Transport et Incision fluviale

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Solomon Joseph
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1 Transport et Incision fluviale 1

2 Sediment transport 2 Summerfield & Hulton, 1994

3 Sediment transport Rivers are by far the most important carriers of sediment on the continents, although glaciers have been even more important at certain times and places. 3

4 Sediment transport Torrent St Pierre, Ecrins, Movie provided by Francois Métivier, IPGP 4

5 Sediment transport 2003 McGraw-Hill Higher Education 5

6 Sediment transport 6

7 Sediment transport Flow is relatively weak and/or the sediment is relatively coarse Flow is relatively strong and/or the sediment is relatively fine 7

8 Sediment transport Depth-integrating sampler Portable filtration equipment automatic vacuum sampler Turbidity probe 8

9 Sediment transport Hydrophone Helley-Smith microphone Small Dam Trap 9

10 Sediment transport Torrent St Pierre, Ecrins,

11 Sediment transport Gabet et al., 2008 Burtin et al.,

Sediment transport Sediment discharge: masse (or volume) of sedimentary material that passes a given flow-transverse cross section of a given flow in unit time.

12 Sediment transport Sediment discharge: masse (or volume) of sedimentary material that passes a given flow-transverse cross section of a given flow in unit time. Sediment load: sediment in a unit-area volume extending from bed to surface. Sediment yield: rate, per unit area, at which sediment is removed from the watershed Sediment yield = sediment discharge total drainage area of the river upstream 12

13 Sediment transport 13 Niobrara river, Wyoming, USA modified from Vanoni, 1975

14 Threshold of movement Kansas State University 14

15 Threshold of movement 2003 McGraw-Hill Higher Education 15

16 Threshold of movement 16

17 Threshold of movement μ w, ρ w τ o = ρ. d. g. sinα w D 17

18 Threshold of movement Flow CG γ Pivot Direction of easiest movement An average particle, in an average position on the bed, subjected to an average fluid force ~horizontal 18

19 Threshold of movement Flow D CG F γ D Pivot = surface. τ = o c 2 D 2 τ ~horizontal o 3 FG = Δmg = c1d ( ρs ρw ) g 19

20 Threshold of movement Flow FD cosγ γ FD F D sinγ F G sinγ CG a 1 a 2 γ Pivot ~horizontal F G cosγ F G γ The condition for the beginning of movement is a F sinγ = a F cosγ 1 G 2 D 20

21 21 Threshold of movement γ ρ ρ τ τ τ γ γ τ ρ ρ tan ) ( cos sin ) ( gd c a a c F a a F D c F g D c F w s c c o D G o D w s G = = = = = γ ρ ρ τ τ tan ) ( Shields parameter * c a a c gd w s c c = =

22 Threshold of movement Shields parameter * τ τ c ρ c = = ( ρs w ) gd a1c a c tanγ Geometrical parameters Geometrical parameters and function of the Reynolds number Same analysis if lift is considered and if the river slope α is not negligible. In this last case γ is replaced by γ α. So, if others conditions remain the same, increasing bed slope decrease the β c. Assumption: The flow is not shallow enough so that the motion of the fluid over the grains affects the free surface. clearly an invalid assumption for very shallow, gravel-bed rivers. 22

23 Threshold of movement Shields,

24 24 Threshold of movement Miller et al., / 2 3 1/ 2 ) ( ] ) [( μ ρ ρ ρ μ ρ ρ ρ τ g D and g w s w w s w o

25 Threshold of movement Miller et al.,

26 Threshold of movement 0.1 mm/s Hjulström diagram 26 Sundborg, 1956

27 Fluvial incision plucking solution cavitation abrasion Modified from Whipple et al.,

28 Fluvial incision Ukak river, Alaska Susquehanna River, Pennsylvania 28

29 Fluvial incision d W Q g r S = tanα sinα ρ w α river bed From Burbank & Anderson, 2001 Stream power : Ω = Q. ρ. g. S Basal shear stress : τ Specific stream power ω = Ω W o w = ρ. d. g.sinα w = τ U o ρ. d. g. S w 29

30 Fluvial incision Three models are commonly proposed 1. Incision is related to stream power (Bagnold, 1977) h h e = Ω KQS t t 2. Incision is related to specific stream power (Seidl et al., 1992; Seidl & Dietrich, h h e = ω KQS / W t t 3. Incision is related to basal shear stress (Howard et al., 1994) h h e = τ KQS / WU t t 30

31 Fluvial incision Empirical laws Flint s Law : S A -a with 0.3 < a < 0.6 Hack s Law :L A b with 0.5 < b < 0.6 Q A c with c ~ 1 W Q d with d ~ 0.5 Manning' s equation :U = 1 N R 2 3 S 1 2 Gauckler-Manning coefficient, dependent on many factors, including river-bottom roughness and sinuosity hydraulic radius 31

32 Three models are commonly proposed Fluvial incision 1. Incision is related to stream power (Bagnold, 1977) h c KA S ~ KAS t 2. Incision is related to specific stream power (Seidl et al., 1992; Seidl & Dietrich h t KA S / Q ~ KA S ~ KA c d c(1 d ) Incision is related to basal shear stress (Howard et al., 1994) c(1 d ) Wd 1 Q 1 A R = ~ Wd ~ ~ d W + 2d W U Q U U R h t 2 3 S 1 2 KQS / LU U A KA 2c(1 d ) 3 U c(1 d ) 2 3 S S / A 1 2 U 2c(1 d ) 5 S A S 2c(1 d ) 3 KA S 1 2 3c(1 d ) 5 S U 7 10 A KA 2c(1 d ) S S 3 10

33 Fluvial incision These three models can be written as a power law h t m S n KA m = 1 n = 1 e Ω m ~ 0.5 n = 1 e ω m ~ 0.3 n ~ 0.7 e τ o 33

34 Fluvial incision h t K ψ ) ( A e S f c ξ critical incision threshold Here we have assumed that incision depends upon the rate of bedrock erosion (detachment-limited model). However incision rate can be limited by the transport capacity. In this case (transport-limited model) Q s h t K'( A x e' 1 w S f ' Q s * τ c ) ξ ' critical shield stress 34

35 Fluvial incision Whipple & Tucker,

36 Stream terrace 2003 McGraw-Hill Higher Education 36

37 Stream terrace Jingou River, North Tian Shan Laonung river, Taiwan Kali Gandaki, Népal 37

38 Stream terrace 38

39 Stream terrace River entrenchment modified from Merritts et al.,

40 Stream terrace Migrated upstream modified from Merritts et al.,

41 Stream terrace Backward erosion cross section profile along river profile modified from Merritts et al.,

42 Stream terrace 42

43 Stream terrace 43 Lavé & Avouac, 2000

44 Stream terrace Lavé & Avouac,

45 Stream terrace Lavé & Avouac,

Dynamique des rivières. res

Dynamique des rivières. res Dynamique des rivières res 1 Rivers are enormously diverse size: varies by many orders of magnitude geometry: highly variable substrate: bedrock or sediment sediment type: sediment size ranges from mud