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From irrotational flows to turbulent dynamos
Stockholm University, Faculty of Science, Department of Astronomy.
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Many of the celestial bodies we know are found to be magnetized:the Earth, many of the planets so far discovered, the Sun and other stars,the interstellar space, the Milky Way and other galaxies.The reason for that is still to be fully understood, and this work is meant to be a step in that direction.

The dynamics of the interstellar medium is dominated by events likesupernovae explosions that can be modelled as irrotational flows.The first part of this thesis is dedicated to the analysis of some characteristics of these flows, in particular how they influencethe typical turbulent magnetic diffusivity of a medium, and it is shownthat the diffusivity is generally enhanced, except for some specific casessuch as steady potential flows, where it can be lowered.Moreover, it is examined how such flows can develop vorticity when they occur in environments affected by rotation or shear,or that are not barotropic.

Secondly, we examine helical flows, that are of basic importance for the phenomenon of the amplification of magnetic fields, namely the dynamo.Magnetic helicity can arise from the occurrence of an instability: here we focus on theinstability of purely toroidal magnetic fields, also known as Tayler instability.It is possible to give a topological interpretation of magnetic helicity.Using this point of view, and being aware that magnetic helicity is a conserved quantity in non-resistive flows,it is illustrated how helical systems preserve magnetic structureslonger than non-helical ones.

The final part of the thesis deals directly with dynamos.It is shown how to evaluate dynamo transport coefficients with two of the most commonly used techniques, namely theimposed-field and the test-field methods.After that, it is analyzed how dynamos are affected by advectionof magnetic fields and material away from the domain in which theyoperate.It is demonstrated that the presence of an outflow, likestellar or galactic winds in real astrophysical cases,alleviates the so-calledcatastrophic quenching, that is the damping of a dynamoin highly conductive media, thus allowing the dynamo process to work better.

Place, publisher, year, edition, pages
Stockholm: Department of Astronomy, Stockholm University , 2012. , 76 p.
Keyword [en]
astrophysics, magnetic fields, insterstellar medium, MHD, dynamo, turbulence, instability
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
URN: urn:nbn:se:su:diva-80958ISBN: 978-91-7447-573-9 (print)OAI: oai:DiVA.org:su-80958DiVA: diva2:560537
Public defence
2012-11-14, sal FB52, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

At the time of the doctoral defence the following paper was unpublished and had a status as follows: Paper nr 5: Submitted

Available from: 2012-10-23 Created: 2012-10-03 Last updated: 2012-10-17Bibliographically approved
List of papers
1. Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows
Open this publication in new window or tab >>Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows
2011 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 84, no 4, 46321- p.Article in journal (Refereed) Published
Abstract [en]

Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the Péclet or magnetic Reynolds number is not too large, and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic cases several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented, as well as numerical results obtained by the test-field method, which applies independently of this approximation. Particular attention is paid to nonlocal and noninstantaneous connections between the turbulence-caused terms and the mean fields. Two examples of irrotational flows, in which interesting phenomena in the above sense occur, are investigated in detail. In particular, it is demonstrated that the decay of a mean scalar in a compressible fluid under the influence of these flows can be much slower than without any flow, and can be strongly influenced by the so-called memory effect, that is, the fact that the relevant mean-field coefficients depend on the decay rates themselves.

Keyword
Magnetohydrodynamics and electrohydrodynamics, Magnetohydrodynamic and fluid equation, Magnetohydrodynamics, Magnetic reconnection
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:su:diva-70042 (URN)10.1103/PhysRevE.84.046321 (DOI)000296534100006 ()
Note
authorCount :4Available from: 2012-01-16 Created: 2012-01-16 Last updated: 2017-12-08Bibliographically approved
2. The α effect with imposed and dynamo-generated magnetic fields
Open this publication in new window or tab >>The α effect with imposed and dynamo-generated magnetic fields
2009 (English)In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 398, no 4, 1891-1899 p.Article in journal (Refereed) Published
Abstract [en]

Estimates for the non-linear α effect in helical turbulence with an applied magnetic field are presented using two different approaches: the imposed-field method where the electromotive force owing to the applied field is used, and the test-field method where separate evolution equations are solved for a set of different test fields. Both approaches agree for stronger fields, but there are apparent discrepancies for weaker fields that can be explained by the influence of dynamo-generated magnetic fields on the scale of the domain that are referred to as meso-scale magnetic fields. Examples are discussed where these meso-scale fields can lead to both drastically overestimated and underestimated values of α compared with the kinematic case. It is demonstrated that the kinematic value can be recovered by resetting the fluctuating magnetic field to zero in regular time intervals. It is concluded that this is the preferred technique both for the imposed-field and the test-field methods.

