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Dynamique des ondes longues et processus dispersifs, en milieu - - PowerPoint PPT Presentation

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5 ime Ecole EGRIN Institut d'tudes Scientifiques de Cargse, 29 mai - 2 juin 2017 Dynamique des ondes longues et processus dispersifs, en milieu littoral et estuarien Philippe Bonneton EPOC/METHYS , CNRS, Bordeaux Univ. tsunami

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SLIDE 1

Philippe Bonneton

EPOC/METHYS, CNRS, Bordeaux Univ.

5ième Ecole EGRIN – Institut d'Études Scientifiques de Cargèse, 29 mai - 2 juin 2017

Dynamique des ondes longues et processus dispersifs, en milieu littoral et estuarien

tsunami ressaut de marée (mascaret)

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SLIDE 2

Introduction Ondes longues z

d0

z = z(x,t) A0

0 c

2

d d A         = =

λ

 

d0 , A0 , 0 𝑈0 0/ 𝑕𝑒0 = 𝑔(𝐵0/𝑒0, 𝑒0/0)

  • ndes longues :

0<< 1

 tsunamis, marées, ondes infragravitaires, ondes de crue, …

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SLIDE 3

Introduction Ondes longues

Tissier , Bonneton et al., JCR2011

40 min 30 min 18 min 7 min

50 km a=2m dispersion

  • ndes longues se propageant en milieu littoral et estuarien

fortes nonlinéarités  dispersion

Formation et dynamique des chocs dispersifs

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SLIDE 4

http://www.kohjumonline.com/anders.html

Sumatra 2004 tsunami reaching the coast of Thailand references:

  • Grue et al. 2008
  • Madsen et al. 2008

Introduction Tsunamis

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SLIDE 5

Introduction Tsunamis

21st November 2016, Sunaoshi River in Tagajo city, Japan (earthquake 7.4)

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SLIDE 6

Introduction Tsunamis

21st November 2016, Sunaoshi River in Tagajo city, Japan (earthquake 7.4)

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SLIDE 7

Tsunamis, Arikawa et al. 2013

Impact on marine structures and buildings

Introduction Tsunamis

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SLIDE 8

Introduction Tidal bore

Bonneton et al. JGR 2015

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SLIDE 9

Introduction Tidal bore

Gironde estuary, Saint Pardon, Dordogne

https://vimeo.com/106090912, Jean-Marc Chauvet, Septembre 2014

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SLIDE 10

Introduction Tidal bore

Sediment transport and erosion

Tidal Bore, Bonneton et al. 2015

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SLIDE 11

Introduction Infragravity-wave

Costa Rica (video: Bonneton, P. 2012) wind waves (T0  10 s)  infragravity waves (T0  1 min)

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SLIDE 12

Urumea River – San Sebastian

Introduction Infragravity-wave

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SLIDE 13

Introduction Plan

  • 1. Introduction
  • 2. Modèles d’onde longue

 notions sur les effets dispersifs  équations de Serre / Green-Naghdi  applications : simulations numériques

  • 3. Distorsion des ondes longues et formation de chocs
  • 4. Dynamique des ressauts de marée et mascarets

Dynamique des ondes longues et processus dispersifs, en milieu littoral et estuarien

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SLIDE 14

Introduction collaborations

 Physical Oceanography  Bonneton, N., Castelle, B., J-P., Sottolichio, A. (EPOC, Bordeaux)  Frappart, F. (OMP, Toulouse)  Martins K. (Bath Univ.)  Tissier, M. (TU Delft)  Long wave modeling  Lannes, D. (IMB, Bordeaux)  Ricchuito, M., Arpaia, L., Filippini, A. (INRIA, Bordeaux)  Marche, F. (IMAG, Montpellier)  Cienfuegos, R. (CIGIDEN, Chile), Barthélémy E. (LEGI, Grenoble)

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SLIDE 15
  • 2. Modèles d’onde longue

 notions sur les effets dispersifs  équations de Serre / Green-Naghdi  applications : simulations numériques

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SLIDE 16
  • d(x) = d
  • ∂u

∂x + ∂w ∂z =

  • z ∈ [−d
, ζ]

