have applied one-dimensional analysis method for the oective scale which is much larger than the river width, two-dimensional analysis method for the prolem of the phenomena scales etween the river width and the water depth, and three-dimensional analysis method for the target phenomena much smaller than the water depth ),). Fig. shows various phenomena scales of flow and sediment transport in rivers and their calculation methods. Because many important phenomena related to the river management and design are affected y the large scale phenomena compared with the water depth, many calculation methods ased on D models have een developed for practical prolems in river )~). On the other hand, smaller scale phenomena than the water depth, D flow structures, can affect larger scale phenomena through ed variations and flow resistances. Although simulations of complex turulence flows and local scouring have een made possile y recent advanced D turulence models ),), Spatial areas impact scales of the oective phenomena Watershed area River width Water depth Sediment diameter Sediment dynamics near gravel ed Sediment diameter D method Sand wave (depth scale) Local scouring Vertical structure Water depth Cascade up Prandtl's first kind of secondary flow Sand wave (width scale) Horizontal structure River width Flood propagation Longitudinal structure Dominant scales of the oective phenomena Dmethod Watershed area D method Fig. Scales and calculation methods of various phenomena in rivers. applications of the D model are still limited to small scale phenomena such as flows and ed variations in experimental channels, ecause of large computational time, many memories, and the huge computational task. For an integrated multi-scale simulation method of flow and sediment transport in rivers, a new calculation method is necessary to complement the D and D models. This paper indicates the applicale ranges and limitations of previous models, and then highlights the need of a new depth integrated

D model Depth integrated model Fig. Various types of depth integrated model including ottom velocity computation method. Hydrostatic pressure distriution [neglecting vertical momentum equation] D model with the assumption of hydrostatic pressure distriution Full D model Functions of vertical velocity distriution Quasi D model (hydrostatic) Helical flow model due to centrifugal force in curved flow Secondary flow model Neglecting vertical velocity distriutions D model General BVC method Shallow water assumption (SWA) (including hydrostatic pressure distriution) BVC method with SWA model without the assumption of the shallow water flow. The present integrated simulation method is ased on the general Bottom Velocity Computation method without the shallow water assumption. We apply and verify the method to flows and ed variations in laoratory channels, which were difficult phenomena to e calculated y previous depth integrated models. This paper also presents a calculation method comined with oservation data to elucidate flow and sediment transport in rivers during a flood. Finally, we discuss issues and future works.. VARIOUS DEPTH INTEGRATED MODELS AND THEIR APPLICABILITY RANGE An advanced depth integrated model, an improved D model, is one of the effective methods to compute large-scale horizontal flow phenomena with considering D flow effects. Many improved depth integrated models have een developed especially for a helical flow in a curved or meandering channel, as shown in Fig.. Those include fully developed secondary flow model ),7) without considering effects of secondary flow on vertical distriution of stream-wise velocity, and refined secondary flow models with non-equilirium secondary flow 8),9) and mean flow redistriution effects ),). A quasi-d model is a more versatile method to evaluate vertical velocity distriutions y depth integrated equations. Equations for vertical velocity distriutions for quasi-d models have een derived from the D momentum equation y using a weighted residual method )~7). Many quasi-d models employ the assumption of the hydrostatic pressure distriution )~), ecause the non-hydrostatic quasi-d model ased on the weighted residual method ),7) is difficult to e solved. To dissolve the limitations of the previous depth integrated models, we have developed a new quasi-d method, the Bottom Velocity Computation (BVC) method. As shown in Fig., ottom velocity computation methods are distinguished y whether the shallow water flow is assumed 8) or not 9)~). The important equation of the BVC method is the ottom velocity equation (), which is derived y depth-integrating horizontal vorticity. Wh z z s ui usi ui i h ws w () xi xi xi Where, u i : ottom velocity, u si : water surface velocity, : depth averaged (DA) horizontal vorticity, h: water depth, W: DA vertical velocity, z s : water level, z : ed level, w s, w : vertical velocity on water surface and ottom. The ottom shear stress acting on the ed i is evaluated with equivalent roughness k s, assuming the equilirium velocity condition in the ottom layer z ). z aks i ( c ) uiu, Ar ln () c ks Where, h/z =e, a=. On the other hand, the ottom pressure intensity is given y Eq.