Dynamique des plages sableuses soumises à l'action des ...

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Dynamique des plages sableuses soumisesà l'action des vagues, de la maréeet des rechargements articiels

David MORELLATO

18 décembre 2008

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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions

Content

1 Introduction

2 Models description

3 Model validation on Deltaume

4 Model validation on Pentrez beach

5 Inuences of waves and tide on a plane sloping beach

6 Articial nourishment study

7 Conclusions

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Content

1 Introduction






7 Conclusions

4/59


Examples of bar systems

3D Sandbars

Truc Vert beach (FR)

Omaha beach (FR)

Longshore Sandbars

Wessex Coast (UK)

Egmond aan Zee (NL)

5/59


Masselink and Short (1993) conceptual beach model

6/59


Time and space scales of the inner-shelf morphodynamicsystem

7/59


Cross-shore processes on sandy beaches

8/59


Topic : dynamic of sandy beaches under waves, tide andarticial nourishments

Questions

How to model cross-shore processes ?

What is the fastest-most accurate way to model beachevolutions ?

What are the eects of waves and tide on beach morphology ?

What is the best way to nourish a beach ?

9/59


Content

1 Introduction






7 Conclusions

10/59


Morphodynamic model

Oceanographic forcing(waves, tide)

FUNWAVE 1D(waves)

1DH sediment transport model(currents and sediment transport)

MORPHOLOGIC EVOLUTION

Morphodynamic Model

t + t

2DV sediment transport model(currents, turbulence

and sediment transport)

11/59


Wave model

Wave model FUNWAVE (Kirby et al., 1998)

Based on Wei et al. (1995)'s equations :

ηt + Mx = 0

uαt + uαuαx + gηx + V = 0

M = (h + η)

»uα +

„zα +

1

2(h − η)

«(huα)xx

+

„1

2z2α −

1

6

“h2 − hη + η

2”«

uαxx

–V = zα

1

2zαuαtxx + (huαt )xx

ff+

1

2

“z2α − η

2”uαuαxx +

1

2

ˆ(huα)x + ηuαx

˜2ffx

+

(zα − η) uα (huα)xx − η

»1

2ηuαtx + (huαt )x

–ffx

with η the free surface, h the water depth and uα the horizontal velocity at zα = 0.531h

uFUNWAVE (z) = uα + z2α−z22

uαxx + (zα − z) (huα)xx

12/59


Wave model

Wave processes and FUNWAVE (Kirby et al., 1998)

Bottom friction Fb = Kgh+ηuα|uα| including wave-ripples

predictors of Nielsen (1992),

Streaming neglected,

Wave breaking from Kennedy et al. (2000) : eddy viscosity ofZelt (1991) and realistic description of the initiation/cessationof wave breaking of Schäer et al. (1993) on free surface slope,

Undertow not well reproducedin uFUNWAVE (z). Needs acorrection :

1st option : Post-treatment ofLynett (2006)2nd option : Turbulenceclosure vertical model

13/59


1DH sediment transport model

Bailard's total transport formula (1981) : bedload and suspension

q1DH(x) = qc0(x) + qcβ(x) + qs0(x) + qsβ(x)

qc0(x) = Cf εc2g(s−1) tanφ |u(x ,−h, t)|2 u(x ,−h, t)

qcβ(x) = − Cf εc2g(s−1) tan2 φ

|u(x ,−h, t)|3β(x)

qs0(x) = Cf εs2g(s−1)wf

|u(x ,−h, t)|3

qsβ(x) = − Cf ε2s

2g(s−1)w2f

|u(x ,−h, t)|5β(x)

Lynett's model (2006)

uLYNETT(z) = uFUNWAVE(z) + uB(z)withuB(z) = δbreaking switch(C roller− uFUNWAVE(η)) exp(k(z−η))−exp(k(zB−η))

1−exp(k(zB−η))δbreaking switch=0 ou 1

14/59


2DV sediment transport model

Turbulence closure vertical model

∂u

∂t−

σ

H

∂η

∂t

∂u

∂σ=

∂u0

∂t+

∂

∂σ

„νt

∂u

∂σ

«1

H2−

1

ρw

∂τzx

∂z

∂k

∂t−

σ

H

∂η

∂t

∂k

∂σ=

1

H2

∂

∂σ

νt

σk

∂k

∂σ

!+

νt

H2

„∂u

∂σ

«2− Cν

k32

lwith νt = l

√k

∂C

∂t−

σ

H

∂η

∂t

∂C

∂σ=

1

H

∂

∂σ

ˆ`wf− wσ

´C˜

+1

H2

∂

∂σ

„εsd

∂C

∂σ

«with ε

sd= νt

q2DV (x) = qsu (x) + qsw (x) + qsl

(x) + qc (x)

q2DV (x) =RHz0

C(z)u(z)dz +RHz0

C(z)uw (z, t)dz +RHz0

C(z)Ul(z)dz + qc0 + qcβ

15/59


Morphologic evolution

Sediment conservation law

∂h∂t = 1

1−ε∂q∂x

resolved with a modied-Lax scheme (idem Rakha et al., 1997)

