Rhine, Netherlands, flood 4 Nov 1998 (Wilbers & Ten Brinke, 2003)

The Impact ofVariability in Dune Dimensions on

Sediment Sorting and Morphodynamics

Astrid Blom

University of Twente US National Center for Earth-surface Dynamics (NCED)

km

bed levelm NAP

Blom et al., WRR, 2003Blom et al., WRR, 2003

Developments Developments

• Sediment continuity framework by Parker, Paola & Leclair (2000): active bed Sediment continuity framework by Parker, Paola & Leclair (2000): active bed described by described by PDF of bed surface elevationsPDF of bed surface elevations

• Extension to dunesExtension to dunes (Blom, 2003, Blom & Parker, 2004) (Blom, 2003, Blom & Parker, 2004)

• Present research: extension to Present research: extension to aggradational / degradational aggradational / degradational casescases

Continuity of non-uniform sedimentContinuity of non-uniform sediment

Existing bed layer models Existing bed layer models (e.g., Hirano, 1971)(e.g., Hirano, 1971)

• Useful, but…Useful, but…

• Inadequate description of sediment fluxesInadequate description of sediment fluxes

• Ellipticity of set of equationsEllipticity of set of equations

• Problematic definition of active layerProblematic definition of active layer

Case study Case study The Ribberink (1987) aggradation experimentThe Ribberink (1987) aggradation experiment

Three sediment continuity models:Three sediment continuity models:

A.A. The Hirano active layer modelThe Hirano active layer model

B.B. The sorting evolution model with The sorting evolution model with regular dunesregular dunes

C.C. The sorting evolution model with The sorting evolution model with irregular dunesirregular dunes

• Flow described using formulation Flow described using formulation backwater curvebackwater curve

• Simple power-based and Simple power-based and surface-basedsurface-based sub-model of sub-model ofsediment transport sediment transport (Ribberink, 1987)(Ribberink, 1987)

cb sediment concentration within the bed (cb= 1 - porosity)Fmi volume fraction content of size fraction i in the active layerFai volume fraction content of size fraction i in the transported sedimentFIi volume fraction content of size fraction i at the interfaceqa sediment transport rate thickness of active layerηI elevation of interface between active layer and substrate

Sediment continuity of active layer:Sediment continuity of active layer:

x

qF

t

ηFc

t

Fc aaiI

Iibmi

b

The Hirano active layer model (1971)The Hirano active layer model (1971)

substrate

active layerηI

Fmi

Faiqa

FIi

Ci concentration of size fraction i at level z (Ci= cb Ps Fi)

Ps probability that the bed level is higher than z

Fi volume fraction content of size fraction i at level z

Dei Eei deposition and entrainment densities of size fraction i at level z

cb sediment concentration within the bed (cb= 1 - porosity)

eieiisbi EDFPc

tt

C

a

x

z

~z

z

Ps

z

Fi

coarsecoarse

finefine

The sorting evolution model (Blom, 2003) The sorting evolution model (Blom, 2003) based on based on Parker-Paola-Leclair (2000) frameworkParker-Paola-Leclair (2000) framework

leelee

qqtoptop

stossstoss

z

x

• Apply theApply the Einstein step length Einstein step length formulation (Einstein, 1950) to the stoss face:formulation (Einstein, 1950) to the stoss face:

deterministic step lengthsdeterministic step lengthsii dΛ

)Λ(xE(x)D isiusiu

• At the lee face entrainment At the lee face entrainment neglectedneglected. Lee face deposition determined by a. Lee face deposition determined by alee sorting functionlee sorting function..

• OnlyOnly bed load transport. bed load transport.