(), depth-integrating the vertical momentum equation. dp hwu hw t x z x h z x Where, dp: pressure deviation from hydrostatic pressure distriution (p=g(z s z)+dp), dp : dp on ottom, : ed shear stress, i : shear stress tensor due to molecular and turulence motions and vertical velocity distriution. To calculate Eqs. () and (), the governing equations for the following unknown quantities are solved: water depth h (Eq.()), DA horizontal velocity U i (Eq.()), DA turulence energy k (Eq.()), DA horizontal vorticity i, (Eq.(7)) horizontal velocity on water surface u si (Eq.(8)), DA vertical velocity W (Eq.(9)). h U h () t x i U ih U iu h zs gh t x xi hdp dp h z i i x x x k k U t x h x ih R t u t si u s i u x P si i i i hd x vh k Pk k xi i dp g z zzs zs Psi xi () () () (7) (8)

Vertical velocity distriution: u i U i u i u i ( ), y Fig. Governing equations and unknown quantities of BVC method x z u sy ( Ct) x x x W U y Depth-integrated continuity eq.: h h U h t x dp P U x u y u x u sx DA horizontal momentum eq.: U i U ih U iu h z h s i hdp z gh i dp t x xi x xi xi DA turulence energy transport eq.: k k k vh k U Pk t x h xi k xi Bottom velocity eq.: u i Wh zs z ui usi i h ws w xi xi xi DA horizontal vorticity eq.: i ih hdi Ri P i t x Horizontal momentum eq. on water surface: u si u si usi dp zs us g Psi t x z zz x s i Poisson eq. for time variation in DA vertical velocity: W ( ) P Ct x x y Where, dp : depth-averaged dp, k =, v=v m v t, v m : kinematic viscosity coefficient, v t : kinematic eddy viscosity coefficient, P k : the production term of turulence energy, : the dissipation term of turulence energy, R i : the rotation term of vertical vorticity (R σi =u si s u i ), s, : rotation of u si, u i, P i : the production term of horizontal vorticity, D ωi : horizontal vorticity flux due to convection, rotation, dispersion and u DA vertical momentum eq. for ottom pressure intensity: dp dp hw hwu z h z t x x x DA: Depth Averaged, BVC: Bottom Velocity Computation, SWA: Shallow Water Assumption ui usi Uiui usi ui Dmodel 二次元解析法 SWA Quasi D 準三次元解析 model ( 浅水流仮定有 ) 三次元解析法 Dmodel H/L - - - Fig. Limitations of various models for shallowness parameter of oective phenomena D model BVC method with SWA General BVC method DA flow field (Water surface profile) 水深平均流速場 河床変動の解析法 Bottom velocity Non SWA 準三次元解析 Quasi D model field ( 浅水流仮定無 ) (ed topography) (9) z Water depth h p /g...8....8... Case( Case 本解析法 BVC ) Case( Case 実験 Exp. ) Case( Case 本解析法 BVC ) Case( Case 実験 Exp. ) Case(D) D Case(D) D.... x Fig. Longitudinal changes in water depth for rapidly varied flow..... q.... x Fig. The experimental conditions on rapidly varied flow over a structure ) over a structure ) Case Case( 本解析法 BVC ) Case( 実験 Exp. ) Case( 本解析法 BVC ) Case( 実験 Exp. ) x = Case q(m /s)...... x Fig.7 Longitudinal changes in ottom pressure intensity for rapidly varied flow over a strucutre ) x =x =. turulence diffusion, P si : the production term of surface velocity (shear stress under the water surface layer), C= k h/t,k =/, =(Wh) n+ (Wh) n, P =(Wh) P (Wh) n, (Wh) P : the predicted Wh calculated y the continuity equation using (u i ) P, (u i ) P : predicted velocity difference calculated y Eq () with (Wh) n. These equations are otained y assuming vertical velocity distriutions. The BVC method is summarized in Fig.. Refer to the literatures 8)~) for details of the equations and the numerical computation methods for the BVC method. To clarify the applicaility ranges and limitations of various numerical methods in Fig., we have investigated magnitude of each term in depth averaged momentum equation () for depth averaged flow analysis and ottom velocity equation () for ed variation analysis 9). Fig. shows summary of the results 9) and limitations of various models for the shallowness parameter s ( s =h /L <<, h : the representative vertical scale (water depth), L : the representative horizontal scale of oective phenomena).

