arXiv subjects

Emmanuel Dormy

Publications and source records attributed to Emmanuel Dormy.

At least 37 records · Page 2Linked to original sources

arXiv2016

Toward an asymptotic behaviour of the ABC dynamo

The ABC flow was originally introduced by Arnol'd to investigate Lagrangian chaos. It soon became the prototype example to illustrate magnetic-field amplification via fast dynamo action, i.e. dynamo action exhibiting magnetic-field amplification on a typical timescale independent of the electrical resistivity of the medium. Even though this flow is the most classical example for this important class of dynamos (with application to large-scale astrophysical objects), it was recently pointed out (Bouya Ismaël and Dormy Emmanuel, Phys. Fluids, 25 (2013) 037103) that the fast dynamo nature of this flow was unclear, as the growth rate still depended on the magnetic Reynolds number at the largest values available so far $(\text{Rm} = 25000)$ . Using state-of-the-art high-performance computing, we present high-resolution simulations (up to 40963) and extend the value of $\text{Rm}$ up to $ 5\cdot10^5$ . Interestingly, even at these huge values, the growth rate of the leading eigenmode still depends on the controlling parameter and an asymptotic regime is not reached yet. We show that the maximum growth rate is a decreasing function of $\text{Rm}$ for the largest values of $\text{Rm}$ we could achieve (as anticipated in the above-mentioned paper). Slowly damped oscillations might indicate either a new mode crossing or that the system is approaching the limit of an essential spectrum.

physics.flu-dyn↗

arXiv2014

Transition between viscous dipolar and inertial multipolar dynamos

We investigate the transition from steady dipolar to reversing multipolar dynamos. The Earth has been argued to lie close to this transition, which could offer a scenario for geomagnetic reversals. We show that the transition between dipolar and multipolar dynamos is characterized by a three terms balance (as opposed to the usually assumed two terms balance), which involves the non-gradient parts of inertial, viscous and Coriolis forces. We introduce from this equilibrium the sole parameter ${\rm Ro}\,{\rm E}^{-1/3} \equiv {\rm Re}\,{\rm E}^{2/3}$, which accurately describes the transition for a wide database of 132 fully three dimensional direct numerical simulations of spherical rotating dynamos (courtesy of U. Christensen). This resolves earlier contradictions in the literature on the relevant two,terms balance at the transition. Considering only a two terms balance between the non-gradient part of the Coriolis force and of inertial forces, provides the classical ${\rm Ro}/{\ell_u}$ (Christensen and Aubert, 2006). This transition can be equivalently described by ${\rm Re} \, {\ell^{2}_u}$, which corresponds to the two terms balance between the non-gradient part of inertial forces and viscous forces (Soderlund {\it et al.}, 2012).

physics.geo-ph↗

arXiv2014

Influence of the mass distribution on the magnetic field topology

Context. Three-dimensional spherical dynamo simulations carried out within the framework of the anelastic approximation have revealed that the established distinction between dipolar and multipolar dynamos tends to be less clear than it was in Boussinesq studies. This result was first interpreted as a direct consequence of the existence of a larger number of models with a high equatorial dipole contribution, together with an intermediate dipole field strength. However, this finding has not been clearly related to specific changes that would have been introduced by the use of the anelastic approximation. Aims. In this paper, we primarily focus on the effects of choosing of a different mass distribution. Indeed, it is likely to have as large consequences as would taking a stratified reference state into account, especially when comparing our results to previous Boussinesq studies. Methods. Our investigation is based on a systematic parameter study of weakly stratified anelastic dynamo models. Results. We show that the tendencies highlighted in previous anelastic dynamo simulations are already present in the Boussinesq limit. Thus they cannot be systematically related to anelastic effects. Actually, a central mass distribution can result in changes in the magnetic field topology that are mainly due to the concentration of convective cells close to the inner sphere.

astro-ph.SR↗

arXiv2014

Predictive Scaling Laws for Spherical Rotating Dynamos

State of the art numerical models of the Geodynamo are still performed in a parameter regime extremely remote from the values relevant to the physics of the Earth's core. In order to establish a connection between dynamo modeling and the geophysical motivation, {it is necessary to use} scaling laws. Such scaling laws establish the dependence of essential quantities (such as the magnetic field strength) on measured or controlled quantities. They allow for a direct confrontation of advanced models with geophysical {constraints}. (...) We show that previous empirical scaling laws for the magnetic field strength essentially reflect the statistical balance between energy production and dissipation for saturated dynamos. Such power based scaling laws are thus necessarily valid for any dynamo in statistical equilibrium and applicable to any numerical model, irrespectively of the dynamo mechanism. We show that direct numerical fits can provide contradictory results owing to biases in the parameters space covered in the numerics and to the role of a priori hypothesis on the fraction of ohmic dissipation. We introduce predictive scaling laws, i.e. relations involving input parameters of the governing equations only. We guide our reasoning on physical considerations. We show that our predictive scaling laws can properly describe the numerical database and reflect the dominant forces balance at work in these numerical simulations. We highlight the dependence of the magnetic field strength on the rotation rate. Finally, our results stress that available numerical models operate in a viscous dynamical regime, which is not relevant to the Earth's core.

