INTERNAL MEMORANDUM No. 117 THE SEDIMENT DIGESTER. Gary Parker February, 2004

Transcription

1 T. ANTONY FALL LAORATORY UNIVERITY OF MINNEOTA INTERNAL MEMORANDUM No. 7 TE EDIMENT DIGETER Gary Parkr Fruary, 4

2 TE EDIMENT DIGETER INTRODUCTION Th marial low wa wri i Novmr,. I rr a am o quaify ro orv y h auhor a h Porgra Gol Mi, Paua Nw Guia i Oor,. TE PENOMENON Iom wa im from h Porgra Gol Mi, Paua Nw Guia, i io io wo wa um, h Ajolk Dum a h Aaw Dum. Th im irou io h um form arhflow whih mov lowly owlo, a ar vually iorora io h fluvial raor of rivr. Of ir hr i h Ajolk Dum. Figur how a viw of h i, iluig h Ajolk a Aaw Dum a h Kaiya Rivr. Th im of h Ajolk Dum i iorora fluvially io h Kaiya Rivr a arri owram. I h imag ar of h Kaiya Rivr flow hrough h mil of h owram of h Ajolk arhflow. A h im of h auhor i vii, howvr, h arhflow ha uh h Kaiya Rivr u agai h orhr vally wall. Figur. Viw of h Porgra Gol Mi, h arhflow of h Ajolk Dum, h arhflow of h Aaw Dum a h Kaiya Rivr. Figur -4 wr ak y h auhor urig a i vii i Oor,. Figur how a viw of h Ajolk arhflow lookig owlo from h um.

3 Figur how a viw of h am arhflow a i aroah h Kaiya Rivr a uh i u agai h orhr vally wall of h rivr. Figur 4 how a viw of h ial of h am arhflow a h Kaiya Rivr Figur. Viw of h Ajolk arhflow lookig owlo from h um i. Th Kaiya Rivr i viil i h ia. Figur. Viw of h Ajolk arhflow a i flow io a alog h vally of h Kaiya Rivr.

4 Figur 4. Viw of h ial of h Ajolk arhflow a h Kaiya Rivr. OVERVIEW Th im igr i a mol for riig how h Kaiya Rivr, Paua Nw Guia ig im from h Ajolk arhflow (or how h Pogma Rivr ig im from h Aaw arhflow). Th arhflow flow oiuouly from um i a h Porgra Gol Mi, Paua Nw Guia. Thy ori h rivr o o i of h rivr vally ovr a igifia lgh. Thi rul i a li our of im o h rivr rahr ha a oi our. Th a oir i illura low i Figur 5 (la) a 6 (ro-io). I Figur h flow i h rivr i ir ou of h ag, a h arhflow irou im from h righ i. Uram am ra y arhflow Rivr Earhflow im ak iway io ram Figur 5. hmai iagram illuraig how h Kaiya Rivr ig h im from h Aaw arhflow. 4

5 rivr arh flow Figur 6. hmai iagram illuraig h aum roioal gomry. Th figur imly a irig iraio. iway im uly from h arhflow o arrow h hal, a i aiio au i o aggra. Th arrowr hal ro y iraig i aaiy for ramwi raor a laral rmoval of arhflow marial. Th rolm oiu a irig a of h iraio of ram wih a hal lvaio. Th am ram u o ri hal wiig from a iiial, ovrly arrow ofiguraio o a quilirium ofiguraio wih a fii, o-vaihig im raor ra i h hal a o furhr wiig. I uh a a h laral iu of im i aum o vaihig. GEOMETRY I Figur 6 o a ravr ooria ir from a fix, vrial wall. Th ramwi ooria i ir io h ag. Th umrg i lo of h hal ak h oa valu. Th mrg i lo of h arhflow i. Flow h i h rgio of h hal i. Th wih of h rgio of h hal, i rgio of h hal a arhflow aov h hal ar fi o, a rivly. Elvaio of h hal i, lvaio of h war urfa i a lvaio of h o of h arhflow i. Travr ia from h vrial wall o h hal iwall irio i ; ravr ia o h war g i a ravr ia o h o of h arhflow i. May of h aramr ar rla gomrially. om of h rlaio ar 5

6 (a,,,,,f) I orr o imlify h rolm, h lvaio of h o of h arhflow i aum o oa hri. CANNEL YDRAULIC For imliiy ormal flow (ay, ramwi uiform flow) i aum hr. L τ o h har r o h rgio of h hal a τ o h ouary har r o h ak, or i lo rgio of h hal (a wll a h vrial wall). Th oiio for ormal flow i τ τ ρg( ) () whr o h ramwi lo (aum o h am for h a ak rgio). W ow aum ha τ ϕτ () whr ϕ i a umr yially w / a 4/5. Thi aumio allow for h oiiliy of a hal ha o o ro i ak (au τ i low h hrhol of moio hr) u a maiai a quilirium im raor ra o h rgio (au τ x h hrhol of moio hr.) Thi orro wih h aalyi of Parkr (978). Maiulaig wih (), i i fou ha τ ϕ ρ g (4) I aiio, i i aum ha h ro-ioally avrag flow vloiy U maiai h am valu o h rgio a o h ak rgio, a ha i aiio a Maig-riklr rlaio for ria hol; 6

