M Onthephase-spacedistributionofheavyparticlesinturbulenceJ D T

D

OCTORATE

T

HESIS

On the phase-space distribution of heavy particles in turbulence

J AN M EIBOHM

Akademisk avhandling för avläggande av doktorsexamen i fysik vid Göte- borgs universitet. Avhandlingen försvaras vid ett offentligt seminarium fredagen den 31 januari 2020, kl 09:00 i PJ-salen, Institutionen för fysik, Fysikgården 2, Göteborg. Avhandlingen försvaras på engelska.

Fakultetsopponent Dr. Massimo Cencini, Istituto dei Sistemi Complessi, Rome

Betygskommitté Dr. Rosemary Harris, Queen Mary University of London

Prof. Torbjörn Lundh, Chalmers tekniska högskola Prof. Sven Åberg, Lunds universitet

Handledare Bernhard Mehlig, Göteborgs universitet

Examinator Stellan Östlund, Göteborgs universitet

On thephase-space distribution

ofheavy particles

inturbulence

J

M

AN

EIB OH M

Depar tmentof

Physics

Univ ersityof

Gothenbur g

Turbulent fluidsladen

withsmall, heavypar

ticlesar ecommo nin

nature.

Promi-

nentexamples ofsuch

turbulentsuspensions are

waterdr opletsin

warm clouds,

asw ellas particulate matteror

livingor ganismsin

theturbulent upperlay

erof

oceans.

Because oftheir

inertia, heavypar

ticlestend todistr ibuteinhomogeneously

over phase-space,and

over configuration

space.

Thisphenomenon isr

eferred to

ascluster ing,and

itis believed

tohav ea strong impacton

ther ateof collisions

between particles .The collisiondynamics

,in turn, iscr ucialfor thetime evolution

ofturbulent suspensions,as

collisionsenable thepar

ticlesto gro win size .

In thisthesis ,I studythe phase-spacedistr

ibutionof heavypar

ticlesin turbu-

lencein terms ofa simplified,statistical

modelthat qualitatively

captures thepar ticle

dynamicson thesmallest lengthscales

ofturbulence .I

usemethods from

dynam-

icalsystems theory,

andthe theory

oflar gedeviations ,to

describe thelong-time

behaviourof thepar ticledistr

ibution.I nmost parts

ofthe thesis,I

investigate sus-

pensionsof identicalpar

ticles, andstudy statisticalobser

vables thatchar

acterise

clustering inphase-space ,and

inconfigur ationspace

.

For these‘

mono-disperse’

suspensionsI analysephase-space

clustering ina

one-dimensionallimit by computingthe

large-deviation statisticsof

phase-space

finite-timeL yapunov

exponents, andthe phase-spaceR

enyidimensions .S

patial

clustering isstudied by

projecting thephase-space

dynamicsto configuration

space.

Isho who wthe large-deviation statisticsof

spatialfinite-time Lyapuno

vexponents is

affectedb ythis projection, andthe

effectsit hason thespatial correlation

dimension.

Finally ,I extendthe

analysist opar ticlesuspensions

oftwo different

sizes . I

show thatthis

‘poly -dispersity’has

astr ongeffect onthe

phase-spacedistr ibution

ofpar ticles,wher

eit leadsto aplateau inthe

distribution ofsepar

ationsand relativ e

velocities .

ISBN978-91-7833-759-0 (PRINT)

ISBN978-91-7833-758-3 (PDF)

Keywor ds:F

luiddynamics, Par

ticle-ladenflo ws,T urbulentaer

osols,Chaotic dynam-

ics,N on-equilibriumstatistical

physics