Tide eects

Water level constant during a morphodynamic step ∆t

(typically 10 minutes)

No tidal currents

Tidal signal :

Sinusoidal (TM2=12H25mn)Spring-to-spring tidal cycle (TM2=12H25mn, TS2=12H00mn)Experimental data

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Two morphodynamic models

FUNBEACH 1DH

Hm0

(x), η(x)

Bathymetry Forcing : wave, tide

Wave model : FUNWAVE 1D

Lynett model

Transport model

Ripple predictor

t+Δt : new h(x)

urms

(x)

fw(x)

q(x)

η0(t), η

0 h(x)

u(x,-h,t)

η(x,t), uα(x,t)

Model /experimental

data

u(x,z),u

rms(x,z)

q(x)

h(x)

fw(x)

FUNBEACH 2DV

Hm0

(x), η(x)

Bathymetry

Hydrosedimentary model: suspension transport

Forcing : wave, tide

Wave model : FUNWAVE 1D

Hydrodynamic model

Bedload transport model

Ripple predictor

t+Δt : new h(x)

urms

(x)

fw(x)

qs(x)q

c(x)

η0(t), η

0 h(x)

u(x,z,t), u*(x,t)

η(x,t), uα(x,t)

Model /experimental

data

q(x)

h(x)

z0(x)

u(x,z),u

rms(x,z)

C(x,z),C

rms(x,z)

u(x,0,t)fw(x)

Validation

Large wave tank experiments : Delta ume'93

Field measurements : Pentrez beach

17/59


Content

1 Introduction






7 Conclusions

18/59


Delta Flume'93 data description

20 40 60 80 100 120 140 160 180 2000

5

10

15

t (h)

65 102 115 130

138145

152160 170

P1.1

P1.2

P2.1

P2.2

P3.1

P3.2

P4.1

P4.2 P5

P6P7

P8P9

U + CU

20 40 60 80 100 120 140 160 180 200−4

−3

−2

−1

0

1

x (m)

z (m

)

1h17h

Test 1b

Hm0 ' 1.40 m, Tp ' 5 s

Duration : 17 H

Oshore bar migration

20 40 60 80 100 120 140 160 180 2000

5

10

t (h)

65 102 115 125130

134138

145152

160 170

Q1

Q2Q3

Q4Q5

Q6Q7

Q8Q9

Q10Q11U + C

U

20 40 60 80 100 120 140 160 180 200−4

−3

−2

−1

0

1

x (m)

z (m

)

1h13h

Test 1c

Hm0 ' 0.60 m, Tp ' 8 s

Duration : 13 H

Onshore bar migration

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Test 1b : Hm0and η

20 40 60 80 100 120 140 160 180 2000

0.5

1

1.5

2H

m0(m

)LIP 11D : Test 1b ( t =1h )

Model dataExperimental data

20 40 60 80 100 120 140 160 180 200−0.1

−0.05

0

0.05

0.1

η (m

)

20 40 60 80 100 120 140 160 180 200−4

−3

−2

−1

0

1

z(m

)

x(m)

20/59


Test 1b : U

−0.4−0.2 0 0.20

1

2

3P1.1

z (m

)

−0.4−0.2 0 0.20

1

2

3P2.1

−0.4−0.2 0 0.20

1

2

3P3.1

−0.4−0.2 0 0.20

1

2

3P4.1

U (m/s)

−0.4−0.2 0 0.20

1

2

3P6

U (m/s)−0.4−0.2 0 0.20

1

2

3P7

U (m/s)−0.4−0.2 0 0.20

1

2

3P8

U (m/s)−0.4−0.2 0 0.20

1

2

3P9

U (m/s)

−0.4−0.2 0 0.20

1

2

3P1.2

−0.4−0.2 0 0.20

1

2

3P2.2

−0.4−0.2 0 0.20

1

2

3P3.2

−0.4−0.2 0 0.20

1

2

3P4.2

z (m

)

U (m/s)−0.4−0.2 0 0.20

1

2

3P5

U (m/s)

Experimental dataWave model dataLynett model dataVertical model data

20 40 60 80 100 120 140 160 180 200−4

−3

−2

−1

0

1

z (m

)

x (m)

