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Effet dynamo dans des géométries cylindriques

Effet dynamo dans des géométries cylindriques

Nous nous intéressons à l’expérience de von Kármán Sodium [3] (VKS) située à Cadarache qui, en septembre 2006, a démontré un effet dynamo au-delà d’un nombre de Reynolds magnétique critique Rm c ≈ 32. Le schéma de l’expérience est montré en figure 3(a). La cavité cylindrique interne, composée de cuivre, est remplie de sodium liquide mis en mou- vement par deux turbines contra-rotatives situées en haut et en bas. Elle est entourée par une autre cavité cylindrique contenant du sodium liquide immobile et dont les parois en cuivre contiennent le système de régulation de la température. L’écoulement généré est du type von Kármán avec deux cellules de vitesse toroidales et poloidales. Le champ de vitesse moyenné en temps et axisymétrisé a été mesuré sur une maquette en eau par l’équipe de Saclay. Il est représenté par ses composantes en coordonnées cylindriques sur la figure 3(c). L’effet dynamo est observé uniquement avec des turbines en fer doux et pas avec des turbines en acier. le champ magnétique qui croît et sature au delà du seuil est à composante axi- symétrique, ce qui prouve l’action des composantes non axisymétriques du champ de vitesse. Nous avons donc développé un nouvel algorithme présenté dans [1] afin de calculer des champs magnétiques avec sauts de perméabilité magnétique. Nous décrivons dans la suite les résultats de dynamo cinématique, i.e. nous intégrons l’équation (1.3) avec le champ de vitesses stationnaire et axisymétrique fourni par l’expérience.
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Etude d'un écoulement en précession. Transition vers la turbulence et application à l'effet dynamo.

Etude d'un écoulement en précession. Transition vers la turbulence et application à l'effet dynamo.

On a vu que les deux premières dynamos fluides réussies de 1999 sont basées sur des dy- namos «théoriques», publiées plus de trente ans auparavant, périodique (G.O. Roberts) [99] ou invariante selon une direction (Ponomarenko, 1973) [134]. Pour se rapprocher de ces flots définis analytiquement et donc de caractère plutôt académique, les expérimentateurs ont été amenés à utiliser des réservoirs avec des parois internes. Pour éviter ce type de contraintes non naturelles, et avec l’incitation d’expériences hydrodynamiques montrant une forte concentration de la vortic- ité, des turbines contra-rotatives aux extrémités d’un cylindre sont utilisées dans l’expérience de Cadarache, qui a obtenu l’effet dynamo en 2006. Dans ce cas, il n’y a plus de parois internes, mais on aboutit à un forçage artificiel si on le compare aux écoulements naturels. Dans ce type de forçage, qui évoque plutôt un dispositif industriel de type transmetteur de couple, chaque axe d’entrainement travaille contre l’autre et 300 kW sont nécessaires pour dépasser de peu un seuil de déclenchement de l’effet dynamo. Il s’agit bien du seuil d’un mode particulier car l’effet dy- namo n’est obtenu qu’avec des turbines en fer doux, et il est prématuré de vouloir conclure sur les propriétés dynamos générales de cet écoulement.
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Effet Dynamo : Etudes des mécanismes d'instabilité et de saturation du champ magnétique

Effet Dynamo : Etudes des mécanismes d'instabilité et de saturation du champ magnétique

C’est Larmor [2] qui eut l’id´ee d’un m´ecanisme similaire `a “l’effet dynamo solide” qu’il d´ecrit ainsi dans le cas du Soleil: “Such internal motion induces an electrical field acting on the moving matter: and if any conducting path around the solar axis happens to be open, an electric current will flow round it, which may in turn increase the inducing magnetic field. In this way it is possible for the internal cyclic motion to act after the manner of the cycle of a self-exciting dynamo”. Il ajoute que ce m´ecanisme peut s’appliquer `a la Terre mais n´ecessite l’existence de mouvements fluides en son centre: “it would require fluidity and residual circulation in deepseated regions”. Notons que son article est ant´erieur `a la mise en ´evidence de l’existence d’un noyau liquide sous la croˆ ute terrestre, comme nous l’avons dessin´e en figure 1.3. Depuis que cela a ´et´e v´erifi´e, le m´ecanisme d’une instabilit´e dynamo dite “effet dynamo fluide” est couramment admis pour expliquer la pr´esence de champ magn´etique sur Terre.
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Mécanique statistique et effet dynamo dans un écoulement de von Karman turbulent