N

ii2

1ii2

1siuis )Λ(xF)Λ(xEΛ(x)q

Sediment fluxes through Sediment fluxes through dune migrationdune migration

The sorting evolution modelThe sorting evolution model

Sediment fluxes through Sediment fluxes through dune migrationdune migration

variability in bedform dimensions variability in bedform dimensions

The sorting evolution modelThe sorting evolution model

(Leclair, 2002)(Leclair, 2002)

e.g. E(z) = e.g. E(z) = E Estossstoss(z) p(z) pbb d dηηbb

Sediment fluxes through Sediment fluxes through net aggradation / degradationnet aggradation / degradation

The sorting evolution modelThe sorting evolution model

• distributed over depth according to exposure to flowdistributed over depth according to exposure to flow

• composition of fluxes uniform over bed elevationscomposition of fluxes uniform over bed elevations

x

qpE-D ai

eaggr/degreiei

• Experiment E8-E9 by Experiment E8-E9 by Ribberink (1987)Ribberink (1987)

• 2 sand fractions2 sand fractions (0.78 mm, 1.29 mm) (0.78 mm, 1.29 mm)

• DunesDunes

• Start from exp E8Start from exp E8

• Over 30h, Over 30h, feed of finesfeed of fines was decreased to 0 was decreased to 0

• Total feed rateTotal feed rate was maintained was maintained steadysteady

The Ribberink aggradation experimentThe Ribberink aggradation experiment

Active part of the bedActive part of the bed

• Mean dune height and PDF troughs assumed steadyMean dune height and PDF troughs assumed steady

• Hydraulic roughness assumed steady (Ribberink, 1987)Hydraulic roughness assumed steady (Ribberink, 1987)

• Mean dune height Mean dune height = 3cm = 3cm

• Active layer thickness Active layer thickness = 1/2 = 1/2

Results: Results: Net aggradation or degradationNet aggradation or degradation

Results:Results: Composition Composition of of active part of bedactive part of bed

Results:Results: Composition Composition ofof bed load transport bed load transportat downstream end of flumeat downstream end of flume

Results: Results: Vertical sortingVertical sorting

• Note: no parameter tuningNote: no parameter tuning

• Taking into account the Taking into account the variability in dune dimensionsvariability in dune dimensions

• allows sediment to be ‘stored’ at lower elevationsallows sediment to be ‘stored’ at lower elevations

• improves the predicted adaptation time scalesimproves the predicted adaptation time scales

• improves the predicted sorting profileimproves the predicted sorting profile

• Reduction to a Reduction to a simplified modelsimplified model

• Applicable toApplicable to alternate bars? alternate bars? (data Lanzoni, Miwa)(data Lanzoni, Miwa)

• ModelModel PDF trough elevations PDF trough elevations (Van der Mark et al., 2005)(Van der Mark et al., 2005)

• New flume experimentsNew flume experiments at VTCHL at VTCHL

Discussion and conclusionsDiscussion and conclusions

The research project is supported by:The research project is supported by:

The Netherlands Organization for Scientific Research (NWO-STW)The Netherlands Organization for Scientific Research (NWO-STW)

University of Twente (Civil Engineering)University of Twente (Civil Engineering)

US National Center for Earth-surface Dynamics (NCED)US National Center for Earth-surface Dynamics (NCED)

The following persons have contributed to the work through discussion:The following persons have contributed to the work through discussion:

Gary Parker, Jan Ribberink, Maarten Kleinhans, Suzanne Hulscher, Gary Parker, Jan Ribberink, Maarten Kleinhans, Suzanne Hulscher,

Suzanne Leclair, Bert Jagers, Kees Sloff, Rolien van der Mark, and David Mohrig.Suzanne Leclair, Bert Jagers, Kees Sloff, Rolien van der Mark, and David Mohrig.

Case study 1: Results, composition active bedCase study 1: Results, composition active bed

leelee

qqtoptop

stossstoss

z

x

• Apply theApply the Einstein step length formulation Einstein step length formulation (Einstein, 1950) to the stoss face: (Einstein, 1950) to the stoss face:

deterministic step lengthsdeterministic step lengthsii dΛ

)Λ(xE(x)D isiusiu

The sorting evolution model (Blom, 2003)The sorting evolution model (Blom, 2003)

• At the lee face neglect entrainment. Lee face deposition determined by aAt the lee face neglect entrainment. Lee face deposition determined by anewly-developed newly-developed lee sorting function lee sorting function ii..

• OnlyOnly bed load transport. bed load transport.

N

ii2

1ii2

1siuis )Λ(xF)Λ(xEΛ(x)q

*z1*z ii

*

ba

imleei

proportion ofsize fraction

z

little coarser than mean grain size

coarse

mean grain size

*ztF

tz*,Fi

ilee,

ileeloc,

Lee sorting function Lee sorting function ii