physics.geo-ph↗

arXiv2013

Energy Fluxes during Dynamo Reversals

Using direct numerical simulations of the equations of magnetohydrodynamics, we study reversals of the magnetic field generated by the flow of an electrically conducting fluid in a sphere. We show that at low magnetic Prandtl numbers, Pm=0.5, the decrease of magnetic energy, ohmic dissipation and power of the Lorentz force during a reversal is followed by an increase of the power injected by the force driving the flow and an increase of viscous dissipation. Cross correlations show that the Lorentz energy flux is in advance with respect to the other energy fluxes. We also observe that during a reversal, the maximum of the magnetic energy density migrates from one hemisphere to the other and comes back to its initial position, in agreement with recent experimental observations. For larger magnetic Prandtl numbers (Pm= 1, 2), the magnetic field reversals do not display these trends and strongly differ one from another.

physics.flu-dyn↗

arXiv2013

Intermittency in spherical Couette dynamos

We investigate dynamo action in three-dimensional numerical simulations of turbulent spherical Couette flows. Close to the onset of dynamo action, the magnetic field exhibits an intermittent behavior, characterized by a series of short bursts of the magnetic energy separated by low-energy phases. We show that this behavior corresponds to the so-called on-off intermittency. This behavior is here reported for dynamo action with realistic boundary conditions. We investigate the role of magnetic boundary conditions in this phenomenon.

physics.flu-dyn↗

arXiv2012

Mechanisms of Planetary and Stellar Dynamos

We review some of the recent progress on modeling planetary and stellar dynamos. Particular attention is given to the dynamo mechanisms and the resulting properties of the field. We present direct numerical simulations using a simple Boussinesq model. These simulations are interpreted using the classical mean-field formalism. We investigate the transition from steady dipolar to multipolar dynamo waves solutions varying different control parameters, and discuss the relevance to stellar magnetic fields. We show that owing to the role of the strong zonal flow, this transition is hysteretic. In the presence of stress-free boundary conditions, the bistability extends over a wide range of parameters.

astro-ph.SR↗

arXiv2012

Revisiting the ABC flow dynamo

The ABC flow is a prototype for fast dynamo action, essential to the origin of magnetic field in large astrophysical objects. Probably the most studied configuration is the classical 1:1:1 flow. We investigate its dynamo properties varying the magnetic Reynolds number Rm. We identify two kinks in the growth rate, which correspond respectively to an eigenvalue crossing and to an eigenvalue coalescence. The dominant eigenvalue becomes purely real for a finite value of the control parameter. Finally we show that even for Rm = 25000, the dominant eigenvalue has not yet reached an asymptotic behaviour. Its still varies very significantly with the controlling parameter. Even at these very large values of Rm the fast dynamo property of this flow cannot yet be established.

physics.flu-dyn↗

arXiv2012

Bistability between equatorial and axial dipoles during magnetic field reversals

Numerical simulations of the geodynamo in presence of an heterogeneous heating are presented. We study the dynamics and the structure of the magnetic field when the equatorial symmetry of the flow is broken. If the symmetry breaking is sufficiently strong, the m = 0 axial dipolar field is replaced by an hemispherical magnetic field, dominated by an oscillating m = 1 magnetic field. Moreover, for moderate symmetry breaking, a bistability between the axial and the equatorial dipole is observed. In this bistable regime, the axial magnetic field exhibits chaotic switches of its polarity, involving the equatorial dipole during the transition period. This new scenario for magnetic field reversals is discussed within the framework of the Earth's dynamo.

physics.flu-dyn↗

arXiv2012

Dipole Collapse and Dynamo Waves in Global Direct Numerical Simulations

Magnetic fields of low-mass stars and planets are thought to originate from self-excited dynamo action in their convective interiors. Observations reveal a variety of field topologies ranging from large-scale, axial dipole to more structured magnetic fields. In this article, we investigate more than 70 three-dimensional, self-consistent dynamo models obtained by direct numerical simulations. The control parameters, the aspect ratio and the mechanical boundary conditions have been varied to build up this sample of models. Both, strongly dipolar and multipolar models have been obtained. We show that these dynamo regimes can in general be distinguished by the ratio of a typical convective length scale to the Rossby radius. Models with a predominantly dipolar magnetic field were obtained, if the convective length scale is at least an order of magnitude larger than the Rossby radius. Moreover, we highlight the role of the strong shear associated with the geostrophic zonal flow for models with stress-free boundary conditions. In this case, the above transition disappears and is replaced by a region of bistability for which dipolar and multipolar dynamos co-exist. We interpret our results in terms of dynamo eigenmodes using the so-called test-field method. We can thus show that models in the dipolar regime are characterized by an isolated 'single mode'. Competing overtones become significant as the boundary to multipolar dynamos is approached. We discuss how these findings relate to previous models and to observations.

astro-ph.SR↗

arXiv2010

The dynamo bifurcation in rotating spherical shells

We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core, i.e. in a rotating spherical shell with thermally driven motions. We show that the nature of the bifurcation, which can be either supercritical or subcritical or even take the form of isola (or detached lobes) strongly depends on the parameters. This dependence is described in a range of parameters numerically accessible (which unfortunately remains remote from geophysical application), and we show how the magnetic Prandtl number and the Ekman number control these transitions.