7 7 D k k C C U k 6 / r / f f α ρ τ (5a,,) whr C f i a friio offii, k i rough high, D o a hararii im grai iz (.g. mia or gomri ma), α r i a imiol offii hr ak o qual o 8. a k i a imiol aramr ha i yially w a 4 ig o h aar viaio of h grai iz iriuio. Fially, war orvaio rquir ha oal war iharg Q w i giv a w U Q (6) olvig for w (4), (5) a (6) i i fou ha / / r w / g Q k ϕ α (7a,) No ha h aual oluio mu ahiv iraivly i i a wak fuio of. A Nwo-Raho iraio hm i uli owar h of hi oum. Th hil umr τ for h rgio i h giv a 7 / / r w / g Q k D D gd ϕ α ϕ ρ τ τ R R R (8a,)

8 I h aov rlaio R o h umrg ifi graviy of h im (uually lo o.65). No ha i aohr aramr ha a aroxima a uiy for uffiily mall valu of /. Th hil umr τ o h ak or iwall rgio i h τ τ ρrgd ϕτ (9) Equaio (7) a (8) oai uful iformaio aou h im igio ro. Thy ifially iia ha a h wih of h rgio i ra, oh h h of flow a h hil r i ira. TREAMWIE EDLOAD TRANPORT L q a q o h ramwi volum loa raor ra r ui wih o h a iwall rgio, rivly. I i aum ha oh a omu from a ommo loa raor rlaio a log a h aroria hil r i u. r h followig aumio i ma: q q RgDDα RgDDα ( τ ).5 ( ϕτ ) τ τ.5 τ ϕτ (a,) I h aov rlaio α. a τ.. Th rlaio ilf i h Parkr (979) aroximaio o h Eii (95) loa raor rlaio. w (8), (9) a () i i ha a ra i wih ira h hil r, a hu h loa raor ra. Aumig ha q a q hav ui of m /, h oal ramwi loa raor ra G loa i M/a i giv a ( q q )( ) G loa R () x TRANVERE EDLOAD TRANPORT I gral, l q o h ramwi volum loa raor ra r ui wih a q o h orroig volum loa raor ra i h ravr irio. Th followig iml aroxima rlaio for ravr loa raor ha rmi y a umr of auhor: 8

9 q q τ τ α τ τ () I h aov rlaio, τ o h ouary har r i h ravr irio, τ o h hil r a o h ramwi har r o h iwall rgio a α a ar oa. Th rlaio ay ha a) i h a of a i lo h loa raor vor i aralll o ha of h ouary har r, a ) i h r of a i lo a omo of loa i ivarialy ir ow h lo. I h Johao-Parkr (989) imlmaio of (), α.65. For h uro of h r aalyi h hal i aum o raigh, o ha τ a aroxima a vaihig. I aiio, i h rgio of h hal h i aum o horizoal, o ha / hr a hu q a aum o vaihig. I h iwall rgio, howvr () ak h form q q α RgDDα τ ϕτ τ τ ( ϕτ ) α ϕτ ϕτ (a) whr τ i giv y (8a). If q i omu i m /, h h orroig ravr raor ra g i owar h hal rgio i M/m/a i giv a 5576 g i q( R ) () 6 x Th gaiv ig i () iur ha a ravr raor from iwall rgio o rgio, whih imli a gaiv valu of q, yil a oiiv valu of g i. EDIMENT CONTINUITY IN TE ED REGION Th Exr quaio for im oiuiy i h rgio wa alray work ou i la, u uforualy ha ram oai om rror. (Th rror ar o imora for mo rolm u ar imora for hi o.) Th rolm i o orrly low. I gral h D vrio of h Exr quaio of im oiuiy a wri a 9

10 q q λ) () ( Thi quaio may igra ovr h rgio o yil q q ( λ) (4) Th fir rm i h aov quaio ru wih h ai of (a) a Figur 6 o ( ( λ ) ( λ ) ) λ ( λ Aorig o Liiz rul a (a), ) (5) q q q q q (6) Thu h o rm i (4) om q q q (7) Aroximaig q a vrywhr qual o q o h rgio, h o rm hu ru o q q q q (8) Fially, h hir rm i (4) ru o q q q (9) r q i aum o vaih u o h iroil wall a, a o ifi i rm of (); q i q ( ϕτ ).5 τ α R gddα () ϕτ 4.5 ( ϕτ )

