Geomagnetism and the dynamo: where do we stand?

Dormy, Emmanuel; Mouël, Jean‐Louis Le

doi:10.1016/j.crhy.2008.07.003

Cited by 12 publications

(6 citation statements)

References 43 publications

(48 reference statements)

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“…One can show in a similar manner that for a subcritical bifurcation with a normal form given by (4)(5), the probability P (X) to meet a given value is…”

Section: Feedback and Couplingmentioning

confidence: 91%

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The Dynamo Bifurcation in Rotating Spherical Shells

Morin

Dormy

2009

Int. J. Mod. Phys. B

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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.

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“…One can show in a similar manner that for a subcritical bifurcation with a normal form given by (4)(5), the probability P (X) to meet a given value is…”

Section: Feedback and Couplingmentioning

confidence: 91%

“…In the absence of noise (ξ ≡ 0), solutions to (4)(5) are: the trivial X = 0 (stable for µ < 0 unstable otherwise), and the four roots of µ + αX 2 − X 4 , for −α 2 /4 µ < 0. Two of these are unstable, the two others being stable (subcritical branch) and continuous for µ 0.…”

Section: Feedback and Couplingmentioning

confidence: 99%

The Dynamo Bifurcation in Rotating Spherical Shells

Morin

Dormy

2009

Int. J. Mod. Phys. B

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“…The hydrodynamics of conducting fluids is of great importance in many terrestrial and astrophysical phenomena. Examples include the generation of magnetic fields via dynamo action in the interstellar medium, stars, and planets [1,2,3,4,5,6,7,8,9,10,11], and liquid-metal systems [12,13,14,15,16,17,18] that are studied in laboratories. The flows in such settings, which can be described at the simplest level by the equations of magnetohydrodynamics (MHD), are often turbulent [5].…”

Section: Introductionmentioning

confidence: 99%

Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence

2011

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We present the results of our detailed pseudospectral direct numerical simulation (DNS) studies, with up to 1024 3 collocation points, of incompressible, magnetohydrodynamic (MHD) turbulence in three dimensions, without a mean magnetic field. Our study concentrates on the dependence of various statistical properties of both decaying and statistically steady MHD turbulence on the magnetic Prandtl number Pr M over a large range, namely, 0.01 ≤ Pr M ≤ 10. We obtain data for a wide variety of statistical measures such as probability distribution functions (PDFs) of moduli of the vorticity and current density, the energy dissipation rates, and velocity and magnetic-field increments, energy and other spectra, velocity and magnetic-field structure functions, which we use to characterise intermittency, isosurfaces of quantities such as the moduli of the vorticity and current, and joint PDFs such as those of fluid and magnetic dissipation rates. Our systematic study uncovers interesting results that have not been noted hitherto. In particular, we find a crossover from larger intermittency in the magnetic field than in the velocity field, at large Pr M , to smaller intermittency in the magnetic field than in the velocity field, at low Pr M . Furthermore, a comparison of our results for decaying MHD turbulence and its forced, statistically steady analogue suggests that we have strong universality in the sense that, for a fixed value of Pr M , multiscaling exponent ratios agree, at least within our errorbars, for both decaying and statistically steady homogeneous, isotropic MHD turbulence.

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“…This fascination is not restricted to fluid turbulence, for which we use the Navier-Stokes equation, but it also extends to other forms of turbulence, such as that in conducting fluids, for which we use the equations of magnetohydrodynamics (MHD) [3,4,5,6,7,8] and on which we concentrate here. The flows of such conducting fluids is often turbulent in a variety of physical settings, including liquid-metal flows in terrestrial laboratories and planetary interiors [9,10,11,12,13,14,15], in stars such as the sun [3,4,6,7], in the solar wind [16,17], and in the interstellar medium [4,5,6].…”

Section: Introductionmentioning

confidence: 99%

Direct Numerical Simulations of Three-dimensional Magnetohydrodynamic Turbulence with Random, Power-law Forcing

Sahoo,

Padhan,

Basu

et al. 2020

Preprint

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We present pseudospectral direct-numerical-simulation (DNS) studies of the three-dimensional magnetohydrodynamic (MHD) equations (3DRFMHD) with a stochastic force that has zero mean and a variance ∼ k −3 , where k is the wavenumber, because 3DRFMHD is used in field-theoretic studies of the scaling of energy spectra in MHD turbulence. We obtain velocity and magnetic-field spectra and structure functions and, from these, the multiscaling exponent ratios ζ p /ζ 3 , by using the extended self similarity (ESS) procedure. These exponent ratios lie within error bars of their counterparts for conventional three-dimensional MHD turbulence (3DMHD). We then carry out a systematic comparison of the statistical properties of 3DMHD and 3DRFMHD turbulence by examining various probability distribution functions (PDFs), joint PDFs, and isosurfaces of of, e.g., the moduli of the vorticity and the current density for three magnetic Prandtl numbers Pr M = 0.1, 1, and 10.

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Geomagnetism and the dynamo: where do we stand?

Cited by 12 publications

References 43 publications

The Dynamo Bifurcation in Rotating Spherical Shells

The Dynamo Bifurcation in Rotating Spherical Shells

Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence

Direct Numerical Simulations of Three-dimensional Magnetohydrodynamic Turbulence with Random, Power-law Forcing

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