Turbulent Heating and Anisotropy in the Solar Wind: A Numerical Study

132 Pages·2019·3.989 MB·English

by  Victor Montagud-Camps

Springer Theses
Recognizing Outstanding Ph.D. Research
Victor Montagud-Camps
Turbulent Heating
and Anisotropy in
the Solar Wind
A Numerical Study
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Victor Montagud-Camps
Turbulent Heating
and Anisotropy in the Solar
Wind
A Numerical Study
Doctoral Thesis accepted by
Paris-Sud University, Orsay, France
123
Author Supervisor
Dr. Victor Montagud-Camps Dr. RolandGrappin
Department ofSurface andPlasma Science Laboratoire dePhysiquedes plasmas
CharlesUniversity EcolePolytechnique
Prague,Czech Republic Palaiseau, France
ISSN 2190-5053 ISSN 2190-5061 (electronic)
SpringerTheses
ISBN978-3-030-30382-2 ISBN978-3-030-30383-9 (eBook)
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’
Supervisor s Foreword
Turbulence is a widespread phenomenon that can be found in a great variety of
naturalflows.Imposedlarge-scaleflows,asrotation,orshearflows,arewell-known
ways to deeply alter the properties of isotropic turbulence, in particular, eddy ani-
sotropy and turbulent dissipation. The solar wind flow is a particularly interesting
example,combiningtwoimportantconstraints:alarge-scaleradialflowandamean
magnetic field, which in a conductive plasma leads to two-symmetry axis in com-
petitionduringtheturbulentcascade. Thisthesis contributesinseveralwaystothe
understanding of turbulence in the solar wind, in the framework of magnetohy-
drodynamics(MHD).Theresultsareimportantforotherastrophysicalflowsaswell.
The several findings presented in this thesis include the first direct numerical
simulations showing a strong slow down of cooling during transport by the solar
wind, the slow down being comparable to the one observed. This demonstration
deals with eddy anisotropies compatible with the one observed in slow winds.
A second study, valid for eddy anisotropies compatible with fast winds, contains
the revelation that the flow cross helicity, characteristic of fast winds, strongly
enhancestheimprintofexpansionontheanisotropyofeddies,butatthesametime
maintainsastrongturbulentdissipation.Commonwisdomwould,inthiscase,have
predicted the reverse, namely that cross helicity should decrease turbulent dissi-
pation. Finally, the obtained slow down of cooling during transport is found to be
comparable in slow and fast winds, which matches the solar wind situation.
The thesis also includes a thorough study of the phenomenology applied to the
problem of turbulent heating (or more properly turbulent slow down of cooling)
during solar wind transport. This phenomenology has been applied recently to the
question of solar wind acceleration, allowing to show that, in the acceleration
region close to the Sun, one should take into account compressibility in the tur-
bulent cascade and not only use incompressible models.
v
vi Supervisor’sForeword
This thesis contains remarkable results, it uses both numerical and phe-
nomenological approaches to make several valuable contributions to the field of
astrophysicalturbulentflows.Forallitsachievements,itconstitutesagoodaddition
to the Springer Theses series.
Palaiseau, France Dr. Roland Grappin
July 2019
Abstract
Physical phenoma based on non-linear processes pose some of the most thrilling
andcomplexproblemstotreatinphysics.Amongthoseproblems,fluidturbulence
is of great relevance due to its presence in multiple physical contexts, from geo-
physicstoastrophysics.Inthelatter,turbulencedevelopsinfluidsmadeofionized
particles whose movements are coupled to the electromagnetic fields that they
create and to those already present in the medium. Such fluids are known as
plasmas.
The Sun, a plasma itself, continuously ejects its atmosphere in all directions,
reaching all the solar system at velocities of several hundreds kilometers per sec-
ond.ThisplasmaisknownastheSolarWindand,duetoitsavailabilityforin-situ
measurements, is one of the most studied examples of turbulence in astrophysical
plasmas.
Thisthesishasforgoalthestudyofturbulentanisotropyandturbulentheatingin
thesolarwindbetween0.2and1Astronomicalunits(Earth’sorbit)withtheaidof
direct numerical simulations. Both issues can be considered as inverse problems:
the majority of in-situ measurements of the solar wind have been done at 1
astronomical unit and despite knowing most of the properties of the solar wind
within the inner heliosphere, information about the properties of solar wind tur-
bulence is in general only available close to Earth’s orbit. As a consequence, we
