transport and diffusion in complex flows - fisica.unige.itseminara/publications/phd.pdf ·...

Transport and diffusion in complex flows

Agnese Seminara

University of Nice-Sophia Antipolis and University of Genoa

June, 25th 2007, Institut non linéaire de Nicesupervisor: A. Celani, co-supervisor: A. Mazzino

Committee:R. Benzi

G. FalkovichD. Bernard

H. KellayG. Ridolfi

N. Zanghì

A. Seminara (University of Nice and Genoa) Transport and diffusion in complex flows Nice, June 25th 2007 1 / 22

Education and teaching

2006 – 2007 teaching experience at the university of Genoa. Lectures onfluid dynamics and turbulent transport

2004 – 2007 double-badged PhD in physics, University of Nice andUniversity of Genoa, supervisors A. Celani and A. Mazzino

2004 – 2005 supervised master’s thesis student - University of Genoa

1999 – 2004 undergraduate studies in physics - University of Genoa


Collaborations and grants

feb – apr 07 visiting student at Harvard University - Division of engineeringand applied sciences, Cambridge, MA (USA)

apr – dec 06 L’Oréal Italia - Unesco fellowship for women in science➔ collaboration with the University of Rome “La Sapienza”,Italy

oct – nov 05 transnational supercomputing programme HPC-Europa➔ collaboration with the Institute IAC (CNR) Rome, Italy

2005 – 2007 VINCI grant for double-badged PhD, financed by theItalian–French University

2004 – 2007 CNRS program PICS➔ collaboration with the Universities of Genoa and Turin

2004 – 2007 PhD grant from the University of Nice, France2004 grant for the education of young researchers, financed by the

University of Genoa


Research

(1) How winding is the coast of Britain?Conformal invariance of rocky shorelines.Keywords: diffusion, conformal invariance,potential theory.

(2) Large-scale statistics of passive scalarturbulence.Keywords: passive scalar, thermal equilibrium,long-range correlations.

(3) Droplet condensation in turbulent flows.Keywords: turbulent transport, correlations, cloudphysics, precipitation.


(1) How winding is the coast of Britain?

Pollution:

Prestige tanker sink, Nov. ’02.

The problem: diffusion toward rocky coasts.How to handle the complexity of the boundary?➠ Conformal invariance allows for a theoretical treatment.


(1) Conformal invariance of rocky shorelinesDiagnostic for conformal invariance? Winding angle:

Gaussianity

〈θ2〉 = 2(D − 1)/D log L

➠ G. BOFFETTA, A. CELANI, D. DEZZANI AND A. SEMINARA

“How winding is the coast of Britain? Conformal invariance of rocky shorelines”under revision


(2) Large-scale structure of passive scalar turbulence

Small scales➠ turbulence

Large scales ?Thermal equilibrium ?

➠ A. CELANI AND A. SEMINARA

“Large-scale structure of passive scalar turbulence”Phys. Rev. Lett. 94, 214503 (2005)

➠ A. CELANI AND A. SEMINARA

“Large-scale anisotropy in passive scalar turbulence”Phys. Rev. Lett. 96, 184501 (2006)


(3) Droplet condensation in turbulent flows

cloud physics respiration engines

➠ A. CELANI, G. FALKOVICH, A. MAZZINO AND A. SEMINARA

“Droplet condensation in turbulent flows”Europhys. Lett. 70, 775 (2005)

➠ A. CELANI, A. MAZZINO, A. SEMINARA AND M. TIZZI

“Droplet condensation in two-dimensional Bolgiano turbulence”J. Turbul. 8, 1 (2007)

➠ A. LANOTTE, A. SEMINARA AND F. TOSCHI

“Condensation of cloud microdroplets in homogeneous isotropic turbulence”submitted to J. Atmos. Sci. (2007)


What is a warm cloud?

1. nucleationheterogeneous nucleation isfar more efficient thanhomogeneous.

2

CCN

H O

2. condensationremarkable broadening of thedroplet size spectra - importantfor successive collisions.

3. collectionlarge droplets collide withsmall ones - high probability ofcoalescence.

2

V1

V


The problem

How to overcome the bottleneck of condensation ?

Turbulence ?

➠ Simple model. Ingredients ?


Condensation in warm clouds

L ~

100

m

.

. m

η ~ 1 mm

µ

3500 drops/cm

R~1 30

U ~ 1 m/s

number of droplets 1015÷1018

Re 108

L/η 106


How do droplets grow?

s = e/es − 1 ➭ dR(t)dt

= A3s(X(t), t)

R(t)

〈s〉 = 0 : no mean growth expected

evaporations < 0 : dry region




= A3s(X(t), t)

R(t)


saturations = 0 : equilibrium water/vapor




= A3s(X(t), t)

R(t)


condensations > 0 : moist region


How do droplets move?

Droplets during condensation:

- do not collide- are smaller than the Kolmogorov scale- are heavier than the surrounding air

X(t) = U(t)

U(t) = −U(t)− v(X(t), t)τd

+ gz

independentpassiveStokes particles


Motion inside clouds

Homogeneous isotropic turbulenceStratification negligible for cloud cores up to ≈ 100 m.

