Three2dimensional Numerical Modell Ing of Submerged Dike Al Ignment in Curved Estuarine Channel 3

http://www.paper.edu.cn 106

J our nal of Hydrodyna mics ,Se r. B ,2005 ,17 (5) :601 - 606 China Ocea n Press , Beijing - Printed in China

THREE2DIMENSIONAL NUMERICAL MODELL ING OF SUBMERGED DIKE AL IGNMENT IN CURVED ESTUARINE CHANNEL 3

Z H EN G J in2hai , L IU Ying2qi , YAN Yi2xin , Z HU Yu2lia ng Resea rc h I nstitute of Coastal a nd Ocea n Enginee ring , Hohai U niversity , Na njing 210098 , China , E2mail :jhz he ng @hhu. edu. cn

( Received J une 15 , 2004)

ABSTRACT : Submerged dikes were frequently built in or a nalytical studies we re conducte d by Ye n curved estuarine channels to improve navigational conditions. (1965) , Krish napp a n a nd L au (1977) , De Ve rie nd A three2dimensional numerical model of tidal motions was de2 (1981) , O dgaa rd ( 1986 ) , J oha nness n a nd Pa r ke r veloped to simulate flows through the submerged dike align2 (1989) , Cha ng (1992) , Wa ng a nd Che ng (2002) . ment in curved estuarine reach of complex bathymetry on the Va rious t hree2dime nsional numerical models have basis of satisfactory calibrations. Through the analysis of the morphological characteristics of the curved channel of the bee n used t o simulate t he curve d c ha nnel flows , Huangpu River mouth in the Yangtze River Delta , a sub2 nota bly by L eschzine r a nd Rodi (1979) , De mure n merged dike alignment project was examined. The effect of a nd Rodi (1986) , Shimizu et al. ( 1990) , De mure n the navigation channel improvement project and its influence (1993) , Meselhe et al. (1995) , Olse n a nd St okest h on the flow regimes , the navigational conditions , the flood (1995) , Ye a nd McCorquodale (1998) , Sinha et al. control and the operating conditions of harbours within the ad2 (1998) , Meselhe a nd Sotirop oulos (2000) , Su et al. jacent water area were evaluated , and the technical feasibility ( 2003 ) . Rece ntly , a series of nume rical simula2 of the navigation channel improvement scheme was demon2 tions were completed using t he CC H E3D model strated. a nd a p rop osed e nginee ring design guida nce of sub2 KEY WORDS : submerged dike alignment , three2dimensional merged dikes was ge ne rated to f ully unde rsta nd t he numerical model , curved estuarine channel , morphological a2 eff ects of dike geomet ry a nd alignme nt on t he f low nalysis p atter ns a nd navigation imp rove me nt in a curved cha nnel ( Xu et al. 2002 , 2003) . 1. INTRODUCTION The objective of t he p rese nt wor k is t o develop Submerge d dikes a re f reque ntly built in curved a nd validate a t hree2dime nsional model f or simula2 river a nd estua rine c ha nnels t o imp rove naviga2 ting flows t hrough a curved estua rine cha nnel of tional conditions a nd/ or t o p rotect ba nks . Ma ny complex bat hymet ry , a nd t o evaluate t he eff ect of eff orts have bee n ma de t o study f low c ha racteris2 t he submerged dike alignme nt sche me on t he navi2 tics a round a dike in a st raight cha nnel exp erime n2 gation c ha nnel imp rove me nt a nd its inf lue nce on tally a nd numerically ( Raja rat na m et al. 1983 ; L iu t he flow regime , t he navigational condition a nd et al. 1994 ; Mayerle et al. 1995 ; Tominaga et al. t he op erating conditions of ha rbours wit hin t he a d2 1997 ; Pe ng et al. 1997 ) . Howeve r , f ew studies jace nt wate r a rea . have investigated ove rall f low p atte rns a round sub2 me rged dikes in curved estua rine c ha nnels . Al2 2. NUMERICAL MODEL t hough ma ny resea rches have bee n ca rried out on For a t hree2dime nsional turbule nt f low of a n curved cha nnel f lows , t he t hree2dime nsional nature incomp ressible Newt onia n f luid wit h t he B ouss2 of t he curve d c ha nnel flow p he nome na is still diff i2 inesq e ddy viscosity app roximation , t he Reynolds2 cult to a nalyse mat he matically. Exp erime ntal a nd/ ave rage d Navie r2St okes equations in Ca rtesia n co2