Tale Experimental hydraulic conditions and the various ed forms ). I q d Bedform type Fr (m /s) Exp. Cal. /78.8* -.7* -. Dune Dune /7.* -.7* -. Duen Dune /7..* -.7* -.88 Anti-dune moving downstream Dune with long wave length /. 9.* -.7* -.7 Plane ed Plane ed /..8* -.9* -. Anti-dune Anti-dune /..8* -.9* -. Anti-dune Anti-dune 7 /..* -.9* -. Anti-dune Anti-dune I: channel slope, q:discharge per unit width, d: sediment particle diameter, Fr : averaged Froude numer (Local Fr varies longitudinally especially for case ~7.). For depth averaged (DA) flow fields, the applicaility range of the D model covers wide ranges of the shallowness parameter. On the other hand, for ottom velocity fields, the applicaility of the D model is limited to the narrow range of the shallowness parameter due to variations in vertical velocity distriutions. This means that a quasi-d model plays a more significant role in ed variation analysis. However, the shallow water assumption is unsuitale for. < s, ecause the magnitude of spatial difference terms in vertical velocity of Eq.() and non-hydrostatic pressure terms of the horizontal momentum equation () and the water surface momentum equation (8) ecomes larger with increasing s. For aove results, a quasi-d model without the shallow water assumption is required for multi-scale simulations of flow and sediment transport in rivers.. Water surface level:9..min. Bed level:9..min. Bed level:8. 9.min. Bed level:7. 8.min. Bed level:. 7.min. Bed level:..min. Bed level:..min. Bed level:..min. -. Fig.8 Calculated dunes for Case method. We can see the arupt drop in the ottom pressure intensity at x= in Fig.7. For Case, the negative pressure intensity was measured there. Although the flow is supercritical, the water depth for x< decreases due to the change in slope at x=. On the other hand, water depth increases due to pressure rising produced y the stream curvature at x=.. These phenomena caused y non-hydrostatic pressure cannot e calculated y the D method, as shown in Fig.. It is demonstrated that the general BVC method can calculate longitudinal profiles of water depth and pressure intensity acting on the ed for rapidly varied flows over a structure, as shown in Fig. and Fig.7.. APPLICATIONS OF THE GENERAL BVC METHOD TO FLOW AND SEDIMENT TRANSPORT IN A NARROW CHANNEL () Rapidly varied flow over a structure A calculation method for flow over a structure is required for many practical prolems with respect to flood and inundation flows. However, it is difficult to evaluate rapidly varied flow y many depth integrated model ecause of the vertical acceleration with the non-hydrostatic pressure distriution. This section discusses the aility of the general BVC method for calculating rapidly varied flows over a structure. Fig. shows hydraulic conditions of the experiments ). Boundary conditions of upstream end for calculations are experimental discharge and water depth, for the state of flow over the structure was a super critical flow. Fig. and Fig.7 show comparisons of longitudinal distriutions of water depth and ottom pressure intensity etween the experiment ) and calculation ) y the general BVC method, respectively. Fig. also shows results y the D () Flow resistance and sediment transport with sand waves The generation of sand waves complicates ehaviors of flood flow, rate of sediment transport and structure of ed topography in rivers. Recently, some researchers have explained the patterns of dunes in a narrow experimental channel y using a vertical D turulence model with a sediment transport model ),). However, it would e unrealistic to apply these models to D flows and ed morphology in rivers due to extremely high computational cost. A few researchers have tried to calculate these phenomena y a depth integrated model ). In this section, the applicaility of the general BVC method for various sand wave calculations is discussed. Tale shows experimental conditions with a variety of channel slopes, discharges and particle size diameters. Those are a part of experimental conditions on various ed forms conducted y Fukuoka et al. ). Boundary conditions of the upstream end for calculations are given y experimental discharge. The shear stresses acting on the ed and side wall are evaluated with equivalent roughness k s =d (d: sediment particle diameter) and Manning s roughness coefficient n=.8, respectively. The time variation in the ed level is calculated y the D continuity

