BEHAVIOR OF ALTERNATE BARS UNDER UNSTEADY FLOW CONDITIONS

Transcription

1 BEAIOR O ALERNAE BAR NER NEAY LOW ONIION Y. Wnbe M. ubno G. Zolezz nd. oh ABRA: In he prevou reerh on he ne mplude bl nd growh o lerne br umed h low hnge n me due o he uned low do no e he generon o lerne br. drul epermen nd bl nl o he ormon o lerne br under uned low ondon re ondued n he preen ud. he wvelengh nd wve hegh o lerne br re gnnl deren under uned nd ed low ondon nd n he rng nd llng ge o he wer level due o he lood wve. nedne lo pl o ul ormve ondon or lerne br epell or grvel bed rver. he reul o bl nl well ompre wh epermenl ndng. Reul ugge h ne mplude ee o he lood-wve on lerne br ormon re no neglgble when nvegng her behvour under uned low ondon. INROION Alerne br n rverbed gve re o low menderng nd lol ourng nd hereore he re loel reled o he ourrene o der. everl ude hve lred he ormon nd hrer o lerne br under ed low ondon. hee mpll ume h low hnge n me due o he pl unedne o low n nurl rver do no lrgel e he developmen o lerne br would our he wo proee would our deren me le. On he onrr ew work hve been mde o nvege her behvor under uned low ondon. nderndng br behvor under uned low ondon nowd requred no onl n he perpeve o der prevenon. Indeed noe h n reen er blzon o bed onguron reul o lood onrol b reervor h led o degrdon o everl rver eoem whoe mnenne requre durbne o he bed onguron. here hve been everl emp b he relee o wer rom reervor o mule nurl loodng. uh rl lood neee eeve eploon o wer reoure well ure lulon o lood wveorm nd o bed durbne. he heorel nd epermenl work o ubno[] nd Mw e l.[] poned ou h he ee o uned low on he ormon o lerne br ould no be gnored when he wo proe he me me le oen our n nure. he wekl nonlner heor preened n ubno[] nlze he ee o mll mplude lood wve on he whole proe o br ormon dung how he Gnzburg-Lndu equon governng he me evoluon o br mplude (ee []) moded wh repe o he ed e. he umpon o he ler work re heren revered: whle removng he reron o lner o he lood wve we ou our enon Agen o vl Engneerng Reerh Inue okkdo Regonl evelopmen Bureu Jpn eprmen o vl nd Envronmenl Engneerng nver o ren Il oundon o okkdo Rver er Prevenon Reerh ener Jpn

2 B η ( ) σ gure oordne em o low nd bed orm gure oordne em o o lood wve o he npen ondon or br ormon umng h br mplude keep relvel mll. BAI EQAION We ormule he problem o br ormon under uned low ondon emplong he dmenonle deph-verged. enn equon nd he onnu equon or he nompreble low nd or he bed lod n rgh hnnel: σ () σ () σ () ( ) Q Q b Q b () In equon ()-() he ll ollowng lng hve been emploed: ( ) ( ) ( ) ( ) ρ ( Q Q ) ( ) ( ) B ( σ B ) ( Q ) Q ( g d ) where me nd re he longudnl nd he rnvere e o oordne repevel nd re he low velo omponen long he nd e repevel nd re he bed hre ree long he nd e repevel ρ he den o wer g he eleron o grv he wer level nd he wer deph. In () η he bed elevon ( ) Q nd b Q re he bed lod rnpor b n nd dreon repevel nd P he poro o bed edmen. gure how he oordne em o he b equon. I ommon obervon h he me le o bed ormon muh greer hn he repone me o low. hereore he me vron o low b he lood wve nd nd wve re normlzed b he duron o lood σ nd B repevel n whh B hl o hnnel wdh nd he be low velo. gure how he oordne em o lood wve.

3 Moreover he ollowng relevn dmenonle prmeer re: B σ B ρ ρ σ ( g d ) Q ρ ( g ) ( P) where nd re he wer level nd wer deph o be low repevel nd ρ he den o edmen. σ mll prmeer beue un o σ nd B re d nd mnue (or hour) repevel. he deph verged low velo nd edmen lue n he rnvere dreon re e o zero he hnnel dewll he boundr ondon ; ± (5) Q b ; ± (6) edmen rnpor n he longudnl nd rnvere dreon epreed repevel ( Qb Qb (oδ nδ ) ung he bed lod unon. In he bove equon δ he devon ngle beween he dreon o low nd edmen rnpor dreon gven b: r ( ) n δ oδ n δ n whh r onn (.) nd he held re whh epreed where d d. LINEARIZAION d ( ) he perurbon mehod doped b ubno[] pple n he heorel e o mll mplude lood wve whh re generll o ne mplude n nurl rver. he novel eure o he preen pproh bl o re lood wve wh ne mplude. In he one o lner perurbon epnon we hen ele lood wve el he me vrng b e o whh perurbon qun due o nd br upermpoed. We hen wre: ( ) ( ( ) ( ) ( )) ε[ ( ) ( ) ( ) ( )] where nd re he unon o me onl nd do no depend on or. urhermore nd re e ( ε ) ( ε) ε ε n whh ε prmeer o perurbon. he ommon obervon h he wvelengh o lerne br he me o lood muh mller wh repe o lood wve ugge o ume h he b e doe no hnge long he longudnl. he b wve deph nd he oed low velo hen onl vr on he me le o he lood wve whle he lope o wer level doe no hnge n me. uh b e gven b equon ()-() order ε where he re epreed ollow: (7) where he ondon << ε re hen gven b ( ) σ h been ued o negle he nerl erm. he equon order (8)

