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<br />744
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<br />HYDRAULIC ENGINEERING '94
<br />
<br />OeCIrIIDCe of Critical ud Suelcritiul F1011
<br />
<br />Critical or sapereritical flow coaditious cbaracterhed 119 of the 930 cross-seetioR
<br />discharge leasure.eats lade at the Ibdy sites between 1980 asd 1989. Critical flo. .as assued
<br />to occur at rroude DUlbers betweea 0.90 and 1.00 to allow for JeaSUlueot errors of velocity and
<br />flow depth; sapercritical flOt Will assale' to occur at Froude aUlbers greater tban 1.00. These
<br />flows lere lOSt CODOn at the Elk Rock gage (slope aiolt 0.01 1'1) OR the debris &Jalaae!!e
<br />deposit of the upper In. At tbil locatioD, about 52& of the flow .easury!sts lere
<br />cbaracteriled as critical or sllpercritical.
<br />fbe relatite (reqaucy of critical ild lupercritical flol. seel. to decrease lith
<br />dhtllee dOWl1streal aad tbe cOlSeqaeat decrease iD chaDDIl gradient. liDeteeD percent of
<br />leasured discbarges at tbe lid Yalley gage (slope aOOtt 0.006 1/1) on tbe In and Daly 31 of
<br />leaslred diacharges on tbe lover T. (slope about 0.0025 1/1' bad Froude Dueen greater tblB or
<br />equal to 0.90. Critical lId slpercritical flon oCClned over a wide taDge of discbarges; 15.3.
<br />100.3/1 at Elk Rod., 11.1 - U7 .'/1 It lid Jalley (upper 80\ of flow dlfatioll), aDd 49.9 . 354
<br />.'/1 at fower Road (.pper 45\ of flow duaUn) Itable 2).
<br />Critical and sapercriticill non were lOSt couoo in tbe years sborUy after tbe
<br />eruptioll aod pealed in 1982 at tbe lid 'alley 9age and 00 the lower T. (fig. 1). This is
<br />attributed to the '1lOOtbing- of chanle1 bOlldiries by blankets of deposited saId tbat were
<br />delhered daring bigb~flOl e'ents that decreased cltlloel rougbnesl and, to a lesser !lteot, to
<br />tbe ilJlosed increases ill chllael gradient. The effect of redlced roaghless WII partiellhrlf
<br />e,idelt d.rilg the stonflow and lale brelkout of 'ebruny 20. 1982, aRd tbe ezploshely
<br />geaerlted Iabar of March 19-20, 1982. Burial of the coarse, IObl1e pneleot by sand on the
<br />hlliDg liD of stonnOl hJdrognphs caosed order of ngnitude reductiols ill ledlau bed~.aterial
<br />particle she (d!>D) follolllg tbesl l!Yuts. It tbe lid ViIlley gage OD the lower If", nrlfied
<br />laoailg's rovgblless coefficients decreased frol lbout 0.030 prior to tbese eJeots to about 0.019
<br />followil~ pUBage of these flon. It the ronr Raid gage OD tbe fl, Ylrifietlllauliog's rougbness
<br />coefficients .ere rHuced frol about 0.027 to aboat 0.014 Ifter Febnary 20, 1982, because of
<br />las.he alODats of Illd depositiou 11089 tbe chauaeI boaldatie.. Valoes of lIalDilgts raugbness
<br />coefficillt iucreased agail at botb the In aad fl gages as low Iud lodente flows eroded
<br />deposited saa' to lean a rougher and coarser ,ranI-cobble bid. Critieill aDd supercritical
<br />flOl8, tns were iuihite' a8 a relult of redoced ftlocities aid the greater elergy lossls
<br />associAted with rougher flows. these elerg} Josses cal iochlde boundary friction, higb
<br />tlrbuIeDce ud ed.ies, flow elpalsiOll and co.traction, sedi_t traasport, aDd hydraulic jolps
<br />Ifriest" 1m),
<br />fhe relatifeJy fr!CJOInt occltrelce of critical and supercr1tiCll flows betllen 1985 I.IId
<br />1987 at the Elk loct gage OD tbe upper In CaD be related lOti! to steep challDe1.gradielts (Ibolt
<br />0.01 1/') coabined witb ID eltrelely wide chaDDel cross-sectiol, rather thao to bydra.lic
<br />slOothiog by depolited laId. Bed-uterial d~o generaUy raDged fru abOlt 2 II to about 70 u at
<br />the gage, with oue brief episode of fililg to about 0.71 D that was docUJellted after stor.flols
<br />of 10veJber 1985. tbis sbort-ten Uliag is Dot suffic:1ent, by itaelf, to elphia the fregaency
<br />of .easarl!C1 critical and slIpercriUcal non at tbe Elk Rock gage betveel 1985 aDd 1987 (table 2j
<br />fig,l),
<br />fhe frl!q1lelcy of leasured critical aa' sDpercriUcal flOl8 decreased witb ti.. IS a
<br />reldt of cballDel adjlsunts (fig. I}. Tbe decrease 11 the frequency of occurresce of these
<br />flows is related to cbuae1-adju.tlett processes. tbe adjustJelt& caused (1} deerelses iD
<br />cbauoe1 gruielt aid flow ,e1acitJ ISilOn, 1992) aud (2) lIenalls 11 hydnulic rOlglmess ISilOB
<br />aid thorDe, i. press). Ilcreased re!aUlI rouglmels wal caused by bed-uterid coarse.ailg aDd by
<br />r!dlctioll8 ill hydUDl1C depth as a reslit of cbaDnel widening. II cOlbinatiol, these adjlStlelts
<br />resulted iD greater redllctioD' il flow velocity thaD iD hydraalic depth .ith till (SiIOD, 1992)
<br />aad iobibited criticill lid ao,ercritical flows by the late 1910's.