Water surface level:..min. Cal.. -. -. -. Bed level:..min. Water surface level:..min. Bed level:..min. -. -. -. -. -. -. -. -. -. Fig.9 Calculated plane eds for Case Water surface level Bed level Water surface level Bed level Water surface level Bed level Water surface level Bed level Fig. Calculated anti-dunes for Case..min...min...min..9.min. equation for sediment transport of the Exner s form. The momentum equation for sediment motion 8) is used to evaluate non-equilirium sediment transport rate. The details of the calculation method are discussed in the literature ). Tale descries types of calculated ed forms for different hydraulic conditions. Fig.8- show time variations in water surface and ed profiles. Each figure shows snapshots at the constant time interval for the duration indicated in the figure. Although the regime of the anti-dune moving downstream, which was seen in the experimental channel, could not e reproduced, the three different types of ed forms, dune (Fig.8), plane ed (Fig.9) and anti-dune (Fig.) were reproduced y the general BVC method. We can see that development of dunes moving downstream with coalescence (Fig.8) and antidunes with intermittent hydraulic umps (Fig.). Fig. shows comparisons of measured and calculated water depth and sediment discharge for Case ~7. The water depths and sediment discharge rates in the experimental channel with different edform types are reproduced y the general BVC method..8... Cal..E.E....8. Exp. () Water depth Case Case Case Case Case Case Case Case Case Case Case Case Case7 Case7.E.E.E.E Exp. () Sediment discharge rate per unit width (m /s) Fig. Comparisons of water depth and sediment discharge for various hydraulic conditions with sand waves. APPLICATIONS OF THE GENERAL BVC METHOD TO D FLOW AND BED VARIATIONS () D flow structures around a cylinder Many studies have een conducted to clarify the pier scour mechanisms. However, few depth integrated models have een proposed for complex D flows with the horseshoe vortex in front of the structure. We investigate the applicaility of the general BVC method for the local flow around the cylinder. The method is applied to the experimental results 7) for the flow around a cylinder on the fixed rough ed. Tale shows the experimental conditions. The size of computational gird around the cylinder was / of the diameter. Experimental discharge is given at the upstream end and water depth is given at downstream end. The present computational method improves our previous computation 9) in evaluating ottom vorticity. Fig. shows instantaneous computed results of (a) depth-

Tale Experimental conditions y Roulund et al. 7) Cylinder diameter. Depth. Channel width. Fr numer. zz /h. U/U: -. -. -.....8. Measured y Roulund et al. () W (m/s):. -. -. -. -..... U=. (m/s). Calculated y BVC method. -. -. -. - -... x/d Fig. Non dimensional vertical velocity distriutions along the center line of a cylinder. -.. (a) Depth averaged velocity Roughened flood plain Main channel with movale ed material dp /g : -. -. -.... u =. (m/s). Slope: /. -. -. -.. () Bottom velocity and non-hydrostatic ottom pressure Fig. Calculation results y the general BVC method for flow around a cylinder in open channel flow averaged velocity, () ottom velocity and non-hydrostatic pressure distriutions. We can see downward and reverse ottom flows induced with low pressure in front of the cylinder and high pressure in oth sides of the cylinder. Those are typical characteristics of the horse shoe vortex. Fig. compares calculation results with the experimental results for velocity distriutions on the longitudinal crosssection along the center line of the cylinder. The opposite rotation vortex was calculated ehind the cylinder compared to measured result. This seems to e caused y the over production of turulent energy in the separation zone y the conventional turulent model: unsteady turulent flows with the Karman Vortex ehind the cylinder were not developed in this calculation as shown in Fig.. However, the calculation result in front of the cylinder provided a good agreement with the measurement result, which is important to calculate local scouring at the ed. Although the calculation method in the separation zone is still remained as issue, it assures to simulate Fig. A compound meandering channel D flow fields in front of a structure. () Bed variation in a compound-meandering channel In a compound-meandering channel, flow patterns change with increasing relative depth Dr=h p /h m (h p : water depth on flood plains, h m : water depth on a main channel) due to the momentum exchange