Dynamo action in rotating convection

2009 ◽  
Vol 5 (H15) ◽  
pp. 347-347
Author(s):  
Gustavo Guerrero ◽  
Elisabete M. de Gouveia Dal Pino
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Hydrostatic Equilibrium ◽  
Computational Domain ◽  
Dynamo Action ◽  
Rotating Convection ◽  
Helical Turbulence ◽  
Large Scale Magnetic Field ◽  
Unstable Layer ◽  
Scale Shear

AbstractWe present MHD numerical simulations of a rotating turbulent convection system in a 3D domain (we have used the finite volume, Goudunov type MHD code PLUTO (Mignone et al. 2007)). Rotating convection is the natural scenario for the study of the dynamo action which is able to generate a large scale magnetic field, like the observed in the sun. Though we have neglected in the present approach the Ω effect, due to a large scale shear, our model is appropriate to test the controversial existence of the so called α effect that arises from helical turbulence (e.g. Cattaneo & Hughes 2006, Käpylä et al. 2009). We start with a two-layer piece-wise polytropic region in hydrostatic equilibrium (e.g. Ziegler 2002), considering one stable overshoot layer at the bottom and a convectively unstable layer at the top of the computational domain. We have allowed this hydrodynamic system to evolve up to the steady state, i.e., after about 10 turnover times (τ). Then, we introduced a seed magnetic field and let the system evolve for more ~40 τ. Our preliminary results are summarized below in Figure 2.

scholarly journals Moffatt-drift-driven large-scale dynamo due to  fluctuations with non-zero correlation times

2016 ◽  
Vol 798 ◽  
pp. 696-716 ◽  
Author(s):  
Nishant K. Singh
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Growth Rate ◽  
White Noise ◽  
Large Scale ◽  
Maximum Growth ◽  
Dynamo Action ◽  
Integro Differential Equation ◽  
Large Scale Magnetic Field ◽  
Finite Memory

We present a theory of large-scale dynamo action in a turbulent flow that has stochastic, zero-mean fluctuations of the ${\it\alpha}$ parameter. Particularly interesting is the possibility of the growth of the mean magnetic field due to Moffatt drift, which is expected to be finite in a statistically anisotropic turbulence. We extend the Kraichnan–Moffatt model to explore effects of finite memory of ${\it\alpha}$ fluctuations, in a spirit similar to that of Sridhar & Singh (Mon. Not. R. Astron. Soc., vol. 445, 2014, pp. 3770–3787). Using the first-order smoothing approximation, we derive a linear integro-differential equation governing the dynamics of the large-scale magnetic field, which is non-perturbative in the ${\it\alpha}$-correlation time ${\it\tau}_{{\it\alpha}}$. We recover earlier results in the exactly solvable white-noise limit where the Moffatt drift does not contribute to the dynamo growth/decay. To study finite-memory effects, we reduce the integro-differential equation to a partial differential equation by assuming that ${\it\tau}_{{\it\alpha}}$ be small but non-zero and the large-scale magnetic field is slowly varying. We derive the dispersion relation and provide an explicit expression for the growth rate as a function of four independent parameters. When ${\it\tau}_{{\it\alpha}}\neq 0$, we find that: (i) in the absence of the Moffatt drift, but with finite Kraichnan diffusivity, only strong ${\it\alpha}$ fluctuations can enable a mean-field dynamo (this is qualitatively similar to the white-noise case); (ii) in the general case when also the Moffatt drift is non-zero, both weak and strong ${\it\alpha}$ fluctuations can lead to a large-scale dynamo; and (iii) there always exists a wavenumber ($k$) cutoff at some large $k$ beyond which the growth rate turns negative, irrespective of weak or strong ${\it\alpha}$ fluctuations. Thus we show that a finite Moffatt drift can always facilitate large-scale dynamo action if sufficiently strong, even in the case of weak ${\it\alpha}$ fluctuations, and the maximum growth occurs at intermediate wavenumbers.

scholarly journals The effect of velocity shear on dynamo action due to rotating convection