Mécanique statistique et effet dynamo dans un écoulement de von Karman turbulent

Fig. 6.2: Sch´ema de la dynamo homopolaire de Bullard. ferromagn´etique connu ne serait capable d’y produire un champ magn´etique. Les dynamiques vari´ees d´ecrites au paragraphe pr´ec´edent poussent elles-mˆemes ` a chercher l’origine de ces champs magn´etiques naturels dans un processus dynamique. L’hypoth`ese la plus vraisemblable ` a ce jour est celle li´ee ` a la conversion d’´energie m´ecanique en ´energie magn´etique par un m´ecanisme d’instabilit´e simple : “l’effet dynamo” . Celui-ci peut ˆetre envisag´e de fa¸con minimaliste en consid´erant la dynamo de Bullard sch´ematis´ee en figure 6.2 : le disque D tournant ` a une certaine fr´equence f dans un champ magn´etique initial ~ B 0 engendre une force ´electromotrice ~ E m le long d’un rayon OR. Cette force ´electromotrice engendre un courant que l’on peut r´ecup´erer dans un circuit spiralant autour du disque. Ce courant induit g´en`ere ` a son tour un champ magn´etique align´e avec l’axe du dispositif. Si on choisit de fa¸con appropri´ee l’orientation relative du circuit ferm´e et le sens de rotation du disque, le champ induit s’ajoute au champ initial. On a construit un syst`eme amplificateur de la moindre graine de champ magn´etique par instabilit´e. Ce m´ecanisme, quand il met en jeu des ´el´ements solides est bien compris et utilis´e depuis le 19`eme si`ecle de fa¸con industrielle pour cr´eer du courant [112]. N´eanmoins, quand Larmor en 1919 [55] propose un m´ecanisme de ce type mettant en jeu des fluides pour expliquer l’origine des champs magn´etiques de la Terre et du Soleil, on n’a admis l’existence d’un noyau liquide au centre de la Terre que depuis peu de temps, et ´evidemment il n’existe aucune th´eorie pour les “dynamos fluides” . Depuis qu’on a mis en ´evidence le caract`ere fluide d’une partie du noyau terrestre et que de nombreuses ´etudes th´eoriques ont mis au jour des m´ecanismes possibles d’amplification du champ magn´etique dans un fluide en mouvement, l’hypoth`ese de Larmor est celle qui est retenue pour expliquer l’existence des champs magn´etiques naturels.
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Champs magnétiques générés par effet dynamo dans les objets astrophysiques en rotation

Champs magnétiques générés par effet dynamo dans les objets astrophysiques en rotation

De plus, consid´erer ` a la fois champ magn´etique et rotation paraˆıt indispensable pour l’´etude des dynamos astrophysiques, vu que les corps c´elestes sont pour la plupart soumis ` a [r]

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Effet dynamo et turbulence magnétohydrodynamique sous-critiques dans les disques d'accrétion

Effet dynamo et turbulence magnétohydrodynamique sous-critiques dans les disques d'accrétion

Avec la d´ecouverte de l’instabilit´e magn´etorotationnelle, dont la propri´et´e essentielle est de g´en´erer de la turbulence en pr´esence d’un champ magn´etique, il est cependant deven[r]

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The turbulent dynamo as an instability in a noisy medium

The turbulent dynamo as an instability in a noisy medium

tential growth in the dynamo regime. This back reaction is provided through the velocity which is subject to the Lorentz-Force, a quadratic form of B. It is usually ignored in the so-called kinematic regime. However, for reasons which will become clearer later, we prefer to work with

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Large-scale dynamo produced by negative magnetic eddy diffusivities

Large-scale dynamo produced by negative magnetic eddy diffusivities

Arguments in favor of negative magnetic eddy diffusivities were previously given in Roberts (1972) and Kraichnan (1976). The atten­ tion in Roberts (1972) was mainly concentrated on a-type dynamo, but some evidence was also given that magnetic fields could grow when orders higher than the first in (2) are relevant. A three-scale argu­ ment was considered in Kraichnan (1976) to show that fluctuations of the a-coefficient at intermediate scales could give a negative contri­ bution to the eddy diffusivity on large scales, but no definite con­ clusion could be drawn. Here, we shall analyze the problem using multiscale techniques, presented in Section 2. The advantage is that the nature and the order of the large-scale dynamics can be systematically identified and the calculation of the eddy-diffusivity tensor is reduced to the solution of auxiliary equations on the elementary periodicity cell. In Section 3, numerical simulations of the auxiliary equations are used to investigate a steady variant of the Taylor-Green vortex, which is found to produce a negative magnetic eddy diffusivity above a critical Reynolds number.
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Magnetar formation through a convective dynamo in protoneutron stars