with vortex motions formed etween high velocity flow in a main channel and low velocity flow in flood plains ),8). For this complex hydrodynamic phenomena, ed variation in a compound-meandering channel could not een explained y the depth integrated models ecause of their assumption of the shallow water flow. In this section, we apply the general BVC method coupled with a non-equilirium sediment transport model 8) to ed-variation analysis in a compound meandering channel. Fig. shows the experimental channel, which has a meandering main channel with movale sand ed and roughened flood plains. The ed variations in the main channel for various relative depths were investigated in the experiment 8). Bed variations in the flows of Dr=. in addition to Dr=.9 are computed and compared with measured results (Fig.). For a simple meandering channel (Dr=.), we can see large scours along the outer ank. However, the increment in the relative depth of a compound meandering channel causes inner ank scours instead of the outer ank scour. The reason of the aove phenomena is that the helical flow structure in a compound meandering channel is different from that in a simple meandering channel due to D

dz: -. -.8 -. -. -... - - - - Dr=.9 dz: -. -.8 -. -. -... - - - - Dr=.( 単断面流れ ) Experiment - - Calculation - - Fig. Bed variations in compound meandering channel for two different types of flow flow interactions etween a main-channel and flood plains. The present calculation results give a etter agreement with experimental results rather than full-d calculation results with the periodic oundary condition 9). This proves that the actual oundary conditions should e given for the ed variation analysis, ecause the periodic oundary condition would give an unrealistic assumption for the analysis. Therefore it would e safe to say that the general BVC method can reproduce ed variations in a compound meandering channel flow with increasing relative depth.. BED VARIATION ANALYSIS USING OBSERVED TEMPORAL WATER LEVEL PROFILES IN RIVER DURING A LARGE FLOOD EVENT It is difficult to know temporal changes in ed elevations during the period of floods ecause of the difficulty of measurement. We have developed the calculation method with oserved temporal changes in water surface profiles ased on the idea that the influences of channel shape and resistance are reflected in temporal changes in water surface profiles ),). The influence of ed variation during flood events is also reflected in temporal changes of water surface profiles in the section where the large degree of ed variation occurs. The aove indicates that the ed variation during a flood event would e Oservation point of water level Fig. Plan-form and contour of ed level of the Ishikari River mouth and oservation points of 98 flood Bed elevation (T.P.m) clarified y using a suitale calculation method. This section demonstrates the ed variation analysis during the August 98 large flood of the Ishikari River. The peak discharge of the flood at the Ishikari River mouth exceeded the design discharge and a large ed scouring occurred in the river mouth. During the flood, temporal data of water levels were measured at many oservation points as shown in Fig.. The cross-sectional ed forms were surveyed efore and after the flood. A lot of researches on the ed variation of the flood have een done. One of the important researches was conducted y Shimizu et al. ) and Inoue et al. ) We developed the BVC method for flood flow with D ed variation analysis using oserved temporal changes in water surface profiles. In this analysis, the concentration of suspended sediment was calculated y D advection-diffusion equations in order to evaluate suspended load affected y the secondary flow in meandering channel ),). Fig. 7 shows temporal changes in oserved and calculated 7

Water level (T.P.m) Water level (T.P.m) 8 7 8 7 Oserved W.L. (Right ank) Oserved W.L. (Left ank) Calculated W.L.(Right ank) Calculated W.L.(Left ank) :-, Aug. :-, Aug. :-, Aug. -k -k -k k k k k k k k 7k 8k 9k k k k k k k 距離標 k (a) Water level profiles during flood rising period Oserved W.L. (Right ank) Oserved W.L. (Left ank) Calculated W.L.(Right ank) Calculated W.L.