2013 ◽  
Vol 717 ◽  
pp. 395-416 ◽  
Author(s):  
D. W. Hughes ◽  
M. R. E. Proctor
Keyword(s):  
Magnetic Field ◽  
Velocity Field ◽  
Large Scale ◽  
Mean Field ◽  
Magnetic Reynolds Number ◽  
Velocity Shear ◽  
Magnetic Field Generation ◽  
Dynamo Action ◽  
Rotating Convection ◽  
The Magnetic Field

AbstractRecent numerical simulations of dynamo action resulting from rotating convection have revealed some serious problems in applying the standard picture of mean field electrodynamics at high values of the magnetic Reynolds number, and have thereby underlined the difficulties in large-scale magnetic field generation in this regime. Here we consider kinematic dynamo processes in a rotating convective layer of Boussinesq fluid with the additional influence of a large-scale horizontal velocity shear. Incorporating the shear flow enhances the dynamo growth rate and also leads to the generation of significant magnetic fields on large scales. By the technique of spectral filtering, we analyse the modes in the velocity that are principally responsible for dynamo action, and show that the magnetic field resulting from the full flow relies crucially on a range of scales in the velocity field. Filtering the flow to provide a true separation of scales between the shear and the convective flow also leads to dynamo action; however, the magnetic field in this case has a very different structure from that generated by the full velocity field. We also show that the nature of the dynamo action is broadly similar irrespective of whether the flow in the absence of shear can support dynamo action.

scholarly journals A physical approach to modelling large-scale galactic magnetic fields

2019 ◽  
Vol 623 ◽  
pp. A113 ◽  
Author(s):  
Anvar Shukurov ◽  
Luiz Felippe S. Rodrigues ◽  
Paul J. Bushby ◽  
James Hollins ◽  
Jörg P. Rachen
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Large Scale ◽  
Milky Way ◽  
Mean Field ◽  
Axially Symmetric ◽  
Dynamo Action ◽  
Disc Galaxy ◽  
Large Scale Magnetic Field ◽  
Dynamo Equation

Context. A convenient representation of the structure of the large-scale galactic magnetic field is required for the interpretation of polarization data in the sub-mm and radio ranges, in both the Milky Way and external galaxies. Aims. We develop a simple and flexible approach to construct parametrised models of the large-scale magnetic field of the Milky Way and other disc galaxies, based on physically justifiable models of magnetic field structure. The resulting models are designed to be optimised against available observational data. Methods. Representations for the large-scale magnetic fields in the flared disc and spherical halo of a disc galaxy were obtained in the form of series expansions whose coefficients can be calculated from observable or theoretically known galactic properties. The functional basis for the expansions is derived as eigenfunctions of the mean-field dynamo equation or of the vectorial magnetic diffusion equation. Results. The solutions presented are axially symmetric but the approach can be extended straightforwardly to non-axisymmetric cases. The magnetic fields are solenoidal by construction, can be helical, and are parametrised in terms of observable properties of the host object, such as the rotation curve and the shape of the gaseous disc. The magnetic field in the disc can have a prescribed number of field reversals at any specified radii. Both the disc and halo magnetic fields can separately have either dipolar or quadrupolar symmetry. The model is implemented as a publicly available software package GALMAG which allows, in particular, the computation of the synchrotron emission and Faraday rotation produced by the model’s magnetic field. Conclusions. The model can be used in interpretations of observations of magnetic fields in the Milky Way and other spiral galaxies, in particular as a prior in Bayesian analyses. It can also be used for a simple simulation of a time-dependent magnetic field generated by dynamo action.

scholarly journals The supernova-regulated ISM – VI. Magnetic effects on the structure of the interstellar medium

2019 ◽  
Vol 488 (4) ◽  
pp. 5065-5074 ◽  
Author(s):  
C C Evirgen ◽  
F A Gent ◽  
A Shukurov ◽  
A Fletcher ◽  
P J Bushby
Keyword(s):  
Magnetic Field ◽  
Interstellar Medium ◽  
Vertical Distribution ◽  
Large Scale ◽  
Dynamo Action ◽  
Hot Gas ◽  
Downward Pressure ◽  
Large Scale Magnetic Field ◽  
The Vertical Distribution ◽  
The Magnetic Field