physics.geo-ph↗

arXiv2009

Chaotic magnetic field reversals in turbulent dynamos

We present direct numerical simulations of reversals of the magnetic field generated by swirling flows in a spherical domain. In agreement with a recent model, we observe that coupling dipolar and quadrupolar magnetic modes by an asymmetric forcing of the flow generates field reversals. In addition, we show that this mechanism strongly depends on the value of the magnetic Prandtl number.

physics.flu-dyn↗

arXiv2009

On the ill-posedness of the Prandtl equation

The concern of this paper is the Cauchy problem for the Prandtl equation. This problem is known to be well-posed for analytic data, or for data with monotonicity properties. We prove here that it is linearly ill-posed in Sobolev type spaces. The key of the analysis is the construction, at high tangential frequencies, of unstable quasimodes for the linearization around solutions with non-degenerate critical points. Interestingly, the strong instability is due to vicosity, which is coherent with well-posedness results obtained for the inviscid version of the equation. A numerical study of this instability is also provided.

math.AP↗

arXiv2009

Magnetostrophic MRI in the Earth's Outer Core

We show that a simple, modified version of the Magnetorotational Instability (MRI) can develop in the outer liquid core of the Earth, in the presence of a background shear. It requires either thermal wind, or a primary instability, such as convection, to drive a weak differential rotation within the core. The force balance in the Earth's core is very unlike classical astrophysical applications of the MRI (such as gaseous disks around stars). Here, the weak differential rotation in the Earth core yields an instability by its constructive interaction with the planet's much larger rotation rate. The resulting destabilising mechanism is just strong enough to counteract stabilizing resistive effects, and produce growth on geophysically interesting timescales. We give a simple physical explanation of the instability, and show that it relies on a force balance appropriate to the Earth's core, known as magnetostrophic balance.

astro-ph.EP↗

arXiv2009

Relations between dynamo-region geometry and the magnetic behavior of stars and planets

The geo and solar magnetic fields have long been thought to be very different objects both in terms of spatial structure and temporal behavior. The recently discovered field structure of a fully convective star is more reminiscent of planetary magnetic fields than the Sun's magnetic field (Donati J.-F. et al., Science, 311 (2006) 633), despite the fact that the physical and chemical properties of these objects clearly differ. This observation suggests that a simple controlling parameter could be responsible for these different behaviors. We report here the results of three-dimensional simulations which show that varying the aspect ratio of the active dynamo region can yield sharp transition from Earth-like steady dynamos to Sun-like dynamo waves.

astro-ph.EP↗

arXiv2009

Direct numerical simulations of the galactic dynamo in the kinematic growing phase

We present kinematic simulations of a galactic dynamo model based on the large scale differential rotation and the small scale helical fluctuations due to supernova explosions. We report for the first time direct numerical simulations of the full galactic dynamo using an unparameterized global approach. We argue that the scale of helicity injection is large enough to be directly resolved rather than parameterized. While the actual superbubble characteristics can only be approached, we show that numerical simulations yield magnetic structures which are close both to the observations and to the previous parameterized mean field models. In particular, the quadrupolar symmetry and the spiraling properties of the field are reproduced. Moreover, our simulations show that the presence of a vertical inflow plays an essential role to increase the magnetic growth rate. This observation could indicate an important role of the downward flow (possibly linked with galactic fountains) in sustaining galactic magnetic fields.

astro-ph.GA↗

arXiv2008

Bypassing Cowling's theorem in axisymmetric fluid dynamos

We present a numerical study of the magnetic field generated by an axisymmetrically forced flow in a spherical domain. At small enough Reynolds number, Re, the flow is axisymmetric and generates an equatorial dipole above a critical magnetic Reynolds number Rmc . The magnetic field thus breaks axisymmetry, in agreement with Cowling's theorem. This structure of the magnetic field is however replaced by a dominant axial dipole when Re is larger and allows non axisymmetric fluctuations in the flow. We show here that even in the absence of such fluctuations, an axial dipole can also be generated, at low Re, through a secondary bifurcation, when Rm is increased above the dynamo threshold. The system therefore always find a way to bypass the constraint imposed by Cowling's theorem. We understand the dynamical behaviors that result from the interaction of equatorial and axial dipolar modes using simple model equations for their amplitudes derived from symmetry arguments.

physics.flu-dyn↗

arXiv2008

Effect of magnetic boundary conditions on the dynamo threshold of von Karman swirling flows

We study the effect of different boundary conditions on the kinematic dynamo threshold of von Karman type swirling flows in a cylindrical geometry. Using an analytical test flow, we model different boundary conditions: insulating walls all over the flow, effect of sodium at rest on the cylinder side boundary, effect of sodium behind the impellers, effect of impellers or side wall made of a high-magnetic-permeability material. We find that using high-magnetic-permeability boundary conditions decreases the dynamo threshold, the minimum being achieved when they are implemented all over the flow.

physics.flu-dyn↗