(Left ank) -k -k -k k k k k k k k 7k 8k 9k k k k k k k 距離標 k () Water level profiles during the flood falling period Fig.7 Temporal changes in water surface profiles :-, Aug. 8:-, Aug. :-7, Aug. :-8, Aug. Bed level (T.P.m) - - - -8 - - - - -8 - Cross-sectional averaged ed level The lowest ed level in the cross-section Oserved efore the flood Oserved after the flood Calculated at the peak stage (:-, Aug.) Calculated after the flood -k -k -k k k k k k k k 7k 8k 9k k k k k k k 距離標 k Fig.8 Longitudinal profiles of ed levels during the 98 flood water surface profiles in flood rising and falling periods. Calculated water surface profiles coincide with oserved water levels affected y ed variations in each time and there are little differences etween calculated and oserved water levels. Fig.8 shows the comparison etween oserved and calculated longitudinal ed forms efore and after the flood. The crosssectional averaged ed elevations after the flood y the calculation are similar and nearly coincide with those of the oserved result. Although the differences in the lowest ed levels at the cross-sections etween measured and calculated results, large ed variations during the flood were explained y the calculation. Fig.9 shows the comparison of ed topographies in the Ishikari River mouth etween calculated and oserved results after the 98 flood. It would e safe to say that calculated results capture the characteristics of oserved ed topography in the meandering channel upstream from the Ishikari River mouth due to the large flood event.. ISSUES AND FUTURE WORKS TOWARD INTEGRATED MULTI-SCALE SIMULATIONS As discussed in this paper, it is important for river channel designs and maintenance managements to elucidate flows and ed variations during floods y the reliale calculation method with use of oserved data. The calculation method should e examined and developed so as to predict the actual phenomena of flows and sediment motions in rivers. The BVC method ased on the depth integrated model can e applied to various flows as indicated in this paper, ecause the method is not (a) Measured () Calculated Fig.9 Comparison of ed topographies in the Ishikari River mouth etween calculated and measured results after the 98 flood restricted y the shallow water assumption. However, the method is difficult to reproduce complex D flow dynamics such as separation zones ehind structures. In relation to this issue, it is needless to say that researches on detail measurements in laoratory channels and developments of turulence models would make an important contriution. On the other hand, the asic researches in laoratories are not always enough to clarify the large scale phenomena in rivers, ecause turulence and vortex motions depend on the flow scale and vary with complex geometries. As discussed in the introduction, practical prolems related to flows and sediment motions in rivers include various scale phenomena which affect each other. For example, Fig. and Fig. show comparisons of horizontal and helical flow structures along a vertical wall in the channel end etween the real scale field experiment and calculation y the general BVC method ). For the section E, computed secondary flow intensity and streamwise velocity in the vicinity of the wall are relatively weak compared with those of the measurement. Main reasons are ecause the difference etween the measurement and calculation in the approaching flow at the section C should e considered. The secondary flow in the channel end is produced y the rotation and deformation of the lateral voriticity in the approaching flow. The approaching flow in the field experiment is affected y various scale factors such as resistance due to sediment particles with diverse sizes and shapes, complex ed topography, channel plan shape and hydraulic conditions at the upstream end. The aove discussion indicates that a calculation method integrating these different effects is necessary for actual flood phenomena. Shimada et al. ),7) have carried out full-scale experiments on 8

-....8.. Large stones Black: ottom velocity Red: surface velocity (m/s) Revetment - Revetment 8 8 G F E (a) Measured D C B 9 A 9 G F E () Calculated D C B 9 A 9 Fig. Comparisons of horizontal flow structures etween the real scale experiment and the general BVC method ).8.. (m/s) 平均水位 Meassured y electromagnetic 電磁流速計 velocity meter 護岸.8.. (m/s) 護岸..8. Section C Measured y ADCP..8. Section C...8....8.. (m/s) 平均水位 Section E Measured y ADCP Meassured y electromagnetic 電磁流速計 velocity meter 護岸 - -...9.8.7.......9.8 (a) Measured (m/s) () Calculated Fig. Comparisons of D flow structures etween the real scale experiment and the general BVC method ).8....8.. (m/s) Section E 護岸 - - levee reaches. Nihei and Kimizu 8) have developed a new monitoring system for the estimation of river discharge comining measured data