Two-dimensional Two-dimensional morphological simulation in morphological simulation in

transcritical flowtranscritical flow

RCEM 2005RCEM 2005Urbana, October 5, 2005Urbana, October 5, 2005

www.PepeVasquez.cwww.PepeVasquez.comom

José A. Vásquez (UBC)José A. Vásquez (UBC)Robert G. Millar (UBC)Robert G. Millar (UBC)Peter M. Steffler (UoA)Peter M. Steffler (UoA)

University of British Columbia (UBC), Vancouver, University of British Columbia (UBC), Vancouver, CanadaCanada

University of Alberta (UoA), Edmonton, CanadaUniversity of Alberta (UoA), Edmonton, Canada

• Previous applications:Previous applications:– Bed aggradation and degradationBed aggradation and degradation– Meander scour and deposition.Meander scour and deposition.– Alternate bars in straight channels.Alternate bars in straight channels.– Dam-break.Dam-break.

• Knickpoint migration:Knickpoint migration:– Importance Importance – Results of the modelResults of the model

2D FE morphodynamic 2D FE morphodynamic model model

www.www.River2DRiver2D..caca 2D Hydrodynamic model. 2D Hydrodynamic model. Computes Computes uu, , vv and and hh..Developed by U of Alberta.Developed by U of Alberta.Finite Elements.Finite Elements.Sub- and Sub- and supercriticalsupercritical flows. flows.Steady and unsteady flows.Steady and unsteady flows.

Freely available.Freely available.Very robust and stable.Very robust and stable.Handles partially wet areas.Handles partially wet areas.FIXED BED.FIXED BED.

The Exner EquationThe Exner Equation(bedload sediment continuity)(bedload sediment continuity)

porosityporosityzzbb bed elevation (m) bed elevation (m)

qqss sediment transport rate (m sediment transport rate (m22/s)/s)

0)1(

y

q

x

q

t

z sysxb

tx

qqz

OUTs

INs

b

1

1For a 1D reach of lengthFor a 1D reach of lengthxx in a time interval in a time interval tt: :

0

0

OUTs

INs

OUTs

INs

qq

qq Aggradation (deposition)Aggradation (deposition)

Degradation (erosion)Degradation (erosion)

Bed aggradationBed aggradation due to sediment due to sediment over-loading (Soni over-loading (Soni et al. 1980)et al. 1980)

0.56

0.58

0.60

0.62

0.64

0.66

0.68

0.70

0.72

0.74

0 2 4 6 8 10 12 14 16 18 20 22

Channel distance (m)

Ele

vati

on

(cm

)

Original bed

Observed

Computed

0.15

0.17

0.19

0.21

0.23

0.25

0.27

0.29

0.31

0.33

0.35

0 2 4 6 8 10 12 14 16 18

Channel distance (m)

Ele

va

tio

n (

m)

Observed bed

Observed WSE

Computed bed

Computed WSE

Original bed

Bed Bed Degradation Degradation by shut-off of by shut-off of

sediment supplysediment supply

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 2 4 6 8 10

Distance / Width

Rel

ativ

e d

epth

Q = 170 L/sh = 20 cmS = 0.18 %

T6

BEND

b = 0.4fs = 2.0

Deposition

Scour

Computed

Measured

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 2 4 6 8 10

Distance / Width

Rel

ativ

e d

epth

Q = 170 L/sh = 20 cmS = 0.18 %

T6

BEND

b = 0.4fs = 2.0

Deposition

Scour

Computed

Measured

Bend scourBend scour

The Waal River (The Netherlands)

Deposition

Erosion

ErosionErosion

50 m from right bank-1969 SoundingsTransversal Bed Slope Shape Factor, fs

-7

-6

-5

-4

-3

-2

-1

0

0 1 2 3 4 5 6 7 8 9 10

Ce Distance (km))