Magnetar formation through a convective dynamo in protoneutron stars

40. C. Jones, A dynamo model of Jupiter’s magnetic field. Icarus 241, 148 (2014). Acknowledgments: We thank R. Bollig, M. Bugli, T. Foglizzo, B. Gallet, D. Götz, and A. Reboul-Salze for the discussions and comments. We thank the anonymous referees for useful comments, which improved the quality of the paper. We thank the online CompOSE database (https://compose.obspm.fr). Numerical simulations have been carried out at the CINES on the Occigen supercomputer (DARI projects A0030410317 and A0050410317). Funding: R.R. and J.G. acknowledge support from the European Research Council (grant no. 715368, MagBURST). H.-T.J. is grateful for the support of the European Research Council (AdG no. 341157, COCO2CASA) and the Deutsche Forschungsgemeinschaft (grants SFB-1258 and EXC 2094). We thank the DIM ACAV and the CEA/IRFU for their financial support of the Alfvén cluster. J.G. acknowledges the support from the PHAROS COST Action CA16214 and the CHETEC COST Action CA16117. This work benefited from the PSI2 program “Gamma-ray bursts and supernovae: From the central engine to the observer”. Author contributions: R.R. contributed to the conception of the project, the simulation code development, simulations, data analysis, visualization, and interpretation of results and wrote the manuscript. J.G. conceived the idea for the project and contributed to data analysis and interpretation of results and wrote the manuscript. H.-T.J. provided the PNS model and contributed to interpretation and preparation of the manuscript. T.G. contributed to simulation code development, data analysis, and interpretation of results and reviewed the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in this paper are present in the paper and/or Supplementary Materials. The code MagIC is freely available online at https:// magic-sph.github.io. The simulation outputs are available upon request. Additional data related to this paper may be requested from the authors.
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Dynamo threshold detection in the von Kármán sodium experiment

Dynamo threshold detection in the von Kármán sodium experiment

Dynamo instability has indeed been observed when the flow is driven by soft-iron impellers fitted with straight blades, with a higher critical magnetic Reynolds number ∼60 for run V tha[r]

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The Lorentz force effect on the On-Off dynamo intermittency

The Lorentz force effect on the On-Off dynamo intermittency

IV. DISCUSSION In this work we have examined how the on-off intermit- tency behavior of a near criticality dynamo is changed as the kinematic Reynolds is varied, and what is the effect of the Lorentz force in the non-linear stage of the dynamo. The predictions of [30, 31, 32, 33], linear scaling of the averaged magnetic energy with the deviation of the con- trol parameter from its critical value, fractal dimensions of the bursts, distribution of the “off” time intervals, and singular behavior of the pdf of the magnetic energy that were tested numerically in [21, 22] were verified for a larger range of Kinematic Grashof numbers when On-Off intermittency was present. Note however that all these predictions are based on the statistics of the flow in the kinematic stage of the dynamo. However it was found that the Lorentz force can drastically alter the On-Off be- havior of the dynamo in the non-linear stage by quench- ing the noise. For small Grashof numbers the Lorentz force can trap the original chaotic system in the linear regime in to a time periodic state resulting to no On-Off intermittency. At larger Grashof numbers Gr > 20 On- Off intermittency was observed but with long durations of the “on” phases that have a power law distribution. These long “on” phases result in a pdf that peaks at fi- nite values of E b . This peak can be attributed to the
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Prédiction du cycle solaire en utilisant un modèle dynamo de type Babcock-Leighton

Prédiction du cycle solaire en utilisant un modèle dynamo de type Babcock-Leighton

Une simplification utilisée pour résoudre les équations de la MHD dans un contexte de dynamo solaire et d’établir le régime cinématique dans lequel on fixe les écoulements v. L’équation 2.2 devient simplement ∂ v/∂ t = 0 et l’équation 2.4 devient linéaire [74]. Les écoulements axisymétriques (d/dφ = 0) considérés ici sont la rotation différentielle et la circulation méridienne. Le premier écoulement, causé par la convection dans l’en- veloppe du Soleil, est une dépendance en latitude de la période de rotation du plasma. Dans l’enveloppe convective du Soleil, la période de rotation du plasma près de l’équa- teur est moins grande que celle du plasma près des pôles. Le cœur radiatif est quant à lui en rotation solide et la tachocline est la couche de transition entre les deux régions [36]. La figure 2.2a montre le profil de rotation à différentes latitudes en fonction de la distance par rapport au centre du Soleil. On y voit bien la zone de transition entre la rotation solide du cœur du Soleil et la rotation différentielle de la zone de convection qui couvre les 30% externe. L’autre écoulement que l’on considère comme constant et qui joue un rôle important dans certains modèles de dynamo solaire est la circulation méri- dienne. Cet écoulement lent transporte le plasma vers les pôles en surface, fait sombrer le plasma vers l’intérieur aux pôles, transporte le plasma vers l’équateur en profondeur et fait émerger le plasma vers l’équateur (figure 2.2b [60]).
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Dynamo regimes and transitions in the VKS experiment