3 Project supported by the National Natural Science Foundation of China ( Grant No : 50339010) and the Frontier Science Fund of Hohai University ( Grant No : 2003408443) . Biography :ZH EN G Jin2hai (19722) , Male , Ph. D. , Associate Professor 转载中国科技论文在线 http://www.paper.edu.cn 206

ordinates ca n be used. Since t he vertical accelera2 of eac h mesh , w hile t he f ree surf ace elevation is tion a re usually ge ntal in estua ries , it is reasona ble calculated in t he x2y f ace of eac h vertical column t o assume t he p ressure dist ribution is hydrostaic , of water . The convective ter m in t he mome ntum e2 t he n t he z 2direction mome ntum equation reduces quations is discretizated by using t he Euleria n2L a2 t o t he hydrostatic law . I n t he vertical direction , a gra ngia n met hod ( Zhu et al. 2000) . σ2t ra nsf or mation is int roduced t o map t he irregula r The kine matic bounda ry conditions at t he f ree bott om t op ograp hy a nd t he surf ace water level into surf ace a nd sea bed a re t hat t he vertical comp one nt a f lat domain w here t he f ree surf ace bounda ry con2 velocity equals zero. The dyna mic bounda ry condi2 ditions could be p recisely applied a nd t he diff icul2 tion at t he f ree surf ace induce d by t he surf ace wind ties f or shap e dep t h va riations a re ove rca me . st ress vect or is ta ke n as ze ro , a nd at t he sea bed in2 The gover ning equations ca n be writte n as duced by t he bott om f rictional st ress vect or is com2 p ute d by t he e mp rical f or mula ( Zhe ng et al. 5η 5 ( Du) 5 ( Dy ) 5w 1999) . + + + = 0 (1) 5t 5 x 5 y 5σ The lateral bounda ry conditions a re set t o be ze ro of t he f low nor mal to t he s horeline . The giv2 5 u 5 u w 5 u 5η e n tidal levels obtaine d f rom t he mat he matical 5 u + v + = - g 5t + u 5 y D 5σ 5 x + f v + 5 x model of t he Ya ngtze Estua ry a re applied along t he op e n bounda ries . 52 u 1 5 5 u 2 + A v ( ) The t hree2dime nsional nume rical model solves 5 u 2 + 2 σ σ 2 A h 5 y D 5 5 5 x2 Eqs . (1)2(4) by applying t he mode splitting tec h2 nique . The comp utational st rategy is as f ollows. 5v 5v 5v w 5v 5η + u + v + = - g - f u + Step 1 : The exter nal mode , a two2dime nsional 5t 5 x 5 y D 5σ 5 y dep t h2integrated model , is e mployed t o obtain t he

2 2 f ree surf ace elevation a nd t he dep t h2integrate d ve2 5 v 5 v 1 5 5v A h + + A v (3) 5 x2 5 y2 D2 5σ 5σ locities . O n t he f irst sweep in t he x 2direction , dep t h ave rage d velocity U n+1 a nd ηn+1/ 2 a re f ound , 5 p a nd on next sweep in t he y 2direction , dep t h aver2 = - ρgD (4) n+1 n+1 5σ aged velocity V a nd η a re obtained. Step 2 : The inter nal mode , a t hree2dime nsional model , is w hereηis t he water surf ace elevation , u , v , a nd w used t o obtain t he t hree2dime nsional velocities a re t he velocity comp one nts in t he horizontal x2, un+1 , vn+1 a nd W n+1 , wit h know n U n+1 ,V n+1 a ndηn+1 . y2 a ndσ2direction , resp ectively ,σ∈[ - 1 , 0 ] , in2 Step 3 : The vertical comp one nt of velocity in p hys2 creasing up wa rd a ndσ= 0 locating at t he water sur2 ical domain , w n+1 , is f ound by insertingηn+1 , un+1 , n+1 n+1 f ace , D = h +ηis t he t otal water dep t h , A h a nd A v v a nd W into t he t ra nsf ormed equation of t he a re t he horizontal a nd vertical eddy viscosity coef2 vertical velocity. f icie nts of turbule nt f low , resp ectively , t is time , p A navigation c ha nnel imp rove me nt p roject is is t he hydrostatic p ressure , f is t he Coriolis p a ra m2 ca rried out very close to t he Wusongkou t raining ete r , g is t he gravitational acceleration , ρis t he wall , t he ref ore t he tidal data at t he Wusong Tidal de nsity of water . Station could not be e mployed t o p rovide t he A f inite2diff ere nce nume rical sc he me was de2 bounda ry conditions. I n orde r t o obtain t he sound velop e d by mea ns of t he imp rove d D ouble2Sweep2 op e n bounda ry conditions , t he mat he matical mod2 Implicit met hod ( Ya n et al. 1999) t o imp rove t he els of t he East China Sea a nd t he Ya ngtze Estua ry comp utational sta bility a nd accuracy. The comp u2 a re also esta blished ( Zhe ng et al. 2001) . The p res2 tation domain is staggere d bot h in time a nd sp ace : e nt t hree2dime nsional hydrodyna mic model covers in time , t he velocity comp one nt in t he x 2direction t he domain f rom t he Hua ngp u Pa rk t o t he mout h is calculated at half2time step dista nce , w hile f ree of t he Ya ngtze Rive r , in w hich a 4000m st retch surf ace elevation a nd t he velocity comp one nt in t he upst rea m of Wusongkou is t he domain of most in2 y 2direction a re comp uted at f ull2time step dis2 terest . ta nce , in sp ace , velocity comp one nts a re comp uted The grid size nea r t he p roject was deter mined resp ectively in t he ce nt re of t he y2σ, x2σ, x2y f ace to be 12. 5m , w hile t he la rger grid size of 75. 0m 中国科技论文在线 http://www.paper.edu.cn 306