∂w ∂x − ∂u ∂z =

  • ∂u

∂t + u ∂u ∂x + w ∂u ∂z = −

  • ρ
  • ∂P

∂x ∂w ∂t + u ∂w ∂x + w ∂w ∂z = −g −

  • ρ
  • ∂P

∂z P(z) = Patm z = ζ ∂ζ ∂t + u ∂ζ ∂x = w z = ζ w =

  • z = −d
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SLIDE 17
  • x = λ
x′,

z = d

z′,

t =

λ

  • √gd
t′,

ζ = A

ζ′,

Φ = A

  • d
λ
  • √gd
Φ′,

P = ρ

gd P′.
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SLIDE 18
  • µ∂u

∂x + ∂w ∂z =

  • z ∈ [− , ǫζ]

∂w ∂x − ∂u ∂z =

  • ǫ∂u

∂t + ǫ

u ∂u

∂x + ǫ

  • µ w ∂u

∂z = −∂P ∂x ǫ∂w ∂t + ǫ

u ∂w

∂x + ǫ

  • µ w ∂w

∂z = − − ∂P ∂z P(z) = Patm z = ǫζ ∂ζ ∂t + ǫu ∂ζ ∂x =

  • µw

z = ǫζ w =

  • z = −
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SLIDE 19
  • ζ(x, t) = A
exp
  • πi(x

λ − t T )

  • = A
exp (i(kx − ωt))

⇒ ω

= gk tanh(kd )

ζ(x, t) = A

exp
  • ik(x − ω

k t)

  • ⇒
  • cφ = ω

k = λ T

cφ = g k tanh(kd

)
  • /
  • cφ
  • k
λ
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SLIDE 20
  • cφ =

g k tanh(kd

)
  • /
  • cφ
  • λ
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SLIDE 21
  • cφ =

g k tanh(kd

)
  • /
  • kd
≫
  • µ
≫
  • cφ =

g k

  • /
  • =

gλ

π
  • /
  • kd
≪
  • µ
≪
  • cφ

= (gd

) /
  • − (kd
)
  • + O((kd
) )

cφ =

− µ k
  • + O(µ
  • )
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SLIDE 22
  • !
  • µ
≪
  • "
  • ǫ
= O( )
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SLIDE 23
  • #
  • ǫζ

−

  • µ∂u

∂x + ∂w ∂z

  • dz

=

  • ǫζ

−

  • ǫ∂u

∂t + ǫ

u ∂u

∂x + ǫ

  • µ w ∂u

∂z + ∂P ∂x

  • dz

=

  • ∂ζ

∂t + ∂hU ∂x =

  • ǫ∂U

∂t + ǫ

U ∂U

∂x + ǫ

  • h

∂ ∂x ǫζ

−

(u

− U ) dz
  • =

−

  • h

∂ ∂x ǫζ

−

P dz

  • $ U =
  • h

ǫζ

− u dz

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SLIDE 24
  • ǫ∂w

∂t + ǫ

u ∂w

∂x + ǫ

  • µ w ∂w

∂z = − − ∂P ∂z

+ ǫΓ = −∂P

∂z Γ = ∂w

∂t + ǫu ∂w ∂x + ǫ µw ∂w ∂z

  • %

P = ǫζ − z + ǫ ǫζ

z

Γ dξ ǫζ

−

P dz =

  • h
+ ǫ

ǫζ

−

dz ǫζ

z

Γ dξ ǫζ

−

P dz =

  • h
+ ǫ

ǫζ

−

Γ(z +

) dz .
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SLIDE 25
  • ∂ζ

∂t + ∂hU ∂x =

  • ∂U

∂t + ǫU ∂U ∂x + ∂ζ ∂x + ǫ h ∂ ∂x ǫζ

−

(u

− U ) dz
  • = −
  • h

∂ ∂x ǫζ

−

(z +

)Γ dz
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SLIDE 26
  • Φ
  • µ
  • Φ =

N

  • j=

µjΦj . µ∂

Φ

∂x

+ ∂ Φ

∂z

=
  • ∂
Φ
  • ∂z
+ µ

∂

Φ
  • ∂x
+ ∂ Φ
  • ∂z
  • + ... =
.
  • ∂
Φ
  • ∂z
=
  • ∂Φ
  • ∂z = c
(x, t) &
  • "
  • ∂Φ
  • ∂z =
  • Φ
= Φ(z = ǫζ) = ψ(x, t) .
  • µ
  • Φ
= −
  • ((z +
) − h )∂ ψ

