dynamique des rivières - université de · pdf filetorrent st pierre, ecrins,...

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Dynamique Dynamique des rivides rivièèresres

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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 to gravel

stage of development: young, with rugged topographyand rapid change, to old, with gentle topography and slow change

climate: ephemeral and flashy to very steady

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Morphology of rivers

wetted perimeters

perimeterwettedareasectionalcrossradiushydraulic −

=

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The base level of a river is the elevation of the water surface of the water body, either the world ocean or a lake along the river course, into which the river flows.

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Poisson, 2002

Northern Tian Shan, China

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The river has some equilibrium longitudinal profile, in the sensethat if conditions of tectonic, precipitation, sediment supply, and base level remain constant the longitudinal profile stays the same.

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Classifying rivers

Rivers can be classified in several ways:

by the nature of their substrate

by the percentage of time they flow

by their relationship to the groundwater table

by their morphology

by the kind of sediment load they carry

by the dominant particle size of the bed sediment

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Classifying riversNature of substrate

detachment limited rivers transport limited rivers

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Classifying riversNature of substrate

Taiwan, bedrock river Tibet, Alluvial river

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Classifying riversPercentage of time river flows

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Classifying riversPercentage of time river flows

Runoff cycle

At the end of the first dry spell the river level lies below the ground water table in the river banks.

After a heavy rainfall the river stage rises rapidly to lie well above the level of the ground water table in the banks. Ground water is stored in the river banks, in the sense that the ground water table is locally and temporarily higher therethan in the surroundings.

At the end of the rainy period both the river stage and the ground water levelare of about the same height and are about at their highest.

Then both the river stage and the ground water table fall back to the dry spell situation shown.

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Classifying riversRelationship to ground water table

(Ground Water Table)

(unsaturatedzone)

(GAINING RIVER)(LOSING RIVER)

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Classifying riversMorphology

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L

l

1sinuosity

sinuosity

≥

=lL

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Meandered Anastomosed

Straight

Minnesota, USA

Braided

Sunwapta River, Alberta, Canada

Columbia River in British Columbia, Canada Yukon, Canada

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wavelength

ampl

itude

radius of

curvature

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2003 McGraw-Hill Higher Education

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point bar

meanderscrolls

Laonong river, Taiwan

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narrow neck

cutoff

sealing

channelrealignment

oxbow lake

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Tortous meanders

Confined meander scrolls

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Torrent St Pierre, Ecrins, FranceMeunier, 2004

~100 m

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Meunier, 2004

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Burbank & Anderson, 2001

1.5<sinus.<1.8sinus.>1.8

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Church, 2006

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Measurements of stream flow

The stage of a river is the height of the water surface of the stream above an arbitrary datum, usually either sea level or an elevation slightly below the channel bed. Stage is related to depth, but the two are not the same.

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The stage of a river is fairly easy to measure. Various kinds of streamgauges are in use.

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Measurements of stream flowThe discharge of a river is the volume rate of flow past a given cross section, measured in cubic meters per second, m3/s.

Most measurement of river discharge makes use of a simple equationthat relates discharge Q past a cross section to the area A of the crosssection and the mean velocity U of flow past that cross section.

UAQ =

u

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Torrent St Pierre, Ecrins, France

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Hydrographs

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Stage-discharge diagram or rating curve

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AB: end of spell without rainfall; all surface runoff has ceased, and groundwater runoff is gradually decreasing.B: surface runoff from a rainstorm reaches the channel.BC: this is the rising limb of the hydrograph; surface runoff increasessharply.

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C: this is the peak or crest of the hydrograph; surface runoff peaks.CD: this is the falling limb or recession limb of the hydrograph. Groundwater runoff peaks here somewhere, then tails off slowly; surface runoff decreases to zero.D: by this time there’s no more surface runoff, only decreasinggroundwater runoff.

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A B

C

D

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Isochrons of equal traveltimes of surface runoff

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The resistance equation for open channel flow

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α

α

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α

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α

α

Hydrostatic fluid pressure on both upstream and downstream are the sameand they act opposite to each other.

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α

α

W

)).(1.( WforceFrictional oτ=

Basal shear stress

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α

α αρ sin.).).(1.(weigththeof

componentDownstream

gAw=

A

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WgA

gAW

wo

wo

αρτ

αρτsin...

sin.).).(1.().1.(

=⇒

=

W

d αρτ sin....

gddWA

wo =⇒=

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Stream power

river bedFrom Burbank & Anderson, 2001

Δx

Δh Stream power = rate of change of potential energy

xtE

lengthunitpowerStream p

ΔΔ

Δ==Ω

.

xhgQQ

tm

tm

tVQ w

ww

w

ΔΔ

=Ω⇒=Δ

⇔Δ

=Δ

=....

.ρρ

ρ

SgQ w ...ρ=Ω⇒xhS

ΔΔ

=

xthgmhgmEp ΔΔ

Δ=Ω⇒Δ=Δ

.....Recall that change of potential energy

Discharge

Slope

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Stream power

river bedFrom Burbank & Anderson, 2001

Δx

ΔhSpecific Stream power = power available per unit area of the bed

WgQS

Wwρω =

Ω=

W

d

txSdg

txdWQ w Δ

Δ=⇒

ΔΔ

=ααρωαα cos/)cos()cos/)(cos(But

αα tanS that and,cos/ thatRecall =Δ

Δ=

txU

Udgw αρω sin So, = Uoτω =⇒

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Drainage networks

Drainage basins, watersheds, catchments

divide

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Drainage networks

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Drainage networks

Putorana Plateau, Russia

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Drainage networks

Canadian shield

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Drainage networks

Wyoming, USA

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Drainage networks

Cantal, France

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Drainage networks

Central Tibet

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Drainage networks

Strahler Stream OrderArthur Newell Strahler, 1918-2002

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Drainage networks

Order Number of Segments

Bifurcation Ratio

1 142 43 1

3.54

1

2

3

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Drainage networks

Order

Num

ber o

f Stre

ams

1 2 3 4 5

15

1050

Rb = 3.58

Order

Mea

n S

tream

Len

gth

1 2 3 4 5

900

2000

4000

Rl = 1.91

Order

Mea

n S

tream

Are

a

1 2 3 4 5

10^6

5*10

^65*

10^7 Ra = 4.65

Order

Mea

n S

tream

Slo

pe

1.0 1.5 2.0 2.5 3.0 3.5 4.0

0.05

0.10

Rs = 1.7

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Drainage networks

Link Contributing Area

Link

Slo

pe

5*10^4 5*10^5 5*10^6 5*10^7

0.00

50.

050

0.50

0

S ~ A^-0.35

Data from Reynolds Creek 30 m DEM, 50 grid cell threshold, points, individual links, big dots, bins of size 100

Flint’s Law

6.03.0. <<= − θθ avecAkS

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Drainage networks

Montgomery et al., 1996

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Drainage networks

Link Contributing Area

Long

est U

pstre

am L

engt

h

10^3 10^5 10^7 10^9

500

5000

5000

0L = 1.7 A^0.51

Hack’s Law

6.05.0. << havecACL hlα

dynamique des rivières - université de · pdf filetorrent st pierre, ecrins,...

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