The Waal (Ochten) anno 1830: Example: the River Allier, France · 2014-02-02 · 3 Long -term average flood Maximum and minimum annual discharge of the Rhine at Lobith 2000 0 4000

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Research group River and delta morphodynamics

Hydraulic Geometry How large is a river?

GEO3-4305, 2014

Dr. Maarten Kleinhans

[email protected]

www.geo.uu.nl/fg/mkleinhans

flow

sediment

transport

morphology

This course: the morphodynamic system

• Introduction

• River flooding

• Hydraulic roughness and

• Bedforms

• Sediment transport

• Mixture effects

• Channel dimensions

• Bars, bends, islands

• Overbank sedimentation

• Channel patterns

Introduction 1. Work done by floods – which floods?

2. Hydraulic geometry – prediction of width

• Parker E-book chapter 3, 2007 WRR paper

3. Partial explanations and future work

• bank stability

BIG QUESTIONS

1. How is channel geometry related to discharge and

how to incorporate meander geometry and floods?

2. Why do channels exist?

What processes explain the dimensions?

Definition of a channel during floods

Bankfull discharge:

width of natural channel, not artificial levees

■difficult! spatial variation in levee height, new banks

Q = uhW (continuity equation ~ mass

conservation)

floodplain width (artificial)

channel

width

channel depth

natural levee

(oeverwal) artificial levees

(winterdijk

of zomerdijk)

The Waal (Ochten) anno 1830: Low flow situation

Example: the River Allier, France • low flow situation

• flood: low-sloping

point bars submerged

2

Example: a river in Alaska, USA

Courtesy Addink

Example: the Amazon leveed

turbidity current channel on the shelf

Pirmez et al

Example: the

River

Waimakariri,

New Zealand

What discharge does most work?

Low flow

(Source: Rijkswaterstaat)

Large discharge

(Source:

Rijkswaterstaat Directie Oost-Nederland

/ Slagboom en Peeters Luchtfotografie,

20 March 2001 (7000m3/s)

Rhine, 1st bifurcation

Discharge peaks and work

Key point:

river channel dimensions

do not co-vary with discharge

during a flood

rather, channel dimensions depend on

an effective discharge

that summarises its variation

Flood probability

Herhalingstijden jaarlijkse afvoermaxima Rijn - Lobith

extrapolatie met kansverdeling

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

1 10 100 1000

herhalingstijd (jr)

afv

oer

(m3/s

)

1926 1995

1993

Recurrence time (yr)

dis

char

ge

3

Long-term average flood

Maximum and minimum annual discharge

of the Rhine at Lobith

0

2000

4000

6000

8000

10000

12000

14000

1900 1920 1940 1960 1980 2000

year

Bo

ven

rijn

dis

ch

arg

e (

m3/s

)

Channel-forming discharge definitions

Bankfull discharge

observed, depends on morphology

Discharge peak frequency

common: flood of once per 1-2.33 year

mean annual flood

Sediment-transport based

most efficient discharge frequency

discharge that transports annual sediment load

Transport efficiency of floods

Multiply sed tr rate with discharge probability

Q

Qs

Qs=u3 to 5

Q

probability

of Q

Qs

Two options:

1. peak of distribution

2. integral discharge that

transports annual sediment load

probability

of Qs

2 1

So, what discharge?

choice specified for relations in literature!

usually: bankfull discharge (+uncertainty)

long-term morphodynamic modelling of

channel:

discharge that transports annual sediment load

long-term morphodynamic modelling

of channel and floodplain??

2. Hydraulic geometry

Historically: regime equations for stable

(irrigation) canal design ■e.g. Lacey (1929) (Punjab)

At-a-station hydraulic geometry

empirical (many streams) ■ e.g. Leopold & Maddock 1953

computer class!

Downstream hydraulic geometry

increasing W,h with increasing catchment A

changes along the river (from highland to lowland)

Why channels exist...

upstream water and sediment feed

water carries sediment more effectively in

flows deeper than thin sheets

will carve a channel

4

At-a-station hydraulic geometry

Lacey type:

perimeter P = aQ1/2 a~4.84

hyd radius R = bQ1/3D1/6 b~0.41

velocity u = cQ1/6D1/6 c~0.50

Leopold-Maddock type (Hey & Thorne 1986):

width w = aQp a~3.67 p~0.45

depth h = bQq b~0.33 q~0.35

velocity u = cQr c~0.83 r~0.20

what are relations between a,b,c and p,q,r ?