65 102 115 130 138 145 152 160 170

P1.1P1.2

P2.1P2.2

P3.1P3.2

P4.1P4.2

P5 P6 P7 P8 P9

21/59


Test 1b : C

0 1 2 30

1

2

3P1.1

z(m

)

0 1 2 30

1

2

3P2.1

0 1 2 30

1

2

3P3.1

0 1 2 30

1

2

3P4.1

C (g/L)

0 1 2 30

1

2

3P6

C (g/L)0 1 2 3

0

1

2

3P7

C (g/L)0 1 2 3

0

1

2

3P9

C (g/L)

0 1 2 30

1

2

3P2.2

0 1 2 30

1

2

3P3.2

0 1 2 30

1

2

3P4.2

z (m

)

C (g/L)0 1 2 3

0

1

2

3P5

C (g/L)

Experimental dataVertical model data

20 40 60 80 100 120 140 160 180 200−4

−3

−2

−1

0

1

z (m

)

x (m)

65 102 115 130 138 145 152 170

P1.1 P2.1P2.2

P3.1P3.2

P4.1P4.2

P5 P6 P7 P9

22/59


Test 1b : transport rates (rst time step) and cross-shoreprole evolution

0 20 40 60 80 100 120 140 160 180 200−5

−4

−3

−2

−1

0

1

2

3

4

5x 10

−5q(

m2 .s

−1 )

x(m)

q

DATA

q2DV

q1DH

q1DH

without LYNETT

100 110 120 130 140 150 160 170 180−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

z(m

)

x(m)

Initial measured cross−shore profileFinal measured cross−shore profileFinal calculated cross−shore profile

23/59


Test 1c : Hm0and η

20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

1H

m0(m

)LIP 11D : Test 1c ( t =1h )

Model dataExperimental data

20 40 60 80 100 120 140 160 180 200−0.05

0

0.05

η (m

)

20 40 60 80 100 120 140 160 180 200−4

−3

−2

−1

0

1

z(m

)

x(m)

24/59


Test 1c : U

−0.4−0.2 0 0.20

1

2

3Q1

z(m

)

−0.4−0.2 0 0.20

1

2

3Q3

−0.4−0.2 0 0.20

1

2

3Q2

−0.4−0.2 0 0.20

1

2

3Q5

−0.4−0.2 0 0.20

1

2

3Q4

−0.4−0.2 0 0.20

1

2

3Q6

U (m/s)

−0.4−0.2 0 0.20

1

2

3Q7

z(m

)

U (m/s)−0.4−0.2 0 0.20

1

2

3Q8

U (m/s)−0.4−0.2 0 0.20

1

2

3Q9

U (m/s)−0.4−0.2 0 0.20

1

2

3Q10

U (m/s)−0.4−0.2 0 0.20

1

2

3Q11

U (m/s)

Experimental dataWave model dataLynett model dataVertical model data

20 40 60 80 100 120 140 160 180 200−4

−3

−2

−1

0

1

z (m

)

x (m)

65 102 115 125130134138145 152 160 170

Q1 Q2 Q3 Q4Q5

Q6Q7

Q8 Q9 Q10 Q11

25/59


Test 1c : C

0 0.5 10

1

2

3Q1

z (m

)

0 0.5 10

1

2

3Q3

0 0.5 10

1

2

3Q2

0 0.5 10

1

2

3Q5

C (g/L)0 0.5 1

0

1

2

3Q4

0 0.5 10

1

2

3Q6

C (g/L)

z (m

)

0 0.5 10

1

2

3Q9

C (g/L)0 0.5 1

0

1

2

3Q10

C (g/L)0 0.5 1

0

1

2

3Q11

C (g/L)

Experimental dataVertical model data

20 40 60 80 100 120 140 160 180 200−4

−3

−2

−1

0

1

z (m

)

x (m)

65 102 115 125130134 152 160 170

Q1 Q2 Q3 Q4Q5

Q6 Q9 Q10 Q11

26/59


Test 1c : transport rates (rst time step) and cross-shoreprole evolution

0 20 40 60 80 100 120 140 160 180 200−2

−1.5

−1

−0.5

0

0.5

1

1.5

2x 10

−5q

(m2 .s

−1 )

x (m)

q

DATA

q2DV

q1DH

q1DH

with undertow correction

100 110 120 130 140 150 160 170 180−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

z(m

)

x(m)

Initial measured cross−shore profileFinal measured cross−shore profileFinal calculated cross−shore profileFinal calculated cross−shore profile (with correction)

27/59


To conclude with Delta Flume experiments :

Synthesis

Good estimation of wave heights, water level, mean velocitiesand mean concentrations of sediment by FUNBEACH,

Good estimation of bar movement for test 1b,

Poor estimation of bar evolutions for test 1c which highlightsthe interest of estimating correctly the bottom velocities(undertow) to get better morphologic predictions,

Due to long computational time and numerical instabilities forFUNBEACH 2DV, establishing of a method of computation :

Calibration of the 2DV transport model on velocity andconcentrations experimental data,Calibration of the 1DH transport model on the 2DV transportmodel in terms of transport rates,Morphologic evolution calculated with FUNBEACH 1DH.

