Magnetic Helicity and the Solar Dynamo

Shebalin, John V.

doi:10.3390/e21080811

Cited by 2 publications

(6 citation statements)

References 31 publications

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“…This principal result and all of the related results, we believe, further enhance the view that magnetic helicity and MHD turbulence play essential roles in understanding the fundamental cause of the geodynamo (and perhaps other astrophysical dynamos [11,12]). Next, we briefly review our numerical method, then summarize our new theoretical and computational results, followed by detailed explanations of how they were found.…”

Section: Introductionsupporting

confidence: 70%

“…As mentioned above and shown in Figure 1, differential oblateness can cause alignment, but, as shown in Figure 2, rotation appears to be the absolute controlling factor. The rotation vector Ω o enters explicitly into the basic equations only in the velocity Equation (10) and not in the magnetic induction Equation (11). However, it does enter into the magnetic induction equation implicitly through the electromotive field E = −u × b because of the hydrodynamic inertial waves present in the velocity field u of a rotating system.…”

Section: Rotation and Dipole Alignmentmentioning

confidence: 99%

“…Non-dimensional density does not appear in (10) because it equals unity. The symbols ν in (10) and η in (11) are shorthand for 1/R E and 1/R M , i.e., the inverses of the kinetic and magnetic Reynolds numbers, respectively. In the dimensional form of the equations, ν is the kinematic viscosity, while η is the magnetic diffusivity; ν = η = 0 for ideal MHD turbulence.…”

Section: Basic Equationsmentioning

confidence: 99%

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Magnetic Helicity and the Geodynamo

Shebalin

2021

Fluids

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We present theoretical and computational results in magnetohydrodynamic turbulence that we feel are essential to understanding the geodynamo. These results are based on a mathematical model that focuses on magnetohydrodynamic (MHD) turbulence, but ignores compressibility and thermal effects, as well as imposing model-dependent boundary conditions. A principal finding is that when a turbulent magnetofluid is in quasi-equilibrium, the magnetic energy in the internal dipole component is equal to the magnetic helicity multiplied by the dipole wavenumber. In the case of the Earth, measurement of the exterior magnetic field gives us, through boundary conditions, the internal poloidal magnetic field. The connection between magnetic helicity and dipole field in the liquid core then gives us the toroidal part of the internal dipole field and a model value of 3 mT for the average core dipole magnetic field. Here, we present the theoretical analysis and numerical simulations that lead to these conclusions. We also test an earlier assertion that differential oblateness may be related to dipole alignment, and while there is an effect, rotation appears to be far more important. In addition, the relationship between dipole quasi-stationarity, broken ergodicity and broken symmetry is clarified. Lastly, we discuss how inertial waves in a rotating magnetofluid can affect dipole alignment.

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Section: Introductionsupporting

confidence: 70%

Section: Rotation and Dipole Alignmentmentioning

confidence: 99%

Section: Basic Equationsmentioning

confidence: 99%

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Magnetic Helicity and the Geodynamo

Shebalin

2021

Fluids

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“…given by [29,31], which also seems to apply to Run 4 because H M has reached a steady constant value. Figure 5 shows the evolution of E M ( k, t) for Runs 3 and 5; in these runs, H M (t)∼0, as Table 2 shows.…”

Section: Computational Resultsmentioning

confidence: 89%

“…Key discoveries in our past work are: (i) That the energy of a quasi-stationary magnetic dipole in Cases I and II is directly proportional to the absolute value of the magnetic helicity of the equilibrium turbulent magnetofluid [29,31]; this also appears to apply to Case IV, as will be shown here; and (ii) that the assumed ergodicity of the statistical ensemble is actually broken at the largest scale [20,24]. Again, these ideal results have been seen to apply at the largest length-scale to real (i.e., forced and dissipative) MHD turbulence [12,13]; thus, modeling and theory provide a solution to the 'dynamo problem,' at least for the model systems considered here.…”

Section: Casementioning

confidence: 99%

Transition to Equilibrium and Coherent Structure in Ideal MHD Turbulence

Shebalin

2023

Fluids

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Transition of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence to near-equilibrium from non-equilibrium initial conditions is examined through new long-time numerical simulations on a 1283 periodic grid. Here, we neglect dissipation because we are primarily concerned with behavior at the largest scale which has been shown to be essentially the same for ideal and real (forced and dissipative) MHD turbulence. A Fourier spectral transform method is used to numerically integrate the dynamical equations forward in time and results from six computer runs are presented with various combinations of imposed rotation and mean magnetic field. There are five separate cases of ideal, homogeneous, incompressible, MHD turbulence: Case I, with no rotation or mean field; Case II, where only rotation is imposed; Case III, which has only a mean magnetic field; Case IV, where rotation vector and mean magnetic field direction are aligned; and Case V, which has nonaligned rotation vector and mean field directions. Dynamic coefficients are predicted by statistical mechanics to be zero-mean random variables, but largest-scale coherent magnetic structures emerge in all cases during transition; this implies dynamo action is inherent in ideal MHD turbulence. These coherent structures are expected to occur in Cases I, II and IV, but not in Cases III and V; future studies will determine whether they persist.

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Magnetic Helicity and the Solar Dynamo

Cited by 2 publications

References 31 publications

Magnetic Helicity and the Geodynamo

Magnetic Helicity and the Geodynamo

Transition to Equilibrium and Coherent Structure in Ideal MHD Turbulence

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