∂x

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SLIDE 27
  • Φ
= ψ(x, t)

Φ

= −
  • ((z +
) − h )∂ ψ

∂x

  • u = ∂Φ

∂x = ∂ψ ∂x + µǫh∂ζ ∂x ∂

ψ

∂x

− µ ((z + ) − h )∂ ψ

∂x

+ O(µ )

U = ∂ψ ∂x + µǫh∂ζ ∂x ∂

ψ

∂x

+ µ ' h ∂ ψ

∂x

+ O(µ )

u = U − µ

(z + ) ∂ U

∂x

+ µ h ∂ U

∂x

+ O(µ )

w = ∂Φ ∂z = −µ(z +

)∂U

∂x + O(µ

)
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SLIDE 28
  • u

= U − µ

(z + ) ∂ U

∂x

+ µ h ∂ U

∂x

+ O(µ )

w = ∂Φ ∂z = −µ(z +

)∂U

∂x + O(µ

)

∂ζ ∂t + ∂hU ∂x =

  • ∂U

∂t + ǫU ∂U ∂x + ∂ζ ∂x + ǫ h ∂ ∂x ǫζ

−

(u

− U ) dz
  • =

−

  • h

∂ ∂x ǫζ

−

(z +

)Γ dz
  • ǫζ

−

(u

− U ) dz = O(µ )

Γ = −µ(z +

)
  • ∂
U

∂x∂t + ǫU ∂

U

∂x

− ǫ

∂U ∂x

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SLIDE 29
  • ∂ζ

∂t + ∂hU ∂x =

  • ∂U

∂t + ǫU ∂U ∂x + ∂ζ ∂x = µ

'h

∂ ∂x

  • h
  • ∂
U

∂x∂t + ǫU ∂

U

∂x

− ǫ

∂U ∂x

  • O(µ)
  • (
)
  • "
  • O(µ
) ǫ = O(µ)
  • *
  • O(µ
) ǫ = O( )
  • (
+ ,
  • #
"
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SLIDE 30
  • .
  • ∂ζ

∂t + ∂U ∂x =

  • ∂U

∂t + ∂ζ ∂x = µ

'

∂

U

∂

x∂t

cφ =

  • + µk
  • '

−/

  • ≃
− µk
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SLIDE 31
  • h(x, t) = d
+ A sech (K(x − Ct))

K =

  • d
  • 'ǫ
  • /(
+ ǫ )
  • /
  • C

= (gd

) / ( + ǫ ) /
  • U

= C(

− d
  • h )
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SLIDE 32

b(x,y)

Lannes and Bonneton (2009)

Long wave modelling 2D SGN

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SLIDE 33

Bonneton, Chazel, Lannes, Marche and Tissier (2011) kd0  3

Reformulation of SGN equations

Long wave modelling 2D SGN

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Lannes and Marche (2014) have proposed a new formulation where the operator to invert is time independent  a considerable decrease of the computational time!

Long wave modelling 2D SGN

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 Numerical strategy: decoupling between the hyperbolic and the elliptic parts

e.g. Duran and Marche (2016), Filippini et al. (2017)

 Strategy for wave breaking: description of broken-wave fronts as shocks by the NSWE, by skipping the dispersive step S2

Bonneton et al. (2011)

Long wave modelling 2D SGN

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SLIDE 36

X (m)

NSWE S-GN S-GN S-GN

X (m) z (m)

Shoaling and breaking of regular waves over a sloping beach

Long wave modelling Applications

Tissier et al. (2012)

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SLIDE 37

X (m) z (m)

Shoaling and breaking of regular waves over a sloping beach

Long wave modelling Applications

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SLIDE 38

Experimental data Model prediction

L1 L2 L3 L4 L5 L6

Breaking point

Validation with Cox (1995) experiments Shoaling and breaking of regular waves over a sloping beach

Long wave modelling Applications

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Truc Vert Beach 2001  Offshore wave conditions:   0°, Hs=3 m, Ts=12 s  Maximum surf zone width: 500 m Bottom topography and pressure sensor locations

Comparison with field data

Long wave modelling Applications

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SLIDE 40

1 2 3 4 5 6 7 8

Validation with Beji and Battjes (1993) experiments Periodic waves breaking over a bar

Long wave modelling Applications

Tissier et al. (2012)