28/59


Content

1 Introduction






7 Conclusions

29/59


Pentrez beach in the bay of Douarnenez

30/59


Pentrez beach and topographic survey

−550 −500 −450 −400 −350 −300 −250 −200 −150 −100 −50 0

2

4

6

8

10

12

14

x(m)

z(m

)

April 27th 2005June 22th 2005September 19th 2005December 15th 2005April 18th 2006September 26th 2006October 26th 2006April 19th 2007October 26th 2007

Macrotidal beach (TR > 4m) with weak tidal currents,

Cross-shore conguration (longshore currents neglected),

Swell with spilling breakers,

Weak morphologic evolution (maximum of 40 cm in theintertidal zone during 30 months).

31/59


MII : Mât Instrumenté en zone Intertidale

3 or 4 Acoustic DopplerVelocimeters VECTOR,

3 or 4 OBS turbidimeters.

at 30, 60, 90 (and 120 cm)over the bottom.

in addition to an oshore(z=-10m) wave sensor.

32/59


Pentrez beach Campains

Campains oshore sensor intertidal sensors Tidal coecients

PENTREZ#1 Wave rider S4DW velocimeter 42 to 62

PENTREZ#2 Wave rider 2 ADV VECTOR 86 to 105

PENTREZ#3 S4DW MII#4 56 to 74

PENTREZ#4 Wave rider MII#3 62 to 96

PENTREZ#3 :18-20 october 2006

PENTREZ#4 :14-16 april 2007

Continuous data acquisition during 46 hours.

33/59


Spectral wave heights and wave spectrum

PENTREZ#3 : Wind Waves

0 0.05 0.1 0.15 0.2 0.25 0.30

0.5

1

1.5

2

2.5

3

f (Hz)

E (

m2 .s

)

PENTREZ 3

t=35H00

0 5 10 15 20 25 30 35 40 450

1

2

3

4

5

6

t (hours)

Hm

0 (m

)

PENTREZ 3

S4DW : −10 mMII−4Offshore

PENTREZ#4 : Swell

0 0.05 0.1 0.15 0.2 0.25 0.30

0.5

1

1.5

2

2.5

3

f (Hz)

E (

m2 .s

)

PENTREZ 4

t=17H00

0 5 10 15 20 25 30 35 40 450

1

2

3

4

5

6

t (hours)

Hm

0 (m

)

PENTREZ 4

DWD : −10 mMII−3Offshore

34/59


Experimental data analysis : PENTREZ#3

0 5 10 15 20 25 30 35 40 450

1

2

3

4

5

Wat

er L

evel

(m

)

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

Hm

0 (m

)

0 5 10 15 20 25 30 35 40 45−0.5

0

0.5

U (

m/s

)

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

Urm

s (m

/s)

0 5 10 15 20 25 30 35 40 45−0.5

0

0.5

V (

m/s

)

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

Vrm

s (m

/s)

30 cm60 cm90 cm120 cm

0 5 10 15 20 25 30 35 40 450

1

2

3

C (

g/L)

t (hours)0 5 10 15 20 25 30 35 40 45

0

1

2

3

Crm

s (g

/L)

t (hours)

35/59


Experimental data analysis : PENTREZ#4

0 5 10 15 20 25 30 35 40 450

1

2

3

4

5

Wat

er L

evel

(m

)

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

Hm

0 (m

)

0 5 10 15 20 25 30 35 40 45

−0.2

−0.1

0

0.1

0.2

0.3

U (

m/s

)

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

Urm

s (m

/s)

30 cm60 cm90 cm

0 5 10 15 20 25 30 35 40 45

−0.2

−0.1

0

0.1

0.2

0.3

V (

m/s

)

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

Vrm

s (m

/s)

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

C (

g/L)

t (hours)0 5 10 15 20 25 30 35 40 45

0

0.2

0.4

0.6

0.8

1

Crm

s (g

/L)

t (hours)

36/59


Experimental vs. FUNWAVE : wave heights

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2PENTREZ 3 : MII−4

Hm

0 (m

)

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2PENTREZ 4 : MII−3

Hm

0 (m

)

t (hours)