Dynamo regimes and transitions in the VKS experiment

5 Low dimensional dynamics 5.1 Observations In order to understand better the observed transitions, we can display a cut in the phase space for the magnetic field recorded in one location, by representing a component of the field as it evolves in time, versus the same component delayed by a time τ . Fig. 7a shows examples of such trajec- tories in the phase space for different regimes: two fixed points are observed, corresponding to the STAT HIGH regime (green curve) and to the STAT LOW regime (blue, where a transient regime can also be seen). Then the two limit cycles (magenta and red) correspond respectively to a periodically oscillating regime and a randomly reversing one. Examples of the 4 types of dynamo regimes are shown in Fig. 7b to e. The transition between the STAT LOW and the STAT HIGH regimes, via the two time dependent regimes, corresponds to the rising branch in Fig. 5c, in the region of 0.2 < θ < 0.27.
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Effect of the Lorentz force on on-off dynamo intermittency

Effect of the Lorentz force on on-off dynamo intermittency

The first examined Reynolds number beyond the laminar regime is Gr= 12.75 共run II兲. In this case two stable solutions of the Navier-Stokes equations coexist. Depending on the initial condition, this hydrodynamic system converges into one of the two attractors. The two velocity fields have dif- ferent critical magnetic Reynolds numbers. The first solution is the laminar flow, which shares the same dynamo properties as the smaller Reynolds number flows. For the second flow, however, the previous stable window between G M ⯝17.8 and

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Water experiments related to the ``Von Kármán Sodium'' Dynamo Project

Water experiments related to the ``Von Kármán Sodium'' Dynamo Project

Abstract. The purpose of the "Von Karman Sodium" (V.K.S.) experiment is to study the "Dynamo Effect", namely the spontaneous generation of magnetic field in a flow of electrically conducting fluid. The device has been built at CEA I Cadarache, in collaboration with CEA I Saclay, Ecole Normale Superieure de Lyon and Ecole Normale Superieure de Paris. It consists of a cylindrical vessel, filled with liquid Sodium, in which two coaxial rotating disks induce a Von-Karman type flow. Several experimental runs have taken place since June 2000. In order to optimize the V.K.S. set-up, a half-scale water prototype has also been built. It has allowed us to measure mean velocity profiles, as well as pressure fluctuations and mechanical power dissipa­ tion. We have observed that under certain circumstances the mean component of the turbulent flow can undergo a global bifurcation.
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Topology and field strength in spherical, anelastic dynamo simulations

Topology and field strength in spherical, anelastic dynamo simulations

LRA,Département de Physique, École normale supérieure, Paris A BSTRACT Dynamo action, i.e. the self-amplification of a magnetic field by the flow of an electrically con- ducting fluid, is considered to be the main mecha- nism for the generation of magnetic fields of stars and planets. Intensive and systematic parameter studies by direct numerical simulations using the Boussinesq approximation revealed fundamental properties of these models. However, this approx- imation considers an incompressible conducting fluid, and is therefore not adequate to describe convection in highly stratified systems like stars or gas giants. A common approach to overcome this difficulty is then to use the anelastic approxi- mation, that allows for a reference density profile while filtering out sound waves for a faster numer- ical integration. We present the results of a sys- tematic parameter study of spherical anelastic dy- namo models, and compare them with previous results obtained in the Boussinesq approximation. We discuss the influence of the stratification on the field geometry and the field strength, and also compare the different scaling laws for the velocity amplitude, the magnetic dissipation time, and the convective heat flux.
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Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow

Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow

6 Laboratoire de Physique Statistique de l’Ecole Normale Sup´ erieure, CNRS UMR 8550, 24 Rue Lhomond, 75231 Paris Cedex 05, France Magnetorotational dynamo action in Keplerian shear flow is a three-dimensional, non- linear magnetohydrodynamic process whose study is relevant to the understanding of accretion processes and magnetic field generation in astrophysics. Transition to this form of dynamo action is subcritical and shares many characteristics of transition to tur- bulence in non-rotating hydrodynamic shear flows. This suggests that these different fluid systems become active through similar generic bifurcation mechanisms, which in both cases have eluded detailed understanding so far. In this paper, we build on re- cent work on the two problems to investigate numerically the bifurcation mechanisms at work in the incompressible Keplerian magnetorotational dynamo problem in the shearing box framework. Using numerical techniques imported from dynamical systems research, we show that the onset of chaotic dynamo action at magnetic Prandtl numbers larger than unity is primarily associated with global homoclinic and heteroclinic bifurcations of nonlinear magnetorotational dynamo cycles. These global bifurcations are found to be supplemented by local bifurcations of cycles marking the beginning of period-doubling cascades. The results suggest that nonlinear magnetorotational dynamo cycles provide the pathway to turbulent injection of both kinetic and magnetic energy in incompress- ible magnetohydrodynamic Keplerian shear flow in the absence of an externally imposed magnetic field. Studying the nonlinear physics and bifurcations of these cycles in differ- ent regimes and configurations may subsequently help to better understand the physical conditions of excitation of magnetohydrodynamic turbulence and instability-driven dy- namos in a variety of astrophysical systems and laboratory experiments. The detailed characterization of global bifurcations provided for this three-dimensional subcritical fluid dynamics problem may also prove useful for the problem of transition to turbulence in hydrodynamic shear flows.
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DYNAMO-MAS: a multi-agent system for ontology evolution from text

DYNAMO-MAS: a multi-agent system for ontology evolution from text

5 Protégé: http://protege.stanford.edu/ . 6 MAY: http://www.irit.fr/MAY . 7 Eclipse: http://www.eclipse.org . other until a stable state is reached. The agents of DYNAMO- MAS use only a local knowledge and behavior to evaluate their relations with other agents, which is expected to set them at their best place in the organization. Then, the MAS proposes a new ontology (the initial ontology that has been enriched and modified) to the ontologist in the GUI (Fig. 7 ). Changes are displayed in the concept panel (➊) and in the term panel (➋): proposed concepts and terms are the underlined one. A second Tab Widgets, called DYNAMO - Virtual Ontologist Proposals (➌), has been added to Pro- tégé. It is a tabular view of the MAS proposals, incorporat- ing non-hierarchical relations that cannot be seen in the two first panels. The ontologist validates, deletes, or modifies the concepts, terms, and relations proposed by DYNAMO-MAS via the Graphical User Interface (➍).
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Towards a 3D dynamo model of the PMS star BP Tau

Towards a 3D dynamo model of the PMS star BP Tau

for the magnetic field is perfect conductor at the inner edge and potential at the outer edge. Then, we initialize the mag- netic computation with a multipole l = 3, m = 2 seed field where the mean magnetic energy is only 10 −5 of the to- tal kinetic energy. After an initial transient phase where the magnetic energy decreases by one order of magnitude, we observe its growth during 500 days in Fig. 5 due to dynamo action. The saturation of the dynamo is reached in the last 400 days. The magnetic Reynolds number based on rms ve- locities at mid-depth is Rm = 1000 but reaches 2500 near the surface. At this stage, the magnetic energy represents only 1 % of the total kinetic energy and 27 % of the convec- tive kinetic energy as shown in Fig. 5.
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DYNAMO-MAS: a multi-agent system for ontology evolution from text

DYNAMO-MAS: a multi-agent system for ontology evolution from text

5 Protégé: http://protege.stanford.edu/ . 6 MAY: http://www.irit.fr/MAY . 7 Eclipse: http://www.eclipse.org . other until a stable state is reached. The agents of DYNAMO- MAS use only a local knowledge and behavior to evaluate their relations with other agents, which is expected to set them at their best place in the organization. Then, the MAS proposes a new ontology (the initial ontology that has been enriched and modified) to the ontologist in the GUI (Fig. 7). Changes are displayed in the concept panel (➊) and in the term panel (➋): proposed concepts and terms are the underlined one. A second Tab Widgets, called DYNAMO - Virtual Ontologist Proposals (➌), has been added to Pro- tégé. It is a tabular view of the MAS proposals, incorporat- ing non-hierarchical relations that cannot be seen in the two first panels. The ontologist validates, deletes, or modifies the concepts, terms, and relations proposed by DYNAMO-MAS via the Graphical User Interface (➍).
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