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SLIDE 41

Validation with Beji and Battjes (1993) experiments Periodic waves breaking over a bar

Long wave modelling Applications

Tissier et al. (2012)

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SLIDE 42

1 2 3 4 5 6 7 8

Validation with Beji and Battjes (1993) experiments

Laboratory data Model prediction

Long wave modelling Applications

Tissier et al. (2012)

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SLIDE 43

8 9 10 11 12 13 14 15

Wave overtopping and multiple shorelines Solitary waves overtopping a seawall (Hsiao and Lin, 2010)

Long wave modelling Applications

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SLIDE 44

Wave overtopping and multiple shorelines Hsiao et Lin (2010) COBRAS model 2D VOF model RANS equations K- SURF-GN

Long wave modelling Applications

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SLIDE 45

Wave overtopping and multiple shorelines

BARDEX II (HYDRALAB project, Delta Flumes, PI: Gerd Masselink) Barrier Dynamics Experiment : shallow water sediment transport processes in the inner surf, swash and overwash zone.

Long wave modelling Applications

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SLIDE 46

Wave overtopping and multiple shorelines

BARDEX II (HYDRALAB project, Delta Flumes, PI: Gerd Masselink) Barrier Dynamics Experiment : shallow water sediment transport processes in the inner surf, swash and overwash zone.

Long wave modelling Applications

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SLIDE 47

Marche et Lannes, 2014

Long wave modelling Applications

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SLIDE 48

Undular bore (dispersive choc)

Data from Soares-Frazao et Zech (2002), Fr = 1.104

Long wave modelling Applications

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SLIDE 49
  • 3. Distorsion des ondes longues et formation de chocs
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SLIDE 50

tsunami bore tidal bore

What are the conditions for tsunami-like bore formation in coastal and estuarine environments? Basic conditions for bore formation

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SLIDE 51

Basic conditions for bore formation

4000 m

deep

  • cean

D0 =150 m

Continental shelf Lc

  • the continental shelf is relatively flat

Bore inception ?

  • D0 , A0 , 0 =2/T0

𝑴w0 = 𝒉D0 0

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SLIDE 52

Basic conditions for bore formation 0 << 1 0 =O(1)

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SLIDE 53

Basic conditions for bore formation 0 << 1 0 =O(1)

40 min 30 min 18 min 7 min

50 km a=2m Serre Green Naghdi model

Tissier , Bonneton et al., JCR2011

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SLIDE 54

Basic conditions for bore formation 0 << 1 0 =O(1)

40 min 30 min 18 min 7 min

50 km a=2m Serre Green Naghdi model

Tissier , Bonneton et al., JCR2011

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SLIDE 55

Basic conditions for bore formation

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SLIDE 56

Basic conditions for bore formation

x

t=ts t=0 t=3ts/4 t=ts/2 t=ts/4

xs

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SLIDE 57

Basic conditions for bore formation

4000 m

deep

  • cean

Continental shelf Lc

see Madsen et al 2008

D0 =150 m

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SLIDE 58

Basic conditions for bore formation

4000 m

deep

  • cean

150 m

Continental shelf Lc

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SLIDE 59

Basic conditions for bore formation

4000 m

deep

  • cean

150 m

Continental shelf Lc

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SLIDE 60

4000 m

deep

  • cean

150 m

Continental shelf Lc Continental shelves D0  150 m

  • tsunamis: A0  2 m, T0  25 min  xs = 460 km
  • tides: T0  744 min  xs >> Lc

 no tidal bore

Basic conditions for bore formation

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SLIDE 61

4000 m

deep

  • cean

150 m

Continental shelf Lc

  • tsunamis: bores may occur in large and shallow (few tens of m) coastal environments:

marine coastal plains (e.g.: deltas, alluvial estuaries) or carbonate platforms (e.g.: coral reef systems)

Basic conditions for bore formation

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SLIDE 62

4000 m

deep

  • cean

150 m

Continental shelf Lc

  • tsunamis: bores may occur in large and shallow (few tens of m) coastal environments:

marine coastal plains (e.g.: deltas, alluvial estuaries) or carbonate platforms (e.g.: coral reef systems)

