Maarten KleinhansBifurcation evolution in meander ing r ivers with adapting widths

Acknowledgements• grantALW-VENI-863.04.016

• Kim Cohen, Esther Stouthamer, Marco van Egmond• JantineHoekstra, Janneke IJmker

• Norm Smith• Erik Mosselman, Kees Sloff, Bert Jagers

H51A-0172

Objective: • model bifurcation evolution and avulsion duration• determine most impor tant factors for duration with model• ver ify on the wor lds best-mapped case: the r iver Rhine

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Waal wins

Nederrijn wins

same length Waal 14% shorter same length +bend Waal 14% shorter +bendno width adaptation

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R/W=inf sin amp 1000m 250yr sin amp -1000m 250yrsin amp 2000m 250yr sin amp -2000m 250yr

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R/W=inf sin amp 1000m 500yr sin amp -1000m 500yrsin amp 2000m 500yr sin amp -2000m 500yr

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HW Rijnice dams

less floodsless bank erosion

more floodsmore bank erosion

Fig. 2. Meander migration at the bifurcation(historical maps redrawn by Van de Ven 1976)

Duration of the last major Rhine avulsion

Fig. 3. 1595 AD map1751 AD map

Residual Rhine channelfar downstream.Silt/clay + organics fill.

Residual Rhine channel near entrance (view on Lobith). Fining-upward sand fill on old sand-gravel channel bed.(Prelim hand coring results Hoekstra & IJmker)

Processes at the bifurcation: meander ing and width adaptation

Conclusions1. Avulsion/bifurcation evolution is strongly forced by meander ing

• in competition with gradient advantage• migrating bend at bifurcation causes fluctuations in discharge division • migrating bends give net faster change than gradient advantage alone

2. Dynamically stable bifurcations do not exist• except when highly asymmetrical i.e. as residual channels, or when exactly equal bifurcates• bifurcations only stabilise (statically) by bank and bed protection (e.g. armouring,

resistive clay, vegetation, bank protection works) of the enlarging bifurcate• evolution can be very slow when gradient advantage and bend effects balance

3. Avulsion is strongly slowed down by width adaptation,i.e. bank and floodplain evolution• too simplified here but nothing better available!

4. Neder r ij n-Waal avulsion evolution forced by meander ing• and gradient advantage• but slowed down by width-adaptation• not affected by sea level rise or tectonics• modelled avulsion duration with realistic bends 1500-2500 years in agreement with data

• Avulsion duration: ~2000 yearsdefined as 10→90% discharge

• Initiation: last centuries BC• several parallel channels• Evolution:• in 325 AD one Waal channel• 12th century discharge Nederrijn

decreased

Meander bend upstream of/at bifurcation:• migrated downstream into bifurcation• favoured Waal with flow and

favoured Nederrijn with sediment

Fig. 1. Geological maps showing the avulsion of the river Rhine to the south

Width and depth evolution• Nederrijn silted up and

narrowed further, vegetated• 1700: avulsion finished

Q

H

Model formulation1. Three 1D model branches: 1 upstream and 2 bifurcates

• Specified: upstream discharge Q, downstream water level H, roughness ks,initial slope S or length L to the sea, grain size D

2. Branches connected at a nodal point• flow division: from backwaters of bifurcates• sediment division: nodal point relation Kleinhans et al. WRR

3. Width W adjustment to discharge• Weq = aQb, dW/dt = (Weq-W)/TW (relaxation, conserve sediment in bed)

4. Nodal point relation• sediment division proportional to width, but• modified by transverse slope effect and spiral flow of bend with radius R

5. Novelty: • meander effect at bifurcation• coupling bank erosion / bank deposition to bed sediment balance

1D model ‘validation’ on 3D modelDetailed data unavailable, consider detailed 3D model as ‘ truth’• Delft3D model software• curvilinear grid, preformed bend, fixed banks• same parameters as in 1D model• scenarios for gradient versus bend advantage

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Delft3D flow division

1D flow division

inner-bend bifurcate wins

outer wins

inner-bend bifurcate wins

outer wins

Fig. 4.Discharge division

evolving in 50 years:3D and 1D model

show similar behaviour.

Bed elevation maps in 3D model after 6 years illustrating bend morphology and bifurcation response (coordinates in m)

Model resultsFig. 5. Discharge division evolving in 2500 years:

Effects of gradient advantage of one bifurcate and/or a fixed bend at the bifurcation

Fig. 6. Discharge division and width evolving in 2500 years:Effects of migrating sinusoidal bends at the bifurcation

Standard scenar ios• same length or Waal 14% shorter• bend R/W=4 much larger effect• faster without width adaptation

Gradient of the Waal• with bend R/W=4• bend compensates ~15% longer

Fixed bend at bifurcation• with Waal 14% shor ter• bends in both directions

Fast migrating bend• net faster than gradient advantage alone

Slow migrating bend• much faster than fast bend• avulsion duration depends on initial position of the bend

Width of slow migrating bend• time-adaptation near ly immediate• wide residual channels• sudden rapid changes

Faculty of GeosciencesUtrecht University

the Netherlandswww.geog.uu.nl/fg/mkleinhans

m.kleinhans@geo.uu.nl

How general is meander ing effect and narrowing?Clear cases where meander at bifurcation favoursouter-bend branch:1. two man-made bifurcations in the Netherlands2. Ganges-Gorai bifurcation3. two Saskatchewan bifurcations in the Cumberland Marshes (see Smith et al. (1998):

Old Channel

New Channel

Saskatchewan New Channel

Steamboat channel

Centre Angling

abandoned channelin outer bend:older but kept open

abandoned channelin inner bend: youngerand more closed

Work in progress1. This work extended:

Kleinhans (River Flow 2008); Kleinhans, Cohen & Stouthamer (in prep)2. 3D modelling of bifurcations in meandering rivers:

Kleinhans, Jagers, Mosselman & Sloff WRR (in review)3. Case study of avulsion splay and upstream channel evolution:

Kleinhans, Weerts& Cohen (RCEM 2007)4. Sediment transport and morphodynamicsat three Rhine bifurcations:

Frings& Kleinhans Sedimentology (accepted)Kleinhans, Wilbersand Ten Brinke (2007) Netherlands J. of Geoscience

5. Sedimentology of closed bifurcates and residual channels in the RhineKleinhans, Hoekstra, IJmker & Cohen (in prep)

Problem: What determines bifurcation stability and avulsion duration?

bend R/W=100bend R/W=10bend R/W=4 (sharpest)

Only bend, equal bifurcates:

bend R/W=100bend R/W=10bend R/W=4 (sharpest)

Inner-bend branch 10% steeper:

WangBolla

Other nodal point relations:x x

++

North Sea

Belgium

100 km

Netherlands

England

Germany

Waal system

Nederrijn system

Bifurcation/avulsion

after Berendsen & Stouthamer (2000)Paleogeography 3200 yr BP

Paleogeography 1250 yr BP