and calculations. These researches are also expected for the clarification of actual flood phenomena. We should put forth a steady effort in measurements and analysis of the flood flows and ed variations in rivers together with asic hydraulic researches in the laoratory. REFERENCES ) Fukuoka, S.: Flood hydraulics and river channel design, Morikita Pulishing Company,. ) Wu, W.: Computational river dynamics, Taylor & Francis, London, 8. ) Shimizu, Y., Itakura, T. and Yamaguchi, H.: Numerical simulation of ed topography of river channels using two-dimensional model, Proceedings of the Japanese Conference on Hydraulics, Vol., pp.89-9, 987. ) Nagata, N., Hosoda, T. and Muramoto, Y.: Characteristics of river channel process with ank erosion and development of their numerical models, Journal of Hydraulic, Coastal and Environmental Engineering, JSCE, No./II-7, pp.-, 999. ) Fukuoka, S., Watanae, A., Hara, T. and Akiyama, M.: Highly accurate estimation of hydrograph of flood discharge and water storage in rivers y using an unsteady twodimensional flow analysis ased on temporal change in oserved water surface profiles, Journal of Hydraulic, Coastal and Environmental Engineering, JSCE, 7/-7, -,. ) Engelund, F.: Flow and ed topography in channel ends, Journal of hydraulics division, Proc. of ASCE, Vol., HY, pp.-8, 97. 7) Nishimoto, N., Shimizu, Y. and Aoki, K.: Numerical simulation of ed variation considering the curvature of stream line in a meandering channel. Proceedings of the Japan Society of Civil Engineers, Vol./II-,pp.-, 99. 8) Ikeda, S. and Nishimura, T.: Three-dimensional flow and ed topography in sand-silt meandering rivers, Proceedings of the 9

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Eng., Vol.7, No., pp.-,. )Onda, S. and Hosoda, T.: Numerical simulation on development process of dunes and flow resistance, Annual Journal of Hydraulic Engineering, JSCE, 8, 97-978,. )Fukuoka, S., Okutsu, K. and Yamasaka, M.: Dynamic and kinematic features of sand waves in upper regime, Proceedings of JSCE, No., 98. 7)Roulund, A., Sumer, B. M., Fredsøe, J. and Michelsen, J.: Numerical and experimental investigation of flow and scour around a circular pile, Journal of Fluid Mechanics, Vol., pp.-,. 8)Fukuoka, S., Omata, A., Kamura, D., Hirao, S. and Okada, S.: Hydraulic characteristics of the flow and ed topography in a compound meandering river, Journal of Hydraulic, Coastal and Environmental Engineering, JSCE, No./II- 7, pp.-, 999. 9)Watanae, A. and Fukuoka, S.: Three dimensional analysis on flows and ed topography in a compound meandering channel, Annual Journal of Hydraulic Engineering, JSCE,, -7, 999. )Fukuoka, S.: What is the fundamentals of river design utilization of visile techniques of sediment laden-flood flows, Advances in River Engineering, JSCE, Vol.7, pp.8-88,. )Shimizu, Y., Itakura, T., Kishi, T. and Kuroki, M.: Bed variations during the 98 August flood in the lower Ishikari River, Annual Journal of Hydraulic Engineering, JSCE, Vol., 87-9, 98. )Inoue, T., Hamaki, M., Arai, N., Nakata, M., Takahashi, T., Hayashida, K., and Watanae, Y.: Quasi-three-dimensional calculation of rivered deformation during 98-year flood in the Ishikari River mouth, Advances in River Engineering, Vol., -,. )Okamura, S., Okae, K. and Fukuoka, S.: Numerical analysis of quasi-three-dimensional flow and ed variation ased on temporal changes in water surface profile during 98 flood of the Ishikari River mouth, Advances in River Engineering, Vol., pp.-,. )Okamura, S., Okae, K. and Fukuoka, S.: Bed variation analysis using the sediment transport formula considering the effect on river width and cross-sectional form in the case of 98 flood of the Ishikari River mouth-, Advances in River Engineering, Vol.7, pp.9-,. )Koshiishi, M., Uchida, T. and Fukuoka, S.: A new method for measuring and calculating three-dimensional flows and ed forms around river anks, Journal of JSCE, Ser.B (Hydraulic Engineering), Vol. 9, No.,, accepted. )Shimada, T., Watanae, Y., Yokoyama, H., and Tsui, T.: Cross-levee reach experiment y overflow at the Chiyoda Experimental Channel, Annual Journal of Hydraulic Engineering, JSCE, Vol., pp.87-87, 9. 7)Shimada, T., Hirai, Y. and Tsui, T.: Levee reach experiment y overflow at the Chiyoda Experimental Channel, Annual Journal of Hydraulic Engineering, JSCE, Vol., pp.8-8,. 8)Nihei, Y. and Kimizu, A.: A new monitoring system for river discharge with an H-ADCP measurement and riverflow simulation, Dooku Gakkai Ronunshuu B, Vol., No., pp.9-,7. (Received Decemer, )