Bed

Lev

el in

met

ers

bel

ow

OL

W62

-3.5

-2.5

-1.5

-0.5

0.5

1.5

2.5

3.5

Deposition

Deposition

Initiation of Alternate Bars in a straight flume

B/H = 34B/H = 34Fr = 0.69Fr = 0.69S = 0.452%S = 0.452%

Dam breakDam break

1 m

0.4 m

DAM

Q = 1 m3/s

0

0.1

0.2

0.3

0.4

0.5

0.6

-10 -7.5 -5 -2.5 0 2.5 5 7.5 10

0

0.1

0.2

0.3

0.4

0.5

0.6

-10 -7.5 -5 -2.5 0 2.5 5 7.5 10

0.40 m

0.12 m

INITIALLY WET INITIALLY DRY

Leal et al. 2003Leal et al. 2003

• Point of sudden change in the bed slope. Point of sudden change in the bed slope. Examples:Examples:

– Meander cut-offsMeander cut-offs– Dam removalDam removal– Bed dredgingBed dredging

Knickpoints Knickpoints

Cantelli et al. 2004Cantelli et al. 2004

Cui and Wilcock, in pressCui and Wilcock, in press

Knickpoint migration in tidal flatKnickpoint migration in tidal flat (Vancouver, (Vancouver, Canada)Canada)

19719700

19719799

20020022

20020044

Experiment of Experiment of Nickpoint Migration Nickpoint Migration (Brush and Wolman 1960)(Brush and Wolman 1960)

0.61

0.62

0.63

0.64

0.65

0.66

0.67

0.68

0.69

10 11 12

Channel distance (m)

Be

d E

lev

ati

on

(m

)

So =

10%

So = 0.125%

So = 0.125% Hydraulic Jump

Knickpoint

WSE

bed

Experiment of Experiment of Nickpoint Migration Nickpoint Migration (First 6 minutes...)(First 6 minutes...)

So =

10%

So = 0.125%

So = 0.125%Hydraulic Jump

Knickpoint

WSE

bed

0.62

0.63

0.64

0.65

0.66

0.67

0.68

8 9 10 11 12 13

0 min

1 min

6 min

Hydraulic jump

Knickpoint

WATER

BED

Experiment of Experiment of Nickpoint Migration Nickpoint Migration (Measurements at 160 minutes)(Measurements at 160 minutes)

0.61

0.62

0.63

0.64

0.65

0.66

0.67

0.68

0.69

0 2 4 6 8 10 12 14 16

Channel distance (m)

Be

d E

lev

ati

on

(m

)

Original

Computed

Measured

Knickpoint

WSE

bed

Qualitative Qualitative dyke-breach test dyke-breach test (Unsteady flow)(Unsteady flow)

0.62

0.63

0.64

0.65

0.66

0.67

10 10.5 11 11.5 12 12.5 13

Distance (m)

Ele

vati

on

(m

)Bed 0 s

Bed 10 s

Bed 60 s

W.S. 0 s

W.S. 10 s

W.S. 60 s

WSE

bed

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 60 120 180 240

Time (s)

Dis

char

ge

(L/s

)

x = 10 m

x = 13 m

DISCHARGE HYDROGRAPH

• River2D-MORphology is a 2D model River2D-MORphology is a 2D model based on triangular FE with capabilities for based on triangular FE with capabilities for transcritical flow morphology. transcritical flow morphology.

• The potential of the model in this field are:The potential of the model in this field are:– Dam removalDam removal– Dam-breakDam-break– Dyke breachDyke breach

• The model also have capabilities for The model also have capabilities for secondary flow in bends and transversal secondary flow in bends and transversal bed correction.bed correction.

In summaryIn summary

• In some problems of transcritical In some problems of transcritical morphology 2D effects such as sand bars, morphology 2D effects such as sand bars, meandering, channel widening might be meandering, channel widening might be important (e.g tidal flat, dam removal in important (e.g tidal flat, dam removal in meandering river) that do not warrant the meandering river) that do not warrant the application of a 1D model.application of a 1D model.

• Present limitations:Present limitations:– Uniform bed material sediment.Uniform bed material sediment.– Lack of numerical upwinding (not good for Lack of numerical upwinding (not good for

sediment waves).sediment waves).

...in summary...in summary