Model FUNWAVE dataExperimental data

37/59


Experimental vs. models : mean velocities

PENTREZ#3

0 5 10 15 20 25 30 35 40 45

−0.2

−0.1

0

0.1

0.2

0.3

U(3

0cm

) (m

/s)

PENTREZ 3: MII−4

0 5 10 15 20 25 30 35 40 45

−0.2

−0.1

0

0.1

0.2

0.3

U(6

0cm

) (m

/s)

0 5 10 15 20 25 30 35 40 45

−0.2

−0.1

0

0.1

0.2

0.3

U(9

0cm

) (m

/s)

0 5 10 15 20 25 30 35 40 45

−0.2

−0.1

0

0.1

0.2

0.3

U(1

20cm

) (m

/s)

t (hours)

PENTREZ#4

0 5 10 15 20 25 30 35 40 45

−0.2

−0.1

0

0.1

0.2

0.3

U(3

0cm

) (m

/s)

PENTREZ 4: MII−3

Vertical model dataLynett model dataTidal−corrected experimental data

0 5 10 15 20 25 30 35 40 45

−0.2

−0.1

0

0.1

0.2

0.3

U(6

0cm

) (m

/s)

0 5 10 15 20 25 30 35 40 45

−0.2

−0.1

0

0.1

0.2

0.3

U(9

0cm

) (m

/s)

t (hours)

38/59


Experimental vs. models : RMS velocities

PENTREZ#3

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

Urm

s(30c

m)

(m/s

)

PENTREZ 3: MII−4

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

Urm

s(60c

m)

(m/s

)

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

Urm

s(90c

m)

(m/s

)

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

Urm

s(120

cm)

(m/s

)

t (hours)

PENTREZ#4

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

Urm

s(30c

m)

(m/s

)

PENTREZ 4: MII−3

Vertical Model dataLynett Model dataExperimental data

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

Urm

s(60c

m)

(m/s

)

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

Urm

s(90c

m)

(m/s

)

t (hours)

39/59


Experimental vs. 2DV model : mean concentrations

PENTREZ#3

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

C(3

0cm

) (m

/s)

PENTREZ 3: MII−4

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

C(6

0cm

) (g

/L)

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

C(9

0cm

) (g

/L)

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

C(1

20cm

) (g

/L)

t (hours)

PENTREZ#4

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

C(3

0cm

) (g

/L)

PENTREZ 4: MII−3

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

C(6

0cm

) (g

/L)

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

C(9

0cm

) (g

/L)

t (hours)

Vertical Model dataExperimental data

40/59


Experimental vs. 2DV model : RMS concentrations

PENTREZ#3

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

Crm

s(30c

m)

(m/s

)

PENTREZ 3: MII−4

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

Crm

s(60c

m)

(g/L

)

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

Crm

s(90c

m)

(g/L

)

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

Crm

s(120

cm)

(g/L

)

t (hours)

PENTREZ#4

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

Crm

s(30c

m)

(g/L

)

PENTREZ 4: MII−3

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

Crm

s(60c

m)

(g/L

)

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

Crm

s(90c

m)

(g/L

)

t (hours)


41/59


Predicted transport rates

PENTREZ#3

0 5 10 15 20 25 30 35 40 45−1

0

1x 10

−4

q (m

2 .s−

1 )

t (hours)

q

1DH

q2DV

PENTREZ#4

0 5 10 15 20 25 30 35 40 45−2

−1.5

−1

−0.5

0

0.5

1

1.5

2x 10

−5

q (m

2 .s−

1 )

t (hours)

q

1DH

q2DV

42/59


Predicted Spring-to-Spring morphologic evolution onPentrez beach

0 50 100 150 200 250 300 3502

4

6

8

z(m

)

0 50 100 150 200 250 300 3500

0.1

0.2

0.3

0.4

0.5

dh+ m

ax (

m)

H

m0=0.4m

Hm0

=0.8m

Hm0

=1.2m

Hm0

=1.6m

0 50 100 150 200 250 300 3502

4

6

8

z(m

)

0 50 100 150 200 250 300 3500

0.1

0.2

0.3

0.4

0.5

t (hours)

dh+ m

ax (

m)

H

m0=0.4m

Hm0

=0.8m

Hm0

=1.2m

Hm0

=1.6m

43/59


To conclude with Pentrez beach measurements :

Synthesis

Good estimation of wave heights by FUNWAVE 1D,

Good estimation of mean and RMS velocities by FUNBEACH2DV and FUNBEACH 1DH,

Good estimation of mean concentration of sediment andworser estimation of RMS concentration of sediment byFUNBEACH 2DV,

FUNBEACH 2DV predicted transport rates for wind waves inPENTREZ#3 worser than swell in PENTREZ#4,

FUNBEACH 1DH cheaper in computer time and more stablethan FUNBEACH 2DV.