  • tides: bores can occur in long shallow alluvial estuaries

L  100 km D0  10 m

Basic conditions for bore formation

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SLIDE 63

4000 m

deep

  • cean

150 m

Continental shelf Lc

Basic conditions for bore formation

in such shallow environments friction can play a significant role

  • tsunamis: bores may occur in large and shallow (few tens of m) coastal environments:

marine coastal plains (e.g.: deltas, alluvial estuaries) or carbonate platforms (e.g.: coral reef systems)

  • tides: bores can occur in long shallow alluvial estuaries
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SLIDE 64
  • 4. Dynamique des ressauts de marée et mascarets
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SLIDE 65

Conditions for tidal bore formation Worldwide tidal bores

Severn River - England Qiantang River – China Kampar River – Sumatra (Bono) Amazon River – Brazil (Pororoca)

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SLIDE 66

Large amplitude spring tide – 10th September 2010

Bonneton et al. JGR 2015

Conditions for tidal bore formation Worldwide tidal bores

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SLIDE 67

Conditions for tidal bore formation Worldwide tidal bores

Gironde/Garonne/Dordogne estuary – France 3 field campaigns : a unique long-term high-frequency database

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SLIDE 68

Conditions for tidal bore formation Worldwide tidal bores

Bonneton et al. JGR 2015 Gironde/Garonne/Dordogne estuary – France 3 field campaigns : a unique long-term high-frequency database

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SLIDE 69

Conditions for tidal bore formation Physical criteria

 Scaling analysis

 Large tidal range (Tr0=2A0)  Small water depth  Large-scale funnel-shaped estuaries

 Chanson (2012) : Tr0 > 4.5-6 m coastal plain alluvial estuaries

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SLIDE 70

Conditions for tidal bore formation Physical criteria

 Scaling analysis

 Large tidal range  Small water depth  Large-scale funnel-shaped estuaries

coastal plain alluvial estuaries

Identify the characteristic scales of the problem:

  • morphology of alluvial estuaries
  • tidal waves
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SLIDE 71

Scheldt estuary Savenije 2012

Conditions for tidal bore formation Alluvial estuary morphology

along-channel coordinate

Tide-dominated alluvial estuaries show many morphological similarities all over the world

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SLIDE 72

Pungue estuary Graas et al. 2008

Conditions for tidal bore formation Alluvial estuary morphology

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SLIDE 73

𝐶 = 𝐶0𝑓−

𝑦 𝑀𝐶0

  • Lb0 : convergence length
  • D0 : characteristic water depth

Conditions for tidal bore formation Alluvial estuary morphology

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SLIDE 74
  • Lb0
  • D0
  • T0=12.4 h

 𝑀𝑥0 = 𝑕𝐸0/0

  • A0=Tr0/2 (mean spring tidal amplitude)

Conditions for tidal bore formation Scaling analysis

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SLIDE 75
  • Lb0
  • D0
  • T0=12.4 h
  • A0=Tr0/2
  • Cf0 : friction coefficient
  • Q0 : freshwater discharge

Conditions for tidal bore formation Scaling analysis

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SLIDE 76
  • Lb0
  • D0
  • T0=12.4 h
  • A0=Tr0/2
  • Cf0 : friction coefficient

 5 external variables Conditions for tidal bore formation Scaling analysis

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SLIDE 77

Conditions for tidal bore formation Scaling analysis

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SLIDE 78

Conditions for tidal bore formation Scaling analysis

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SLIDE 79

Conditions for tidal bore formation Scaling analysis

𝐸𝑗 =

𝐷𝑔0𝑀𝑐0𝐵0 𝐸02

> 1.5

K  1, for tidal bore estuaries

Bonneton et al., JGR 2015

 necessary condition for tidal bore formation by not a sufficient one

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SLIDE 80

Conditions for tidal bore formation Scaling analysis

 explore the 3D dimensionless external parameter space: (0 , 0 , 0)

  • Field data: 21 convergent alluvial estuaries

Bonneton, P., Filippini, A.G., Arpaia, L., Bonneton, N. and Ricchiuto, M 2016. Conditions for tidal bore formation in convergent alluvial estuaries. ECSS, 172, 121-127