4 (9) () () r Q () Equon (8) how h he hnnel bed doe no hnge wh me under lood wve; hereore he qu equlbrum umpon or edmen moon emploed n he preen model. he perurbon o he ron oeen her velo nd o he bed lod unon re obned rellng her dependene on he held prmeer nd on he wer deph. We hen wre: [ ] { } ) ( ) ( ε where he qune nd re obned rellng h ; he beome: () () (5) (6) d (7) (8) nll nd re epreed (9) () he nl ondon or wer-ure lope e w nd he ollowng equon derved rom Equon (7): () where w Equon (9) () nd () order ε hen beome:

5 () () r Q () GROW RAE O ALERNAE BAR Aumng n ndenel long -domn he oluon ) ( n be epreed ordng o he ollowng ourer epnon uomll ng he boundr ondon (5) nd (6): { } { }{ }.. E (5) where n o ep E he mgnr un.. denoe he onjuge o omple number nd he longudnl wve number o lerne br ( L B wh L o lerne br wvelengh). ubung Equon () nd (5) no Equon () () () nd () eld he ollowng epreon: (6) (7) (8) r Q (9) nd Ĥ re epreed unon o ung Equon () o (). We nll obn he ollowng equon: d G () where he omple oeen d G epreed b r Q d G () n whh { } Equon () onrol he me evoluon o he perurbon o low deph due o he preene o lerne br n lner one. Equon () olved

6 ree ure elevon ree ure elevon hrge 8 6 hrge Ω Ω 5.E-.E-.E-.E-.E- Ωu Ω nonlner (ubno) Br mplude (ubno) gure lood ondon o ubno[] gure u nd br mplude b ubno[] ep[ G]on. () when G ( d ) ndependen o (ee []). he growh re o lerne br under ed low Ω epreed b rel pr o G. nder uned low ondon nd G ( d ) re unon o. hereore he oluon o Equon () beome ep () ' ' on. G d () he rel pr o he erm n qure brke o Equon () he mplon or Ω o lerne br. When vlue pove lerne br grow; when he vlue negve he br re dmped. he growh re o lerne br or n wve number obned b provdng he uble unon or ron oeen nd bed lod unon nd gven vlue o d nd whh hdrogrph. he wvelengh m orrepondng o he mmum growh re Ω m or Ω eleed b he nbl proe nd hould no be gnnl m moded b nonlner ee uggeed b []. he growh re gven b Equon () ompred wh he br mplude gven b ubno reul[] ung he lood wve hown n gure. gure ompron reul. ubno[] ele me-verge dhrge b qun. reul how eene o br even he r o lood when edmen do no move. h reul onrd hdrul phenomen. On he oher hnd he preen ud how more rel reul. 5 EXPERIMEN he epermen were ondued n order o mke ler how br ormon der under ed nd uned low ondon. A rgh hnnel wh 5m n lengh nd.m n wdh w ued. A bed wh lope o /8 w ormed wh l nd. he prle dmeer w.76mm nd he ubmerged pe grv o edmen w.65. Epermenl ondon re hown n ble where nd denoe ed nd uned low ondon repevel. he number o he uned low epermen nde he dmenonle elped me dvded b he lood duron. he vron o wer deph n he uned epermen w djued ordng o Equon (). I behvour hown n gure 5. δ ( α ) γ ().E

7 ble Epermenl ondon Epermenl hrge eph me number m d / m mn ned low Equon (8) ed low Oberved Wer eph ned low ed low Z b Z b gure 5 Br hegh nd wer deph n epermen m ned low ed low gure 6 Br wve number n epermen where we e he onn vlue α.5. γ.5 δ. he bed w lened beore he r o epermen n eh e. low w opped n he uned epermen or he obervon o bed onguron eh meuremen. Eh o he uned low epermen w onnuoul lowed rom he begnnng me o lood beue w neer o preven ee o nermede op on boom developmen. he mrk n gure 5 nde he me whh he bed onguron were meured. Epermenl reul re hown n ble gure 5 nd gure 6. nder ed low ondon lerne br ppered n - o - epermen bu no n -5 nd -6 epermen. I n be d h lerne br were ormed when wer deph n hee epermen le hn.5m. On he oher hnd under uned low ondon lerne br were onnl preen. ompred wh he me whh br do no orme under he ned low ed low m