44/59


Content

1 Introduction






7 Conclusions

45/59


Numerical study

Objective

Eects of various parameters on beach morphodynamic withFUNBEACH 1DH :

Wave height,

Tide range,

Wave spectrum,

Beach slope,

Grain size.

General conditions of test-cases

Plane sloping beach,

14 tidal cycles of constant wave forcing,

Constant tide range.

46/59


First test-case : Sensivity of bar formation to Wave Heightand Tide Range

Conditions

Wave height : 0.4m, 0.8m, 1.2m, 1.6m and 2 m,

Tide range : 0m, 1m, 2m, 3m, 4m, 5m and 6m,

Beach slope : βp =1%,

Grain size : d50 = 0.144mm,

Swell conditions : Tp = 14.3s,

0 0.05 0.1 0.15 0.2 0.25 0.30

0.5

1

1.5

2

2.5

3

f (Hz)

E (

m2 .s

)

47/59


Bar evolution

Hm0 variable and TR=0m

60 80 100 120 140 160 1800

0.5

1

dh+ m

ax (

m)

60 80 100 120 140 160 1801000

1200

1400

1600

t (hours)

xh+ m

ax (

m)

H

m0=0.4m

Hm0

=0.8m

Hm0

=1.2m

Hm0

=1.6m

Hm0

=2.0m

Hm0=1.2m and TR variable

60 80 100 120 140 160 1800

0.5

1

dh+ m

ax (

m)

60 80 100 120 140 160 1801000

1200

1400

1600

t (hours)

xh+ m

ax (

m)

TR=0m

TR=1m

TR=2m

TR=3m

TR=4m

TR=5m

TR=6m

48/59


Morphologic evolution after 14 tidal cycles

Hm0 / TR 0m 1m 2m 3m 4m 5m 6m

0.4m BS BI - - - - -

0.8m BS BS - - - - -

1.2m 3BS 2BS BS BI BI - -

1.6m 3BS 2BS BS BS BI BI BI

2.0m 5BS 2BS 2BS BS BI BI BIn BS : n Subtidal Bar ; n BI : n Intertidal Bar ; Bold Form : Big Bar.

Bar elevation and position

0 1 2 3 4 5 60

0.5

1

dh+ m

ax (

m)

0 1 2 3 4 5 61000

1500

2000

Tide Range (m)

xh+ m

ax (

m)

Hm0

=0.4m

Hm0

=0.8m

Hm0

=1.2m

Hm0

=1.6m

Hm0

=2.0m

Bar migration and accretion velocities

0 1 2 3 4 5 6−0.5

0

0.5

Vx (

m.h

−1 )

0 1 2 3 4 5 60

2

4

6x 10

−3

Tide Range (m)

Vz (

m.h

−1 )

Hm0

=0.4m

Hm0

=0.8m

Hm0

=1.2m

Hm0

=1.6m

Hm0

=2.0m

49/59


To conclude with this numerical study :

Synthesis

The number, the volume, the distance to coastline and thevelocities of bars increase with the wave height.

This response decreases when :

the tide range increases,the wave spectrum width increases,the median grain size increases,the beach slope decreases,the wave period decreases.

Spring-to-spring tidal cycle : morphology is more inuenced byspring tide period.

50/59


To conclude with this numerical study :

Masselink and Short (1993) beach model vs. numerical model

0 10 20 30 40 50 60

0

5

10

15

Ω

RT

R

NO SANDBAR

1 LITTLE SANDBAR

n LITTLE SANDBARS

1 BIG SANDBAR

n SANDBARS (WITH 1 BIG SANDBAR)

51/59


Content

1 Introduction






7 Conclusions

52/59


Beach nourishment with a native sand deposit

Dean's (1998) method(equilibrium concept)

Questions

What is the best place to nourish abeach ?

Which prole is the most stable ?

Method

Evolution with FUNBEACH 1DH of anarticial nourishment after 15 days ofswell on a plane sloping beach.

800 900 1000 1100 1200 1300 1400 1500 1600−2

−1

0

1

2

3

4

5

6

x (m)

z (m

)

xinitial

xfinal

hinitial

→h

final →

53/59


Numerical study

Test-cases

Plane sloping beach (β=1%,d50 = 0.144).

Articial nourishment of66,7 m3/ml.

Without tide : 5 wave heightsfrom 0.4m to 2m and 7 positionsacross the prole fromzMWL=-5m to zMWL= +1m.