ABSTRACT We explore the effect of magnetic fields on the vertical distribution and multiphase structure of the supernova-driven interstellar medium in simulations that admit dynamo action. As the magnetic field is amplified to become dynamically significant, gas becomes cooler and its distribution in the disc becomes more homogeneous. We attribute this to magnetic quenching of vertical velocity, which leads to a decrease in the cooling length of hot gas. A non-monotonic vertical distribution of the large-scale magnetic field strength, with the maximum at |z| ≈ 300 pc causes a downward pressure gradient below the maximum which acts against outflow driven by SN explosions, while it provides pressure support above the maximum.

scholarly journals Dynamo generated field emergence through recurrent plasmoid ejections

2010 ◽  
Vol 6 (S273) ◽  
pp. 256-260
Author(s):  
Jörn Warnecke ◽  
Axel Brandenburg
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Solar Atmosphere ◽  
Large Scale ◽  
Computational Domain ◽  
Dynamo Action ◽  
Layer System ◽  
Forcing Function ◽  
Magnetic Buoyancy ◽  
The Magnetic Field

AbstractMagnetic buoyancy is believed to drive the transport of magnetic flux tubes from the convection zone to the surface of the Sun. The magnetic fields form twisted loop-like structures in the solar atmosphere. In this paper we use helical forcing to produce a large-scale dynamo-generated magnetic field, which rises even without magnetic buoyancy. A two layer system is used as computational domain where the upper part represents the solar atmosphere. Here, the evolution of the magnetic field is solved with the stress–and–relax method. Below this region a magnetic field is produced by a helical forcing function in the momentum equation, which leads to dynamo action. We find twisted magnetic fields emerging frequently to the outer layer, forming arch-like structures. In addition, recurrent plasmoid ejections can be found by looking at space–time diagrams of the magnetic field. Recent simulations in spherical coordinates show similar results.

scholarly journals Generation of large-scale magnetic fields due to fluctuating in shearing systems

2018 ◽  
Vol 84 (6) ◽  
Author(s):  
Naveen Jingade ◽  
Nishant K. Singh ◽  
S. Sridhar
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Growth Rate ◽  
Magnetic Fields ◽  
Correlation Time ◽  
Large Scale ◽  
Dynamo Theory ◽  
Dynamo Action ◽  
Stochastic Fluctuations ◽  
Large Scale Magnetic Field

We explore the growth of large-scale magnetic fields in a shear flow, due to helicity fluctuations with a finite correlation time, through a study of the Kraichnan–Moffatt model of zero-mean stochastic fluctuations of the$\unicode[STIX]{x1D6FC}$parameter of dynamo theory. We derive a linear integro-differential equation for the evolution of the large-scale magnetic field, using the first-order smoothing approximation and the Galilean invariance of the$\unicode[STIX]{x1D6FC}$-statistics. This enables construction of a model that is non-perturbative in the shearing rate$S$and the$\unicode[STIX]{x1D6FC}$-correlation time$\unicode[STIX]{x1D70F}_{\unicode[STIX]{x1D6FC}}$. After a brief review of the salient features of the exactly solvable white-noise limit, we consider the case of small but non-zero$\unicode[STIX]{x1D70F}_{\unicode[STIX]{x1D6FC}}$. When the large-scale magnetic field varies slowly, the evolution is governed by a partial differential equation. We present modal solutions and conditions for the exponential growth rate of the large-scale magnetic field, whose drivers are the Kraichnan diffusivity, Moffatt drift, shear and a non-zero correlation time. Of particular interest is dynamo action when the$\unicode[STIX]{x1D6FC}$-fluctuations are weak; i.e. when the Kraichnan diffusivity is positive. We show that in the absence of Moffatt drift, shear does not give rise to growing solutions. But shear and Moffatt drift acting together can drive large-scale dynamo action with growth rate$\unicode[STIX]{x1D6FE}\propto |S|$.