was used f a r away f rom it . The time step was set to be 5s f or t his comp utation. For t he calibration of p rese nt model , t he top2 ograp hic data of Sep t . 1999 a nd t he tidal level data a nd t he synchronous hydromet ric measure me nts f rom Sep t . 11 t o 18 in t he flood season were e m2 ployed , w hich we re p rovided by t he Sha nghai Sur2 vey a nd Resea rc h I nstitute of Navigation. The n t he Ma nning roughness was chose n as 0. 012. For t he validation of p rese nt model , t he t op o2 grap hic data of J a n. 2000 a nd t he tidal level data a nd t he synchronous hydromet ric measure me nts f rom J a n. 15 t o 23 in t he dry season we re e m2 ployed. From t he comp a risons of t he field survey data a nd comp utations , as s how n in Fig. 1 to Fig. 3 , a satisf actory agree me nt is obtained. Figure 4 s hows

ebb maximum tidal flow p atte rn nea r t he p roject . Fig. 2 Comparison of velocity Results de monst rate d t hat t he p rese nt model is ef2 f icie nt a nd cap a ble of describing t he tidal motion in t he curved reach of t he Hua ngp u Rive r Mout h.

Fig. 3 Comparison of discharge we re const ructed along t he ba nks of t he Hua ngp u River , a t ributa ry e mp tying int o t he Ya ngtze Riv2 Fig. 1 Comparison of water level er , as show n in Fig. 5. A mong t hese bert hs , t he containe r te rminals at Zha nghua ba ng a nd J un2 3. SUBMERGED DIKE AL IGNMENT SCHEME gonglu a re t he most imp orta nt ones. The ref ore , AND ITS EFFECTS navigational conditions in t he Hua ngp u Rive r f rom The Sha nghai Port , ha ndling a bout 4. 2 × 108 t Wusongkou t o Zha nghua ba ng sections a re consid2 of ca rgo a nd ove r 1 × 107 TEU t o a nd f rom more ered t o be t he lif eline of t he Sha nghai Port ( Xu t ha n 400 p orts in 160 count ries a nd regions in a nd Yin 2003) . 2003 , is t he la rgest p ort of China . Wit hin t he Howeve r , ma ny c ha nges in t he morp hological Sha nghai Port , t he re is a wate r a rea of over 3619. 2 2 cha racte ristics have ta ke n place in t he p ast dec2 6km , a nd a la nd a rea of over 500km . There a re a des . For exa mple , t he water dep t h in f ront of t he 322 p ublic bert hs , in w hich 107 ones a re f or vessels Wusongkou t raining wall is becoming la rge r a nd of ove r 10000 D W T. Most of t he quays of t his p ort 中国科技论文在线 http://www.paper.edu.cn 406