With tide : Hm0=1.2m with 6tide ranges from 1m to 6m and 9positions across the prole fromzMWL=-5m to zMWL= +3m.

3 slopes : 1.5%, 2% et 3%.

0 200 400 600 800 1000 1200 1400 1600 1800 2000−10

−5

0

5

10

x (m)

z (m

)

Mean Water Level

0 200 400 600 800 1000 1200 1400 1600 1800 2000−10

−5

0

5

10

x (m)

z (m

)

Mean Water LevelHigh Tide Level, TR=3mHigh Tide Level, TR=6m

Low Tide Level, TR=3mLow Tide Level, TR=6m

800 850 900 950 1000 1050 1100 1150 1200−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

x (m)

z (m

)

Slope of 1.5 %Slope of 2.0 %Slope of 3.0 %

54/59


Dierent types of morphologic response

0 200 400 600 800 1000 1200 1400 1600 1800−15

−10

−5

0

5

10

x (m)

z (m

)SLIGHT SPREADING

Mean Water Level

Initial profile at t = 0HFinal profile at t =360H10

0 200 400 600 800 1000 1200 1400 1600 1800−15

−10

−5

0

5

10

x (m)

z (m

)

OFFSHORE MIGRATION AND GROWTH

Mean Water Level


0 200 400 600 800 1000 1200 1400 1600 1800−15

−10

−5

0

5

10

x (m)

z (m

)

LARGE SPREADING TO DESTRUCTION

High Tide Level

Low Tide Level


0 200 400 600 800 1000 1200 1400 1600 1800−15

−10

−5

0

5

10

x (m)

z (m

)

STABILITY

High Tide Level

Low Tide Level


55/59


Synthesis of simulated evolutions

On microtidal beaches :

Before the breaking zone : slight spreading,In the breaking zone : growth,After the breaking zone : large spreading to destruction,Near the shoreline : stability.

On mesotidal and macrotidal beaches :

Before the low-tide breaking zone : slight spreading,In the lower intertidal zone : large spreading to destruction,In the upper intertidal zone : stability.

Inuence of the slope of the articial nourishment :

An articial nourishment with highest slope moves slowest,The wave height is most reduced with articial nourishmentwith highest slope.

56/59


Practical recommendations of beach nourishments

Bars and berms are the best locations to nourish microtidalbeaches,

The upper intertidal zone is the best location to nourishmesotidal and macrotidal beaches,

Steep nourishments are recommended.

need to be conrmed by further studies.

57/59


Content

1 Introduction






7 Conclusions

58/59


Conclusions

Development of a new morphodynamic model able toreproduce beach processes :

Wave propagation, wave breaker and bottom friction includingwave ripples, thanks to FUNWAVE model,Undertow and near-bed velocities, thanks to Lynett (2006) andturbulence closure vertical model,Beach evolution and bar movement.

Lynett-Bailard approach (1DH) faster and more accurate thanthe turbulence closure vertical approach (pseudo-2DV).

Inuence of several parameters on beach morphology :

The number, the volume, the distance to coastline and thevelocities of bars increase with the wave height.This response decreases when the tide range, the wavespectrum width and the median grain size increase, and whenthe beach slope and the wave period decrease.

Appropriated locations and forms for beach nourishments havebeen identied.

59/59


Prospects

FUNBEACH 1DH and FUNBEACH 2DV + MII to study othereld sites,

Multi-class approach to study grain size evolution of the beach,

Eective 2DV approach : see Lynett and Liu's (2004)multi-layer model,

Account for the longshore component : FUNWAVE 2D =⇒FUNBEACH 2DH and FUNBEACH 3D with a potentialalternative for long term simulations given by a phase-averagedmodel like XBEACH (Roelvink et al., 2008).

60/59


61/59


Second test-case : Wave spectrum

Wind waves

Hm0 / TR 0m 1m 2m 3m 4m 5m 6m

0.4m BS BI - - - - -

0.8m BS 2BS - - - - -

1.2m 3BS 2BS - - - - -

1.6m 2BS 2BS BS BS - - -

2.0m 2BS 2BS BS BS - - -

Monochromatic wave

Hm0 / TR 0m 1m 2m 3m 4m 5m 6m

0.4m 2BS BI BI BI BI BI BI

0.8m BS 2BS BI BS BI BS BI BI BI

1.2m 5BS BS BI 2BS BI BS BI BS BI BS BI BS

1.6m 3BS 2BS 2BS 2BS BI BS BI BS BI BS

2.0m 2BS 2BS 2BS 3BS 2BS BI BS BI

=⇒Narrower wave spectrum inscreases bar dynamics.