8 Epermenl number nd br Wve lengh m Br hegh m - Alerne br Alerne br Alerne br Alerne br No br No br Alerne br Alerne br Alerne br Alerne br Alerne br Alerne br Alerne br Alerne br....6 ed low uned epermen ehb lg me or he growh o he wve hegh o lerne br. he wvelengh nd wve hegh o lerne br n he rng perod o wer level re deren rom hoe n he llng ge when he ondon he me n erm o wer deph. 6 MOEL ALIAION ble Epermenl reul Oberved une I overed bed Equon (9) m Z b l bed An-dune overed bed In order o ver he pbl o. heorel model developed n h pper operonl ompron re θ mde beween he epermen nd model reul. o nvege he bed rene gure 7 Bed rene n ed low epermen n he epermen he meured ron oeen hown n gure 7. gure 7 lo how he ron oeen n he l bed dune I overed nd n-dune overed bed whh re luled b he mehod o h nd urok[5]. he ron oeen n h epermen n rnge beween he vlue n he l bed nd dune I overed bed nd n be ppromed b.69. (5) he bed lod unon propoed b n Rjn[6] ued n he model. he heorel reul re luled ung hee unon nd Equon () or he hdrogrph. gure 8 how he ompron beween he lerne br hegh oberved epermen nd h preded b he heor under ed low ondon. he vlue o Z b n gure 8 he lerne br hegh. he br growh re preded b he heor under ed low h he me enden he meured vlue o br hegh. In he epermen n whh lerne br do no genere he growh re Ω o he heor under ed low ondon negve nd he epermen reul nd he heor how good orrepondene. he oberved behvour o br hegh n uned low epermen nno be eplned b he reul o he heor under ed low ondon. he relonhp beween he lerne

9 Ω Zb (ed low Epermen) Ω Zb(ned low Epermen) -.E-5-5.E-6.E 5.E-6.E-5.5E-5.E-5.E-5.5E-5.E-5 5.E-6.E -5.E E Z b / gure 8 heorel reul under ed low nd br hegh n epermen Ω m Ω m m (ned low Epermen) (ed low Epermen) Zb/ m gure 9 heorel reul under ed low nd br wvelengh n epermen Ω Zb(ed low Epermen).E-.E-.6E- 8.E-.E Zb(ned low Epermen) Zb/ -8.E Z b / gure heorel reul under uned low nd br hegh n epermen m Zb(ed low Epermen) Zb(ned low Epermen) m gure heorel reul under uned low nd br wvelengh n epermen br wvelengh preded b he heor under ed low ondon nd meured n he epermen hown n gure 9. nder ed low he lulon reul he low ge do no gree wh he meuremen reul. I eem h wo pr o ndbr ombne o orm ngle pr o lerne br n he epermen when he wvelengh horen beond hrehold vlue. he lulon l o reprodue h phenomenon. Even when wer deph beome lrger he heorel br wvelengh bgger hn he epermenl one. gure nd how ompron beween he reul o he heor under uned Ω -8.E-.E 8.E-.6E-.E-.E-

10 low ondon nd he epermen. he preded growh re Ω dpl behvour whh mlr o h o he oberved br hegh under he uned low n he epermen. In prulr he heor n pred he ourrene o lerne br under uned low even under he ondon n whh br were no oberved n ed low epermen. In he uned e he heor pred vlue o br wvelengh whh horer hn he oberved vlue. owever he uned low oluon lerl reprodue he le dpled b here hrer br wvelengh whh nno be reprodued b he ed heor. 7 ONLION Epermenl evdene uppor h he behvour o lerne br under uned low ondon deren rom h under ed low. A lner bl nl o lerne br ormon under uned low ondon preened n h pper. he heorel reul ompre vourbl wh he epermenl ndng under uned low. he heorel oluon uppor h he wvelengh nd wve hegh o lerne br n he rng perod o he lood re que deren rom hoe ourrng n he llng ge. ANOWLEGEMEN h reerh w uppored b he ellowhp provded b he Jpnee ene nd ehnolog Agen. pel hnk re lo eended o he okkdo Regonl evelopmen Bureu Jpnee Mnr o Lnd Inrruure nd rnpor whh gve he r uhor ruul opporune o ud he nver o ren Il. REERENE [] ubno M. Growh o lerne br n uned low. Wer Reoure Reerh ol. 7 No [] Mw.. Iked nd. n Growh nd rnormon proe o lerne br under he nuodl-wve lood ondon. Proeedng o he 55 h Annul onerene o he JE 5-5. (n Jpnee) [] olombn M. G. emnr nd M. ubno ne mplude lerne br. Journl o lud Mehn. ol [] Wnbe Y. nd M. ubno Inluene o bed lod nd upended lod on lerne br. Proeedng o drul Engneerng JE ol (n Jpnee) [5] h. Bed orm nd hdrul relon or lluvl rem Applon o oh proe n edmen rnpor eded b. W. hen nd. kkw hper [6] n Rjn L.. edmen rnpor pr I: bed lod rnpor Journl o drul Engneerng ol. No. AE