Post on 19-May-2022
ECOLE D
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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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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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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
Examples of bar systems
3D Sandbars
Truc Vert beach (FR)
Omaha beach (FR)
Longshore Sandbars
Wessex Coast (UK)
Egmond aan Zee (NL)
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
Masselink and Short (1993) conceptual beach model
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
Time and space scales of the inner-shelf morphodynamicsystem
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
Time and space scales of the inner-shelf morphodynamicsystem
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
Time and space scales of the inner-shelf morphodynamicsystem
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
Cross-shore processes on sandy beaches
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
Cross-shore processes on sandy beaches
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
Cross-shore processes on sandy beaches
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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 ?
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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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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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)
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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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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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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)
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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)
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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)
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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.
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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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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
Pentrez beach in the bay of Douarnenez
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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).
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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.
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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.
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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)
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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)
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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)
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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)
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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)
Vertical Model dataExperimental data
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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.
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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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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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.
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
)
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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.
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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
52/59
Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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 →
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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 %
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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
)
LARGE SPREADING TO DESTRUCTION
High Tide Level
Low Tide 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
)
STABILITY
High Tide Level
Low Tide Level
Initial profile at t = 0HFinal profile at t =360H10
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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.
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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.
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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
58/59
Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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.
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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).
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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.
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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.
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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.
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
Vertical 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
Crms
(z) (g/L)
z (m
)
PENTREZ 4 t=26H10mn
Vertical Model dataExperimental data
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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)
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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
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Introduction Models Deltaume Pentrez Waves and Tide Articial Nourishment Conclusions
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