11 r h ha quaiy i oiiv, iurig ha a ravr im raor i h gaiv irio (from h iwall rgio o h rgio) giv a oiiv oriuio o h im. w (4), (5), (7), (9) a (), h, h igral quaio for im orvaio i h rgio om q ( λ) () EDIMENT CONTINUITY IN TE UMERGED IDEWALL REGION Equaio () i ow igra from o i aora wih h fiiio of Figur 6. q q ( λ ) () W ow igra h rm o y o. w a lvaio oy h rlaio o ha ( ) () (4) Thu h followig rul i oai; λ ) ( λ )( ) ( (5) Furhr ruig wih (,,f) i i fou ha λ λ ) ( ) ( (6) Progrig o h x rm of (), aorig o Liiz rul or hu q q q q (7a)

12 q q q q (7) I i aum hr ha q, < < q q, < < (8), whr q a q ar giv y (a,). Ruig (7) wih () a (8), h, q q q (9) Progrig o h la rm, q q q () Th volum ravr ra of livry of im r ui im r ui ramwi ia from h mrg iwall rgio o h umrg iwall rgio i hr o a, whr () q No ha h ha quaiy i agai oiiv for h gomry of Figur 6. Thu () ru wih h ai of () a () o q () Th igral form () fially ru wih h ai of (6), (9) a () o q λ () ( ) q EDIMENT CONTINUITY IN TE EMERGENT EARTFLOW IDEWALL REGION Equaio () i ow igra from o i aora wih h fiiio of Figur 6.

13 q q ( λ ) (4) W ow igra h rm o y o. w a lvaio oy h rlaio ( ) (5) Diffriaig h aov xrio wih r o im a rallig ha i hr aum o a ifi oa, i i fou wih h ai of (,,) ha (6) w (6) a () h followig rul i oai; ( ) λ ) ( λ ) ( (7) i hr i o ramwi fluvial raor i h mrg arhflow zo, q a aum o vaih hr, o ha h o rm i (4) a ro. Th hir rm i (4) igra o yil q q q (8) Th volum ravr ra of livry of im r ui im r ui ramwi from h o of h arhflow i hr o a, whr (9) q No ha h ha quaiy i agai oiiv for h gomry of Figur 6. I h r aalyi i aum o a giv aramr rmi y h movm of h arhflow, a i of h ram ilf. Thu (4) ru wih h ai of (), (7 9) a () o (4) ( λ )( ) Th aramr ifi i m / a rla o h iu ra of arhflow marial from h i g i i M/m/a y h rlaio

14 5576 g i ( R ) (4) 6 x REDUCTION TO RELATION FOR WIDT VARIATION Th limiaio of from () a (4) rul i h rlaio\ ( λ ( λ ( ) ) )( ) q ( λ q ) (4) uiuig () io (4), h quaio for h voluio of ram wih i fou o ( λ ( ) ) ( λ )( ) q q q (4) Th aov quaio a furhr imlifi y oig ha aorig o (7), r (44a) whr 4

15 5 o o r (44) a ϕ α / / r w / o g Q k (44,,,f) Ruig (4) wih (44a) h followig rul i oai; ( ) q q q ) r( ) ( λ (45) CAE OF VANIING TREAMWIE VARIATION Coir a a for whih all aramr, iluig ar oa i h ramwi irio. For hi a () a (45) ru o ) ( λ (46) ( ) ) r( ) ( λ (47)

16 I i hi a ha i oir i h rah rogram. NEWTON-RAPON CEME FOR TE FLOW Equaio (7a,) a wri i h form whr f o () (48) o / k Qw αr g ϕ / / (49a,,,) Takig h rivaiv of (48) wih r o, f () o 9 (5a,) Th Nwo-Raho hm for h i hu f() w (5) f () KINEMATIC WAVE IN WIDT Th form of (45) ugg h oiiliy of hal wih voluio i h form of a uram-migraig kimai wav. I ariular, h quaio a rwri a X (5) whr 6

17 X ( λ ) A ( λ ) ( ) A r( q q ) ( ) r( ) q (5a,,,) ACKNOWLEDGEMENT Th im igr wa iir y oulig work rform y h auhor for h Porgra Gol Mi. REFERENCE Eii,. A., 95, Th -loa Fuio for im Traoraio i O Chal Flow, Thial ulli 6, U.. D. of h Army, oil Corvaio rvi. Johao,., a Parkr, G., 989, Liar hory of rivr mar, i Rivr Marig, AGU War Rour Moograh, Vol (. Ika a G. Parkr,.), Parkr, G., 978, lf-form rivr wih al ak a moil : Par II, h gravl rivr, Joural of Flui Mhai, 89(), Parkr, G, 979, yrauli gomry of aiv gravl rivr, Joural of yrauli Egirig, 5(9), Parkr, G., a E. D. Arw, 985, orig of loa im y flow i mar, War Rour Rarh, (9):