scholarly journals The magnetic helicity density patterns from non-axisymmetric solar dynamo

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Valery V. Pipin
Keyword(s):  
Magnetic Field ◽  
Differential Rotation ◽  
Conservation Law ◽  
Large Scale ◽  
Solar Dynamo ◽  
Magnetic Helicity ◽  
Dynamo Model ◽  
Density Distributions ◽  
Large Scale Magnetic Field ◽  
Helicity Conservation

We study the helicity density patterns which can result from the emerging bipolar regions. Using the relevant dynamo model and the magnetic helicity conservation law we find that the helicity density patterns around the bipolar regions depend on the configuration of the ambient large-scale magnetic field, and in general they show a quadrupole distribution. The position of this pattern relative to the equator can depend on the tilt of the bipolar region. We compute the time–latitude diagrams of the helicity density evolution. The longitudinally averaged effect of the bipolar regions shows two bands of sign for the density distributions in each hemisphere. Similar helicity density patterns are provided by the helicity density flux from the emerging bipolar regions subjected to surface differential rotation.

scholarly journals Propagation of an MHD Shock in the Vicinity of a Magnetic Neutral Sheet

1980 ◽  
Vol 91 ◽  
pp. 323-326
Author(s):  
D. J. Mullan ◽  
R. S. Steinolfson
Keyword(s):  
Magnetic Field ◽  
Cosmic Rays ◽  
Solar Corona ◽  
Large Scale ◽  
Field Structure ◽  
Neutral Sheet ◽  
Solar Cosmic Rays ◽  
Magnetic Field Structure ◽  
Large Scale Magnetic Field ◽  
Highly Correlated

The acceleration of solar cosmic rays in association with certain solar flares is known to be highly correlated with the propagation of an MHD shock through the solar corona (Svestka, 1976). The spatial structure of the sources of solar cosmic rays will be determined by those regions of the corona which are accessible to the flare-induced shock. The regions to which the flare shock is permitted to propagate are determined by the large scale magnetic field structure in the corona. McIntosh (1972, 1979) has demonstrated that quiescent filaments form a single continuous feature (a “baseball stitch”) around the surface of the sun. It is known that helmet streamers overlie quiescent filaments (Pneuman, 1975), and these helmet streamers contain large magnetic neutral sheets which are oriented essentially radially. Hence the magnetic field structure in the low solar corona is characterized by a large-scale radial neutral sheet which weaves around the entire sun following the “baseball stitch”. There is therefore a high probability that as a shock propagates away from a flare, it will eventually encounter this large neutral sheet.

Turbulent dynamo action at low magnetic Reynolds number

1970 ◽  
Vol 41 (2) ◽  
pp. 435-452 ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Magnetic Reynolds Number ◽  
Dynamo Action ◽  
Ohmic Dissipation ◽  
Magnetic Energy Density ◽  
Magnetic Diffusivity

The effect of turbulence on a magnetic field whose length-scale L is initially large compared with the scale l of the turbulence is considered. There are no external sources for the field, and in the absence of turbulence it decays by ohmic dissipation. It is assumed that the magnetic Reynolds number Rm = u0l/λ (where u0 is the root-mean-square velocity and λ the magnetic diffusivity) is small. It is shown that to lowest order in the small quantities l/L and Rm, isotropic turbulence has no effect on the large-scale field; but that turbulence that lacks reflexional symmetry is capable of amplifying Fourier components of the field on length scales of order Rm−2l and greater. In the case of turbulence whose statistical properties are invariant under rotation of the axes of reference, but not under reflexions in a point, it is shown that the magnetic energy density of a magnetic field which is initially a homogeneous random function of position with a particularly simple spectrum ultimately increases as t−½exp (α2t/2λ3) where α(= O(u02l)) is a certain linear functional of the spectrum tensor of the turbulence. An analogous result is obtained for an initially localized field.

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