<br />!be occonelce of criticill aod supercritical flOls il the 'n and 'I appear to ba,e been
<br />closely related to steep chauoel gradiuts aDd to the delhery of saDd-sized sedi.lot tbat
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<br />CRITICAL & SUPERCRITICAL FLOWS
<br />
<br />V LLEY WASHIJ'tIGTON
<br />
<br /> NORTH FORK TOurLE RIVER AT KID A ". ""~ ",~ l'<='
<br />You To'" f~0.9 Mean Max. MIn.. ~ M:. V """'" 51". F2;0.9
<br /> 0''', now. Q Q 9 mI) (ftVs) (PV'~) ',' -,
<br /> (m'ls) (m'/s) (mh) (s .. .. .. ',30
<br /> .. ..
<br /> , '53 -- O.OtOO ",.
<br />1980 30 2.1" 3.14 1.48 0.0250
<br /> " 52.2 IS. 11.1 0,_ 39.t
<br />1?~1 " 1.73 0.0230
<br /> <6, 34,' ',54 4.46
<br />[}'IR2 " '" 0.0053 2B.3
<br />" ',30 1.80 0.0260
<br /> 110 '" 22,' >S,
<br />11'183 60 " '" 1.111 0.0250 0.0062 27.2
<br /> " <6' 60,' 33.S ',04 7.30
<br />1~8~ 44 1.111 1.68
<br /> 29.6 11.11 1.75
<br /> " , 22.5 001160 2.60
<br />I'JKS ''" .. 0.0270
<br />I~~~ '" , '" ,- 0,00
<br /> .. .. -- "
<br />19~1 34 0 0,00
<br /> ..
<br />1'18R ,r. 0 .. .. 0,00
<br /> - -- -- .. 18.5
<br />1989 ZO 0 .. ..
<br /> ,- -
<br />1"IJl ." " '~OUTLE RIVER NEAR ELK ROO(.. WASHINGTON
<br />
<br />i'Y~U
<br />
<br />11984
<br />1985
<br />''''
<br />\<)81
<br />T""
<br />
<br />NORTH FORK
<br />F~O.9 Mean MaJ<.
<br />flows Q Q
<br />(m'fs) (""fs)
<br />
<br />'00
<br />~
<br />61.1
<br />41.6
<br />51.6
<br />
<br />""""
<br />F~0.9
<br />
<br />,,~
<br />"'"
<br />-,
<br />0.0100
<br />0,0090
<br />0.0110
<br />0.0110
<br />
<br />..... """
<br />V Manning
<br />(mI5) "n"
<br />
<br />To'"
<br />"'"
<br />
<br />..... """ ,""",
<br />Q V V
<br />(m'/s) (mi.) (mJo'
<br /> ~"
<br />16.0 1.98 3.23
<br />16.3 2.13 3.03
<br />IS.3 2.11 2.S1
<br />
<br />1.62
<br />1.48
<br />',66
<br />
<br />, 19.9
<br />ZO 30.0 51.6
<br />IS 38.9 '00
<br />" 26,0 40.1
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<br />"
<br />Z2
<br />"
<br />..
<br />
<br />c;TON'
<br />
<br /> LOWER roU'fLI. WASHJN ........
<br /> MO<. M_ -
<br /> F2.0.9 ..... ,""", MO<. - ..... S.... Fl!:0.9
<br />Yw T"" Q Q V V V ........
<br /> 0'" .... Q ...., ...', ...', 'n' -,
<br /> (nil.) (nil.) ftr//.) 0
<br /> -- n n --
<br />'''' 60 0 .. .. .. 0,_ ,,.
<br /> ..,. 2.4' 3.41 1.83 0,"
<br /> " n '" '54 0.0023 3.30
<br />"" 2.63 3.19 ~08 O.oz
<br />,'" 61 , '" '" ,,. -- 0
<br /> .. .. -- n
<br />1914 " 0 n .. n -, 0
<br /> -- n -, ,-
<br />'''' " 0 n -- -- 0
<br /> -- ,- -,
<br />,,,. " 0 ,- -- -, n 0
<br /> -- -- n n
<br />"" " 0 .. -- -- n 0
<br /> n " " ..
<br />1911 26 0 n n .. .. 0
<br /> ,- .. .. -,
<br />'''' 16 0 -- -- ,- n "
<br /> .. .. -- --
<br />T"" ... 13 n .. ..
<br />
<br />I Om from g&f>(:S 1I Caslle Rock llIId .II. Tower Road (bible I).
<br />
<br />d su er critical flows at three sites
<br />Table 2. ...-Occurrence of critical an P
<br />in the Toutle River system.
<br />I reduced hydraulic rougbtess. For flols of a
<br />"slOothed- cbalnel bOlUldlries aDd, CODSeq~eDt J, ttlat the red\l.cti01l i. Mallning's "0" tbrOUgb
<br />gino discharge and vatet-surface slope, It seelS to caose a cblllge in tbe state of no.
<br />burial of rougbness elelenl& liS eaougb, in sale ca~es, of the sand-sized lateriallilh a
<br />fru subcrititallo ~upercritiCill. SDbsequen\:r~~:"eloCitY by IIposiog the gruel-cobble bed,
<br />consequent increase ID rOllgl:lUISS aDd decrease 't.atandSIlPercriticalflolsolllbelfrTalld
<br />retuned flow to tile sQbcritical state. aovlveri9~~~ l~fi9' 1} as channel gradients lere reduced
<br />n probably becalt ntt I)CCUHtutti b,. tile late .s Bulted in rougber, su'rmitital {1I)IS.
<br />and a geoera1 tupon1 tread of bed-uterid consenllg re
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