Flow and Sediment Transport. 1. Fluid Flow in Rivers. Flow in Rivers 6/9/ Fluid flow
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1 6/9/ Flow and Sediment Tranport. Flid flow Uniformit and teadine, trblene, bondar laer, bed hear tre, veloit. Sediment tranport Inipient motion, bedload, pended load, beform. Flid Flow in River Otline. Flow niformit and teadine. Laminar and trblent flow 3. Mixing-length g onept 4. Trblent bondar laer 5. Mean bondar hear tre 6. Veloit ditribtion and the Law of the Wall 7. Depth-averaged veloit Flow in River Open Channel Flow River are nonniform, ntead, hdraliall rogh trblent flow Q w d U AU U A Uniform Flow: x U A Nonniform Flow: x (Bridge, 3) Open Channel Flow Laminar flow, Re < (vio fore dominate) U A Stead Flow: t U A Untead Flow: t Tpe Flow Trblent flow, Re > 4 (trblent fore dominate) trblent fore Re vio fore Ud Large mae of flid eddie are being tranported (Hornberger et al., 998)
2 6/9/ Laminar and Trblent Flow Trblent veloit time erie For m deep flow: Re = 3, U ~.3 m/ Re = 3, U ~.3 m/ Sqehanna River near Waverl, PA d ~ m, U ~ m/, Re ~,, trblent fore Re vio fore Ud (Bridge, 3) Mixing length onept Trblent bondar laer l: the vertial ditane over whih the momentm of a flid parel i hanged (mixing length) Renold Stre v l (Bridge, 3) (Bridge, 3) Vio blaer treak Trblent brting proe (Bridge, 3) ~7% of all trblene in open hannel flow i de to the brting proe (Allen, 985; Bridge, 3)
3 6/9/ Grain roghne effet on trblent bondar laer (Falo, 977) Large-ale Trblent Motion (Nakagawa & Nez, 98) U* D Reg (Jlien, 998) (Fergon et al., 996) (Belanger et al. ) Bondar Shear Stre gds d Conervation of downtream momentm: Impelling fore (downtream omponent of weight of water) = reitive fore * ; ln * * Law of the Wall d ' w' L d p ' w' in vi x Derived from Renoldaveraged Navier-Stoke eqation (Gomez, 6) Nearl niveral e Important amption: Prandtl mixing length theor Zero lope (?!) Contant hear tre (no vertial gradient;?!) (Bridge, 3) neg. (Talor, 9; Prandtl, 95, 96) Utilit of the Law of the Wall Depth Averaged Veloit (m/) * regreion ln (m) zero - veloit roghne height k 3. Appliation of the "Law of the wall" ln * From regreion data : lope * ln interept lope (m) , i=4 3, 3 (m/) Depth -integrated flow veloit : d General form : U d d Speifi form : i i i i i i n U d i i i where :, ; n d; n n n i the nmber of mearement 3
4 6/9/. Sediment Tranport Fore Ating on Stationar Grain Otline. Inipient motion riteria for niize and mixed-ize ediment. Mode of ediment tranportt 3. Bedload tranport 4. Spended load 5. Bedform (Middleton and Sothard, 984) Threhold of Motion gd.45 Smooth Tranitional Rogh Motion No Motion (Middleton and Sothard, 984) (Shield,936; Jlien, 998) F F D G D 3 gd gd (Miller et al., 977) Sample Callation Entrainment of mixed-ize ediment What i for D =.5 m qartz-denit partile? gd gd Pa.45 De to:. Relative Protrion. Pivoting angle 4
5 6/9/ Sample Callation What i for. and. m qartz-denit partile in a mixtre with D 5 =.5 m? i Entrainment of mixed- ize ediment gd.6 D i For.m.45 For.m.45 i gd.6 D i Pa Pa.4 Uing Shield for niize i ediment.7 Pa 7.3 Pa Mode of ediment tranport Mode of ediment tranport a* Wahload: D.63 mm (Leeder, 999) (Bridge, 3) Mearing bedload tranport Bedload Tranport Obervation i b f HS i b f Q trap Gravel-bed tream (Bnte et al., 4) Gravel-bed tream (Cdden & Hoe, 3) HS Bedload trap (K. Bnte) Helle-Smith ampler 5
![6/9/ Bedload Tranport Eqation (a) Meer-Peter and Müller [948]](/docs-images/89/99199223/images/6-0.jpg "eqation b d 5 (b) Meer-Peter and Müller eqation b d i Meer-Peter")
![56 d 5 () Aker and White [973] eqation b d i (d) Bagnold eqation](/docs-images/89/99199223/images/6-2.jpg "b d m q Bagnold (966) a tan b * * Abraham and Gao (6; following")
![[98] eqation b d i (Parker et al.](/docs-images/89/99199223/images/6-5.jpg "hiding fntion) Prediting bedload tranport Barr et al.")
6 6/9/ Bedload Tranport Eqation (a) Meer-Peter and Müller [948] eqation b d 5 (b) Meer-Peter and Müller eqation b d i Meer-Peter and Mller (948) g qb 8 gd g 3 3 Barr et al. (4) q 57 A b q* f 3.4 Q Q, d, 5.45 q* 3.56 d 5 () Aker and White [973] eqation b d i (d) Bagnold eqation b d m q Bagnold (966) a tan b * * Abraham and Gao (6; following Bagnold, 966, 973) i G b U G T g 3.4 T (e) Bagnold eqation b d mqb (g) Parker et al. [98] eqation b d i (Parker et al. hiding fntion) Prediting bedload tranport Barr et al. (4) (e) Bagnold eqation b d mqb (h) Parker et al. [98] eqation b d i (Andrew [983] hiding fntion) (Barr et al., 4) Spended Sediment Simple riterion for penion: a* Mearing pended load tranport DH59 Hand line Sampler DH48 Wading Sampler D74 Hand line Sampler (van Rijn, 993) Other: Sper-ritial flme, ISCO, OBS, Aoti Spended Sediment Sediment-diffion balane (eqilibrim): C C C q h a Cd Spended ediment profile and Roe eqation Z downward ettling + pward diffion Total pended load Roe eqation: C C a d a d a z z * (van Rijn, 993) 6
7 6/9/ Ripple Spended Load Obervation Mobile orbital ripple with aoti probe, P. Thorne Dne Upper-tage plane bed Bedload heet Mobile river dne with aoti probe, Wren et al. (7) Stohati imlation, Man (7) Conlion. River flow i ntead, non-niform, trblent, and hdraliall rogh. Ditribtion of veloit and bed hear tre an be determined 3. Sediment threhold ondition defined b Shield riterion, a modlated b mixtre 4. Rate of bedload and pended load tranport treated eparatel 7
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