62/59


Third test-case : beach slope

Beach slope βp =0.5%

Hm0 / TR 0m 1m 2m 3m 4m 5m 6m

0.4m - - - - - - -

0.8m BS BI - - - - -

1.2m 6BS BS - - - - -

1.6m 9BS 3BS 2BS - - - -

2.0m 4BS 3BS - - - - -

Beach slope βp =2.0%

Hm0 / TR 0m 1m 2m 3m 4m 5m 6m

0.4m - - - - - - -

0.8m BS BS BS - - - -

1.2m BS BS BS BS BS BS BS

1.6m BS BS BS BS BS BS BS

2.0m BS BS BS BS BS BS BI BS

=⇒Steeper beach inscreases bar dynamics.

63/59


Fourth test-case : grain size

Median grain size d50 =0.063mm

Hm0 / TR 0m 1m 2m 3m 4m 5m 6m

0.4m 2BS BI BI BI BI BI BI

0.8m 4BS BS BS BI BI BI BI

1.2m 3BS BS BS BS BI BI BS BI BS BI BS

1.6m 5BS BS BI BS BI BS BI BI BS 2BI BS 2BI BS

2.0m 3BS 3BS BI BS BS BI BI BS 2BI BS 2BI BS

Median grain size d50 =0.200mm

Hm0 / TR 0m 1m 2m 3m 4m 5m 6m

0.4m BS - - - - - -

0.8m BS - - - - - -

1.2m 3BS BS - - - - -

1.6m 3BS BS BS - - - -

2.0m 3BS 2BS BS - - - -

=⇒Finer sand beach inscreases bar dynamics.

64/59


Vertical proles example (t=26H10mn PENTREZ#4)

−0.2 −0.1 0 0.1 0.2 0.30

0.5

1

1.5

2

2.5

3

3.5

4

U(z) (m/s)

z (m

)

PENTREZ 4 t=26H10mn

Vertical Model dataLynett Model dataNon−corrected experimental dataTidal−corrected experimental data

0 0.1 0.2 0.3 0.4 0.50

0.5

1

1.5

2

2.5

3

3.5

4

Urms

(z) (m/s)

z (m

)

PENTREZ 4 t=26H10mn

Vertical Model dataLynett Model dataExperimental data

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

4

C(z) (g/L)z

(m)

PENTREZ 4 t=26H10mn


0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

4

Crms

(z) (g/L)

z (m

)

PENTREZ 4 t=26H10mn


65/59


Wave, Velocity and Sediment concentration spectra(t=26H10mn PENTREZ#4)

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

f (Hz)

E (

m2 .s

)

Experimental dataFUNWAVE Model data

0 0.05 0.1 0.15 0.2 0.25 0.30

1

2

3

4

f (Hz)

SP

U(3

0cm

) (m

2 .s−

1 )

Experimental dataVertical Model data

0 0.05 0.1 0.15 0.2 0.25 0.30

1

2

3

4

f (Hz)

SP

U(6

0cm

) (m

2 .s−

1 )

0 0.05 0.1 0.15 0.2 0.25 0.30

1

2

3

4

f (Hz)

SP

U(9

0cm

) (m

2 .s−

1 )

0 0.05 0.1 0.15 0.2 0.25 0.3

0.5

1

1.5

f (Hz)

SP

C(3

0cm

) ((

g.L−

1 )2 .s)

Experimental dataVertical Model data

0 0.05 0.1 0.15 0.2 0.25 0.3

0.1

0.2

0.3

0.4

f (Hz)

SP

C(6

0cm

) ((

g.L−

1 )2 .s)

0 0.05 0.1 0.15 0.2 0.25 0.3

0.005

0.01

0.015

0.02

0.025

f (Hz)

SP

C(9

0cm

) ((

g.L−

1 )2 .s)

66/59


Transport rates components

0 5 10 15 20 25 30 35 40 45−4

−3

−2

−1

0

1

2

3

4x 10

−4

q (m

2 .s−

1 )

t (hours)

q

s2DV

qsu

qsw

qsl

0 5 10 15 20 25 30 35 40 45−5

−4

−3

−2

−1

0

1

2

3

4

5x 10

−5

q (m

2 .s−

1 )

t (hours)

q

s2DV

qsu

qsw

qsl

67/59


Long simulations on a plane sloping beach

100 200 300 400 500 600 700 800 900 1000 1100 12000

0.5

1

1.5

dh+ m

ax (

m)

100 200 300 400 500 600 700 800 900 1000 1100 12001000

1100

1200

1300

1400

1500

1600

t (hours)

xh+ m

ax (

m)

TR=0m

TR=1m

TR=2m

TR=3m

TR=4m

TR=5m

TR=6m

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