need to infer the initial conditions of the solar wind turbulence at 0.2 AU and
compare the results of the simulations to its arrival at 1 AU. From the simulations
that match the observations at 1 AU and the radial evolution of other plasma
properties, we deduce what are the physical mechanisms in both cases.
Inthefirstpartofthisthesis,wewillintroducethecontextonwhichthisworkis
framed. A general overview of the solar wind and the lower layers of the helio-
sphere will be followed by an introduction of the modeling of plasmas to end up
with description of the equations that is used in our simulations, the Expanding
BoxModelequations.Then,wewilldefineturbulence,andthetechniquesthathave
been developed to study this physical phenomenon. We then explain how the
measurements of plasma and turbulence properties in the solar wind have been
done.
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viii Abstract
The following part is dedicated to our study of turbulence anisotropy. At large
scales, in-situ measurements of the turbulence at 1 AU show two preferred direc-
tions to transfer coherent energy via nonlinear couplings, the perpendicular to the
meanmagneticfieldinthecaseofslowwindsandtheparalleltothesameaxisfor
fast winds. We willrevisit apreviouspaper inthis area byVerdiniand Grappin in
2016thatalreadytreatedthisproblem.Inourcase,wewillexplorethevariationof
physical parameters that were neglected and have proven to be decisive in the
development of turbulent anisotropy. We will present several models of initial
turbulentanisotropythatmanagetoreproducetheobservationsat1AUandwewill
discuss the suitability of each one.
Inthethirdpart,wefocusonturbulentheatinginfastandslowwinds.Between
0.3and1AU,protontemperature ofthesolarwindhasbeenobservedtodiminish
as a power law of heliospheric distance. An adiabatic expansion of the solar wind
would lead to a faster decrease than what is observed. This has suggested that
turbulencecanbealocalsourceofheatingresponsibleforthetemperaturegradient
flatter than the adiabatic cooling predictions. Here, we will show a 1D analytical
model of hydrodynamic turbulence in and expanding in an expanding box,
developed to give an idea on how this parameter can change turbulence and the
temperaturegradient.WewillshowtheresultsfoundusingtheEBMequationsina
3D numerical box. First, we will see how the temperature gradient can be repro-
duced in the case of slow winds. The extension of this result to fast winds will be
reached right after.
In thefourth and final part, we acknowledge thelimitations encountered by our
simulations and the physics that have been neglected. We address the absence of
temperature anisotropy, and multiple particle species, specially electrons, whose
contribution to the studied problems have been neglected. In the case of the tem-
perature anisotropy, we make a proposition of future work based on the modifi-
cationoftheEBMequationstoaccountforprotontemperatureanisotropy.Forthe
electrons and other species, instead of proposing new modifications to EBM, we
discuss alternative models of solar wind that confer to electrons the main role in
solar wind dynamics.
Acknowledgements
Thepresentdocumentistheresultof3yearsofworkasaPh.D.studentofRoland
Grappin and Filippo Pantellini. I would like to thank them for their mentoring and
scientific discussions that we have had along these years, but also for our
day-to-day conversations accompanied with tea or coffee.
I also want to thank Roland, the Doctoral School of Astronomy and
Astrophysics of Paris Area (ED127) and the Department of Physics of Paris-Sud
University for submitting my thesis to the Springer Theses programme.
I would also like to express my gratitude to Andrea Verdini, who has always
managed to find some time to answer my many doubts and questions.
I am thankful to Viviane Pierrard and to Franck Plunian, referees of my thesis,
whose attentive reading of my work and their corrections have allowed me to
improve my manuscript.
Itisnotpossibleformenottomentionmyfriends,whohavebeenbymysideall
along these years.
I would also like to acknowledge all the help and support that I have received
frommyformerlaboratory,theLaboratoiredePhysiquedesPlasmasandtothank
all its members: the administrative and technical teams, the direction and the sci-
entific groups, specially the space plasma, numerical simulations and turbulence
groups.
Last,butnotleast,tomyfamily:Iwouldneverbeabletothankyouenoughall
that you have done for me, but I will always try, thank you!
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