Keyword
hydrodynamics, magnetic fields, MHD, turbulence
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:su:diva-32538 (URN)10.1111/j.1365-2966.2009.15108.x (DOI)000269906400023 ()
Available from: 2009-12-12 Created: 2009-12-12 Last updated: 2017-12-12Bibliographically approved
3. Magnetic-field decay of three interlocked flux rings with zero linking number
Open this publication in new window or tab >>Magnetic-field decay of three interlocked flux rings with zero linking number
2010 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 81, no 3, 36401- p.Article in journal (Refereed) Published
Abstract [en]

The resistive decay of chains of three interlocked magnetic flux rings is considered. Depending on the relative orientation of the magnetic field in the three rings, the late-time decay can be either fast or slow. Thus, the qualitative degree of tangledness is less important than the actual value of the linking number or, equivalently, the net magnetic helicity. Our results do not suggest that invariants of higher order than that of the magnetic helicity need to be considered to characterize the decay of the field.

National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
urn:nbn:se:su:diva-49938 (URN)10.1103/PhysRevE.81.036401 (DOI)000276199400076 ()
Note

authorCount :3

Available from: 2010-12-20 Created: 2010-12-20 Last updated: 2017-12-11Bibliographically approved
4. Vorticity production through rotation, shear, and baroclinicity
Open this publication in new window or tab >>Vorticity production through rotation, shear, and baroclinicity
2011 (English)In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 528, A145- p.Article in journal (Refereed) Published
Abstract [en]

Context. In the absence of rotation and shear, and under the assumption of constant temperature or specific entropy, purely potential forcing by localized expansion waves is known to produce irrotational flows that have no vorticity. Aims. Here we study the production of vorticity under idealized conditions when there is rotation, shear, or baroclinicity, to address the problem of vorticity generation in the interstellar medium in a systematic fashion. Methods. We use three-dimensional periodic box numerical simulations to investigate the various effects in isolation. Results. We find that for slow rotation, vorticity production in an isothermal gas is small in the sense that the ratio of the root-mean-square values of vorticity and velocity is small compared with the wavenumber of the energy-carrying motions. For Coriolis numbers above a certain level, vorticity production saturates at a value where the aforementioned ratio becomes comparable with the wavenumber of the energy-carrying motions. Shear also raises the vorticity production, but no saturation is found. When the assumption of isothermality is dropped, there is significant vorticity production by the baroclinic term once the turbulence becomes supersonic. In galaxies, shear and rotation are estimated to be insufficient to produce significant amounts of vorticity, leaving therefore only the baroclinic term as the most favorable candidate. We also demonstrate vorticity production visually as a result of colliding shock fronts.

Keyword
turbulence, dynamo, magnetohydrodynamics (MHD), ISM: bubbles, galaxies: magnetic fields, galaxies: ISM
National Category
Physical Sciences Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:su:diva-69076 (URN)10.1051/0004-6361/201015661 (DOI)000288541600092 ()
Note

authorCount :2

Available from: 2012-01-10 Created: 2012-01-10 Last updated: 2017-12-08Bibliographically approved
5. Turbulent dynamo with advective magnetic helicity flux
Open this publication in new window or tab >>Turbulent dynamo with advective magnetic helicity flux
(English)Manuscript (preprint) (Other academic)
National Category
Physical Sciences
Identifiers
urn:nbn:se:su:diva-80956 (URN)
Available from: 2012-10-03 Created: 2012-10-03 Last updated: 2012-10-15Bibliographically approved
6. Turbulent transport in hydromagnetic flows
Open this publication in new window or tab >>Turbulent transport in hydromagnetic flows
Show others...
2010 (English)In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T142, 14028Article in journal (Refereed) Published
Abstract [en]

The predictive power of mean-field theory is emphasized by comparing theory with simulations under controlled conditions. The recently developed test-field method is used to extract turbulent transport coefficients both in the kinematic and the nonlinear or quasi-kinematic cases. A striking example of the quasi-kinematic method is provided by magnetic buoyancy-driven flows that produce an alpha effect and turbulent diffusion.

National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:su:diva-66246 (URN)10.1088/0031-8949/2010/T142/014028 (DOI)000285777700030 ()
Conference
2nd International Conference and Advanced School on Turbulent Mixing and Beyond
Note

authorCount :6

Available from: 2011-12-19 Created: 2011-12-19 Last updated: 2017-05-04Bibliographically approved
7. Breakdown of chiral symmetry during saturation of the Tayler instability
Open this publication in new window or tab >>Breakdown of chiral symmetry during saturation of the Tayler instability
2012 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 86, no 1, 016313- p.Article in journal (Refereed) Published
Abstract [en]

We study spontaneous breakdown of chiral symmetry during the nonlinear evolution of the Tayler instability. We start with an initial steady state of zero helicity. Within linearized perturbation calculations, helical perturbations of this initial state have the same growth rate for either sign of helicity. Direct numerical simulations (DNS) of the fully nonlinear equations, however, show that an infinitesimal excess of one sign of helicity in the initial perturbation gives rise to a saturated helical state. We further show that this symmetry breaking can be described by weakly nonlinear finite-amplitude equations with undetermined coefficients which can be deduced solely from symmetry consideration. By fitting solutions of the amplitude equations to data from DNS, we further determine the coefficients of the amplitude equations.

National Category
Physical Sciences
Identifiers
urn:nbn:se:su:diva-80437 (URN)10.1103/PhysRevE.86.016313 (DOI)000306415900005 ()
Note

AuthorCount:4;

Available from: 2012-09-19 Created: 2012-09-19 Last updated: 2017-12-07Bibliographically approved

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