la rge r , w hic h is ba dly e nda ngering t he saf ety of t he morp hological cha racteristics could be summed t he t raining wall , t he curvature of t he reach is be2 up as f ollows. D ue t o t he const ructions of quays coming smaller a nd s maller , w hich heavily inf lu2 a nd t he a dva nces of bulkhea ds , t he accretion of e nces t he navigation conditions , t he rive rbed in t he shoaly la nd in f ront of bulkhea ds develop e d. f ront of t he Zha nghua ba ng Ter minal is becoming Theref ore , t he river widt h a bove t he dep t h con2 deep e r a nd deep er , w hic h would result in t he f ail2 t our of 0m beca me s maller , w hich resulted in t he ure of t he quays . conce nt ration of t he f low wit hin t he main cha nnel. Toget her wit h t he actions of circulation curre nts of t he be nd reach a nd t he f lood a nd e bb tides in t he estua ry , t he rive rbed nea r t he Puxi dist rict was scoure d a nd t he deep quir ks f or med , w hile t he ri2 verbed nea r t he Pudong dist rict was silted up . Mo2 reover , t he flow in a nd out of t he Yuncaoba ng River is also t he imp orta nt f act or w hich st re ngt h2 e ns t he scour of deep quir ks . From Fig. 5 , it is see n t hat t he Yuncaoba ng River is located at t he up2 st rea m of deep quirks a nd t he dow nwa rd of t he concave ba nk in t he be nd reach. As a result , t he flood tide int o t he Yuncaoba ng Rive r going along t he concave ba nk would st re ngt he n t he scour , in

Fig. 4 Tidal flow pattern of interested domain (ebb peak) t he mea nw hile , t he e bb tide f rom Yuncaoba ng River conflue nces wit h t he main curre nt f rom t he upst rea m of t he Hua ngp u River Mout h , w hic h also Figure 5 shows t he diff ere nt unde rwate r t op o2 st re ngt he ns t he scour of deep quir ks nea r t he Puxi grap hic f eatures in t he scale of 1 :2000 of t he estu2 dist rict . a rine cha nnel of t he Hua ngp u River f rom Wuso2 ngkou t o Zha nghua ba ng in 1966 , 1986 , a nd 1999. The navigation cha nnel imp rove me nt p roject From t he Yuncaoba ng Rive r Mout h to t he J un2 consists of 4 sp ur dikes a nd 5 subme rged jetties , as gonglu Container Ter minal , t he re were little cha n2 show n in Fig. 5. The sp ur dikes will be const ructed ges of t he dep t h cont ours of 0m , 5m a nd 10m nea r in f ront of t he Wusongkou t raining wall. The lon2 t he side of t he Pudong dist rict . That is t o say , t his gitudinal sp acing betwee n two dikes is 60m. The ( reac h was in sta ble condition. However , t he river2 crest elevation of dike is + 1. 0m Wusong Sea L ev2 be d in t his reac h nea r t he side of t he Puxi dist rict el) . The widt h on t he t op of dike is 4. 0m a nd t he was scoured a nd beca me deep e r , a nd t he deep le ngt h is 25m. The slop es a re 1 ∶2 a nd 1 ∶5 f or t he quir ks exte nded towa rd bot h t he upst rea m a nd dike body a nd dike hea d resp ectively. All t he crest dow nst rea m . It ca n be f ound f rom Fig. 5 t hat t he elevations of t he subme rged jetties a re - 17. 0m dep t h cont our of 10m st retched more t ha n 1200m ( Wusong Sea L evel) , t heir widt h on t he t op of jet2 t owa rd t he upst rea m f rom 1966 t o 1999 , in t he ties a re 4. 0m a nd t he slop es of jetty body a re 1 ∶3. mea nw hile t he dep t h cont our of 15m st retc hed In f ront of t he Wusong Passe nger D ock , t here is a more t ha n 600m t owa rd t he upst rea m in t he sa me jetty of 50m long , w hic h would be reduce d by 4 % stage . From t he Yuncaoba ng Rive r Mout h to t he of t he cross2section a rea below t he dep t h cont our Wusongkou , t he dep t h cont ours of 0m a nd 5m nea r of 0m. Nea r t he Yunca oba ng River Mout h , t here t he side of t he Pudong dist rict moved a bout 30m a re two jetties of 80m sp acing betwee n t he m. Each t owa rd t he Puxi dist rict , w hereas t he dep t h con2 is 90m long a nd would also re duce 4 % of t he cross2 t our of 10m in f ront of t he Passe nger D oc k moved section a rea below t he dep t h cont our of 0m . In a bout 90m t owa rd t he Pudong dist rict f rom 1966 to f ront of t he Zha nghua ba ng Container Ter minal , 1999. Nea r t he Puxi dist rict , t he re we re two deep t here a re two jetties of 110m a nd 120m long a nd quir ks of more t ha n 15m in 1966 , w hile in 1999 t he re ducing 9. 1 % a nd 5. 5 % of t he cross2section a rea deep quir k of more t ha n 20m exited a nd t he dep t h below t he dep t h contour of 0m , resp ectively. The cont our of 15m linked t oget her . sp acing betwee n t hese two jetties is 200m. The reasons w hich could reasona bly explain 中国科技论文在线 http://www.paper.edu.cn 506