Effect of vegetation

1. grassy banks w = 4.33Q0.5

2. 1-5% tree/shrub cover w = 3.33Q0.5

3. 5-50% tree/shrub cover w = 2.73Q0.5

4. >50% tree/shrub cover w = 2.34Q0.5 (Hey & Thorne 1986)

Many other equations

sand/gravel, meandering/braided

Why does vegetation matter?

Consistent predictors for gravel beds

nondimensional width, depth:

relations:

a=4.63, p=0.0667

b=0.382, q=-0.0004

d=0.101, s=0.344

u = Q/(Wh) Parker et al. 2007, J. Geophys. Res., 112, F04005,

doi:10.1029/2006JF000549

5/2

5/1

5/2

5/1

2

~,

~,

~

bf

bf

bf

bfbf

Q

hgh

Q

WgW

DgD

QQ

sqp QdSQbhQaW~

,~~

,~~

Example calculations

Do Lacey, Hey-Thorne and Parker et al.

calculate W,h,u

two rivers:

Q = 2500 m3/s

D = 0.3 or 3 mm

Downstream geometry (1): slope

Concave long-profiles

slope decreases downstream

logarithmic or exponential approximation

Why?

mountains do not have straight slopes

discharge increases downstream (tributaries)

sediment transport capacity increases

downstream fining?

S = aQb Dc

a ~ 0.05, b ~ -0.4, c ~ 0.7

Knighton fig 5.26

5

Downstream geometry (2)

imagine a river:

with increasing downstream discharge

decreasing downstream grain size

and increasing downstream silt-clay deposition

S = 0.05 Q-0.4 D0.7

w = 5.54 Q0.58 M-0.37 M=%mud

h = 0.12 Q0.42 M0.35

Schumm (1971, eq. 5.23-24 in Knighton p. 175)

Downstream implications?

Downstream implications

decreasing slope

higher water levels, longer backwaters

flow deceleration despite Q increase!

mud deposition!!

slowing increase of width

mud deposition increases strength of banks

faster increase of depth

width-depth ratio smaller

change from braided to meandering

pattern possible

Threshold channel concept

Imagine river in sand without mud / vegetation

θc,banks < θc,bed (slope of bank!)

initially: θ >> θc

so, erosion of bank toe and collapse of bank!

eroded sediment deposited on bed

shallowing

continue until θ = θc in bankfull conditions

‘threshold channel’

Example: the

River

Waimakariri,

New Zealand

Effect on bankfull Shields number

threshold channels: θbf ~ 1.2θc ~ 0.02-0.06

channels with cohesive banks: higher

Parker hypothesis E-book chapter 3, 24

next class: channel patterns

effect of width on bar pattern

effect of bank strength on channel pattern

Bank strength! Now add vegetation (roots) or mud to bank

equilibrium channel will be narrower

bank strength:

bank height and gradient

soil cohesion

root strength

Coulomb friction (remember Mohr circles?)

hydraulic head

■water inflow before flood and outflow after flood

banks weaker after flood peak

NB capacity to remove eroded bank material

6

Example: the River Allier, France • low flow situation

• flood: low-sloping

point bars submerged

Bank erosion is not simple

An

dre

w S

imo

n e

t a

l (U

SG

S)

Slingebeek

Brahmaputra

Bank stability and toe erosion model

Andrew Simon et al (USGS)

Mohr-Coulomb equation:

where

τf = shear stress at failure (Pa)

σ = normal stress (Pa)

μw = pore-water pressure (Pa)

φ’ = effective angle of internal friction

c' =effective cohesion (Pa)

■ chemical bonding, plant roots!

'tan' wfailure c

http://www.ars.usda.gov/Research/docs.htm?docid=5044

Geometry of meanders

Empirical relations

discharge

wavelength

→ e.g. λ=10W

7

Bend migration

Sharper bend, faster erosion

why the optimum?

Empirical curves

bend in theerosion M

tcoefficien and radius bend critical with

:/for and

: caseIn

2

2

kc

cW

rk

W

McWr

r

cWk

W

Mcr/W

Allier Big questions

How is channel geometry related to

discharge and how to incorporate meander

geometry and floods?

Why do channels exist? What processes

explain the dimensions?