∂tv + v ·∇v = −∇p + ν∆2v + f


The vapor field

Generalization of Twomey’s model

∂ts + v ·∇s = D∆s + A1w − sτs

τ−1s = An〈R〉

S. Twomey Geophys. Pura eAppl. 43, 243 (1959)

H. R. Pruppacher, J. D. KlettMicrophysics of clouds andprecipitation, Kluwer Academic,Dordrecht (1997)

Passive scalar schemeRole of spatial fluctuations coming from turbulence?


Large or small scales?


Spreading of the spectrum

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 1 2 3 4 5 6 7

r 0 P

(r)

r/r0

t=τL/5t=τL/2

t=τL

Despite the zero mean supersaturation, 40%droplets reach 20 µm radius after one large-eddyturnover time (few hundreds seconds).


A segregation effect (2D)

0

5

10

15

20

25

30

35

40

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

P(s

)

ss

P(s

) Eulerian

Lagrangian

Due to turbulent transport,droplets are correlated with watervapor and segregate in moistregions.

A similar phenomenology isobserved when convection isaccounted for.


From small scales toward large scales (3D)

To simulate a cloud of about(100m)3 at CINECA wewould need the whole 1024processors for 100 years

N L Re srms(t = 0) cpu time643 0.09 m 312 1.5 × 10−3% 1 h

1283 0.18 m 860 2.5 × 10−3% 12 h2563 0.36 m 2240 4.5 × 10−3% 145 h5123 0.60 m 4380 1.2 × 10−2% 1110 h· · · · · · · · · · · · · · ·

850003 100 m 107 2% 105 years

18 cm

9 cm 60 cm

36 cm


Fluctuations of s and spreading

0

100

200

300

-0.04 -0.02 0 0.02 0.04

P(s

)

s[%]

L=9 cm

0

0.2

0.4

0.6

0.8

1

1.2

4.985 4.99 4.995 5 5.005 5.01 5.015

P(r

) no

rmal

ised

to 1

r [µm]

10-510-410-310-2

10-1 100

t/TL

Final broadening vs Reynolds number.

0.001

0.01

0.1

1

10

100 1000

σ R

2 [µ

m2 ]

Reλ



0

100

200

300

-0.04 -0.02 0 0.02 0.04

P(s

)

s[%]

L=9 cmL=18 cm

0

0.2

0.4

0.6

0.8

1

1.2

4.985 4.99 4.995 5 5.005 5.01 5.015

P(r

) no

rmal

ised

to 1

r [µm]

10-510-410-310-2

10-1 100

t/TL


0.001

0.01

0.1

1

10

100 1000

σ R

2 [µ

m2 ]

Reλ



0

100

200

300

-0.04 -0.02 0 0.02 0.04

P(s

)

s[%]

L=9 cmL=18 cmL=36 cm

0

0.2

0.4

0.6

0.8

1

1.2

4.985 4.99 4.995 5 5.005 5.01 5.015

P(r

) no

rmal

ised

to 1

r [µm]

10-510-410-310-2

10-1 100

t/TL


0.001

0.01

0.1

1

10

100 1000

σ R

2 [µ

m2 ]

Reλ



0

100

200

300

-0.04 -0.02 0 0.02 0.04

P(s

)

s[%]

L=9 cmL=18 cmL=36 cmL=60 cm

0

0.2

0.4

0.6

0.8

1

1.2

4.985 4.99 4.995 5 5.005 5.01 5.015

P(r

) no

rmal

ised

to 1

r [µm]

10-510-410-310-2

10-1 100

t/TL


0.001

0.01

0.1

1

10

100 1000

σ R

2 [µ

m2 ]

Reλ


Trend and extrapolation

R2 = 2A3s ➠ σR2(τL) ∼ σsτL ∼ Re5/2λ

0.001

0.01

0.1

1

10

100 1000

σ R

2 [µ

m2 ]

Reλ

prediction

extrapolation

the trend gives a spreading of around 25± 3 µm2 for L ≈ 100 m,Reλ ≈ 2500 after τL ≈ 150 s


Perspectives

➠ Condensation and turbulenceLaboratory-like framework, work in progressin collaboration with:- Carlo Massimo Casciola (Università di Roma “La Sapienza”)- Antonio Celani (INLN–CNRS, Nice)- Nicoletta Marati (Università di Roma “La Sapienza”)- Francesco Salvadore (Università di Roma “La Sapienza”)

Study of the successive collision stageLarge Eddy Simulations of cloud dynamics (?)

➠ Rocky coastsstudy of the mechanism of formation of rocky coasts to checkwhether conformal invariance can be understood in terms ofphysical processesvalidation of the results for the flux of pollutant toward a rocky coastthrough the study of realistic pollutant dispersion

➠ Passive scalarproblem of the passive scalar in decaystudy of other systems of statistical mechanics where anunexpected breakdown of Gibbs equilibrium might arise3D-hydrodynamic turbulence


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