Fig. 5 Submerged dike alignment scheme in the Huangpu River Mouth

Af te r t he completion of t he navigation cha n2 would have little influe nce on t he f low regimes , nel imp rove me nt p roject , t he f low velocities wit hin t he navigational conditions , t he flood cont rol a nd t he subme rged jetties a nd t he sp ur dikes would be2 t he op erating conditions of ha rbours . come s maller , w hich would be be nef icial t o t he sedime nt dep osition in deep quir ks a nd t he saf ety of t he quays in t he Puxi dist rict a nd t he Wusongkou REFERENCES t raining wall. Af ter t he completion of t he p roject , t he maxi2 [1 ] CHAN G H. H. Fluvial processes in river engineering mum cha nge of t he tidal level is 10mm , w hich il2 [ M ]. Malabar , USA : Krieger Publishing CO. , 1992. [2 ] DEMUREN A. O. A numerical model for flow in me2 lust rates t hat t he p roject will have little inf lue nce andering channels with natural bed topography [ J ]. on t he f lood cont rol a nd t he op e rating conditions Water Resource Research , 1993 ,29 (4) :126921277. of ha rbours. [3 ] DEMUREN A. O. and RODI W. Calculation of flow Af ter t he completion of t he p roject , t he and pollutant dispersion in meandering channels [ J ]. cha nge of t he flow direction is less t ha n 15°. Com2 Journal of Fluid Mechanics , 1986 ,172 :65292. p a rison of t he pla ne velocity field bef ore a nd af ter [4 ] DE V ERIEND H. J . Velocity redistribution in curved t he p roject s hows t hat no obvious c ha nge occurs , rectangle channels [ J ]. Journal of Fluid Mechanics , w hich de monst rates t hat t he p roject will have little 1981 ,107 :4232439. [5 ] J O HANN ESSON H. and PAR KER G. Velocity redis2 inf lue nce on t he f low regimes a nd t he navigational tribution in meandering rivers [J ]. Journal of Hydraulic conditions. Engineering , 1989 ,115 (8) :101921039. [6 ] KRISHNAPPAN B. G. and LAU Y. L . Transverse 4. CONCL USING REMARKS mixing in meandering channels with vary bottom topog2 B ot h calibration a nd validation de monst rated raphy[J ]. Journal of Hydraulic Research , 1977 ,15 (4) : t hat t he p rese nt t hree2dime nsional f inite2diff ere nce 3512369. hydrodyna mic model was efficie nt t o simulate tidal [7 ] L ESCHZIN ER A. and RODI W. Calculation of strong2 f lows t hrough subme rged dike alignme nt in t he ly curved open channel flow [J ]. Journal of the Hydrau2 lics Division , ASCE, 1979 ,105 (10) :129721314. curved estua rine c ha nnel in t he Hua ngp u River [8 ] L IU Jian2hua , TOMINA GA A. and NA GAO M. Nu2 wit h complex bat hymet ry. The p rese nt numerical merical simulation of the flow around the spur dikes model was applied t o study t he submerge d dike a 2 with certain configuration and angles with banks [J ]. lignme nt sche me in t he Hua ngp u River Estua ry. Journal of Hydro2science and Hydraulic Engineering , Comp utations illust rated t hat t he navigation cha n2 1994 , 12 (2) : 852100. nel imp rove me nt p roject would be efficie nt a nd it [9 ] MA YERL E R. , TORO F. M. and WAN G S. S. Y. 中国科技论文在线 http://www.paper.edu.cn 606