  • Numerical simulations: 225 runs of a shallow water model

Filippini, A.G., Arpaia, L., Bonneton, P., and Ricchiuto, M. 2017. Modelling analysis of tidal bore formation in convergent estuaries. in revision

slide-81
SLIDE 81

1 Chao Phya Thailand 2 Columbia USA 3 Conwy UK 4 Corantijn USA 5 Daly Australia 6 Delaware USA 7 Elbe Germany 8 Gironde France 9 Hooghly India 10 Humber UK 11 Limpopo Mozambique 12 Loire France 13 Mae Klong Thailand 14 Maputo Mozambique 15 Ord Australia 16 Pungue Mozambique 17 Qiantang China 18 Scheldt Netherlands 19 Severn UK 20 Tha Chin Thailand 21 Thames UK

  • 21 convergent alluvial estuaries
  • 9 tidal bore estuaries

Conditions for tidal bore formation Field data

D0, Lb0, A0=Tr0/2 , Cf0

slide-82
SLIDE 82

Conditions for tidal bore formation Field data

Tidal bore estuaries: 0  2.4  2D parameter space (0 , 0)

1 Chao Phya Thailand 2 Columbia USA 3 Conwy UK 4 Corantijn USA 5 Daly Australia 6 Delaware USA 7 Elbe Germany 8 Gironde France 9 Hooghly India 10 Humber UK 11 Limpopo Mozambique 12 Loire France 13 Mae Klong Thailand 14 Maputo Mozambique 15 Ord Australia 16 Pungue Mozambique 17 Qiantang China 18 Scheldt Netherlands 19 Severn UK 20 Tha Chin Thailand 21 Thames UK

slide-83
SLIDE 83

Conditions for tidal bore formation Field data

Tidal bores occur when 0 > c(0)

c(0)

1 Chao Phya Thailand 2 Columbia USA 3 Conwy UK 4 Corantijn USA 5 Daly Australia 6 Delaware USA 7 Elbe Germany 8 Gironde France 9 Hooghly India 10 Humber UK 11 Limpopo Mozambique 12 Loire France 13 Mae Klong Thailand 14 Maputo Mozambique 15 Ord Australia 16 Pungue Mozambique 17 Qiantang China 18 Scheldt Netherlands 19 Severn UK 20 Tha Chin Thailand 21 Thames UK

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SLIDE 84

Numerical investigation of the 2D parameter space (0 , 0)

225 runs with 0 = 2 Conditions for tidal bore formation Numerical simulations

Filippini, A.G., Arpaia, L., Bonneton, P., and Ricchiuto, M. 2017

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SLIDE 85

Conditions for tidal bore formation Numerical simulations

SGN / SV

Filippini et al. 2017

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SLIDE 86

Conditions for tidal bore formation Numerical simulations

Filippini et al. 2017

SGN / SV

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SLIDE 87

Numerical investigation of the 2D parameter space (0 , 0)

225 runs with 0 = 2 Conditions for tidal bore formation Numerical simulations

2D nonlinear shallow water model developed by Ricchiuto, JCP 2015

  • shock capturing residual distribution scheme
  • 2nd order in space and time
  • unstructured grids suitable for real estuarine applications

Filippini et al. 2017

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SLIDE 88

Conditions for tidal bore formation Numerical simulations

𝑇𝑛𝑏𝑦 = 𝑛𝑏𝑦 𝜖 𝜖𝑦

  • ne example on the 225 runs

Filippini et al. 2017

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SLIDE 89

Conditions for tidal bore formation Numerical simulations 0 = 2

𝑇𝑛𝑏𝑦 𝑇𝑛𝑏𝑦 Filippini et al. 2017

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SLIDE 90

Conditions for tidal bore formation Numerical simulations

Filippini et al. 2017

𝑈𝑠 = 𝑈𝑠 𝑀𝑑 − 𝑈𝑠(0) 𝑈𝑠(0)

rate of change of the tidal range

Theoretical zero-amplification curve:

(Savenije et al. 2008)

00 = 0(0

2 + 1)

damping amplification

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SLIDE 91

Conditions for tidal bore formation Estuary classification

Tidal bores occur when 0 > c(0)

c(0)

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SLIDE 92

Conclusion

tsunami ressaut de marée (mascaret)

Ondes longues et chocs dispersifs

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SLIDE 93

25 km

Large scale phenomenon  tidal wave Small scale wave phenomenon  tidal bore

  • LTW  100 km
  • TTW  12.4 h
  • LTB  10 m
  • TTB  1 s

Conclusion

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SLIDE 94

Conclusion

slide-95
SLIDE 95

Thank you for your attention