Verification of a three2dimensional numerical model [20 ] WAN G De2guan and CH EN G Li. Numerical modelling simulation of the flow in the vicinity of spur dikes[J ]. of compound channel flows [J ]. Journal of Hydrody2 Journal of Hydraulic Research , 1995 ,33 (2) :2432256. namics , Ser. B, 2002 ,14 (4) : 1062109. [10 ] M ESEL H E E. A. and SO TIROPOULOS F. Three2di2 [21 ] XU Yi2chun and WAN G SAM S. Y. Numerical simula2 mensional numerical model for open2channels with free2 tion of the three2dimensional flow structure around sub2 surface variations [J ]. Journal of Hydraulic Research , merged dikes[ A ]. Proceedings of 5th International Con2 2000 ,38 (2) : 1152121. ference on Hydro2science and Engineering[ C]. Warsaw , [11 ] MESL H E E. A. , SO TIROPOULOS F. and PA TEL Poland , 2002 , 2762281. V. C. Three2dimensional numerical model for open2 [22 ] XU Yi2chun , WAN G SAM S. Y. and J IA Ya2fei. Nu2 channels[ A ]. Proceedings of the International Confer2 merical analysis of effect of submerged dike alignment ence of Hydropower [ C ]. Charlottesville , USA , 1995 , on navigational improvement in a curved channel [ A ]. 210022120. Proceedings of XXX IAHR Congress[ C ]. Thessaloniki , [12 ] OD GAARD A. J . Meander flow model I : Development Greece , 2003 , 5432549. [J ]. Journal of Hydraulic Engineering , 1986 , 112 (12) : [23 ] XU Zu2xin and YIN Hai2long. Development of two2di2 111721136. mensional hydrodynamic and water quality model for [13 ] OL SEN N. R. B. and STO KEST H S. Three2dimen2 Huangpu River[J ]. Journal of Hydrodynamics , Ser. B, sional numerical modelling of water flow in a river with 2003 , 15 (2) : 1211. large bed roughness[J ]. Journal of Hydraulic Research , [24 ] YAN Yi2xin , ZHU Yu2liang and XU E Hong2chao. Hy2 1995 , 33 (5) : 5712581. drodynamics for the formation and development of ra2 [14 ] PEN GJing , KAWA HARA J . and TAMAI N. Numeri2 dial sandbanks[J ]. Science in China , Ser. D , 1999 , 42 cal analysis of three2dimensional turbulent flows around (1) : 13221. submerged groins [ A ]. Proceedings of XXVII IAHR [25 ] YE Jian and MCCORQUODAL E J . A. Simulation of Congress[ C]. San Francisco , USA , 1997 ,5232530. curved open channel flows by 3D hydrodynamic model [15 ] RAJ ARA TNAM N. and NWACHU KWU B. A. Flow [J ]. Journal of Hydraulic Engineering , 1998 , 124 (1) : near groin2like structures[J ]. Journal of Hydraulic En2 6872698. gineering , 1983 ,109 (3) : 4632480. [ 26 ] YEN B. C. Characteristics of subcritical flow in a mean2 [16 ] SHIMIZU Y. , YAMA GUCHI Y. and ITA KURA T. dering channel[ D ]. Ph. D. Thesis , Iowa City , USA : Three2dimensional computation of flow and bed deform2 University of Iowa , 1965. ation[J ]. Journal of Hydraulic Engineering , 1990 , 116 [27 ] ZH EN G Jin2hai , YAN Kai and YAN Yi2xin. Distribu2 (9) : 109021107. tion of wave2induced excess momentum fluxes over [17 ] SIN HA S. K. , SO TIROPOULOS F. and OD GAARD depth and application to three dimensional numerical A. J . Three2dimensional numerical model for flow modelling of wave2current interactions [J ]. Journal of through natural rivers [J ]. Journal of Hydraulic Engi2 Hydrodynamics , Ser. B, 1999 ,11 (4) : 67274. neering , 1998 , 124 (1) :13224. [ 28 ] ZH EN G Jin2hai , YAN Yi2xin and ZHU Yu2liang. [18 ] SU Xiao2hui , L I C. W. and CH EN Bi2hong. Three2di2 Three2dimensional computation of tidal flow around mensional large eddy simulation of free surface turbu2 submerged cross2river tunnel in the curved reach of lent flow in open channel within submerged vegetation Huangpu river [ A ]. Proceedings of XXIX IAHR Con2 domain[J ]. Journal of Hydrodynamics , Ser. B, 2003 , gress[ C]. Beijing , China , 2001 , 6302638. 15 (3) :35243. [ 29 ] ZHU Yu2liang , ZH EN GJin2hai , MAO Li2hua and YAN [19 ] TOMINA GA A. , NA GAO M. and N EZU I. Flow Yi2xin. Three2dimensional nonlinear numerical model structures and mixing processes around porous and sub2 with inclined pressure for saltwater intrusion at the merged spur dikes [ A ]. Proceedings of XXVII IAHR Yangtze River Estuary[J ]. Journal of Hydrodynamics , Congress[ C]. San Francisco , USA , 1997 ,5412547. Ser. B, 2000 , 12 (1) : 57266.