Magnetic Helicity and the Solar Dynamo

Solar magnetism is believed to originate through dynamo action in the tachocline. Statistical mechanics, in turn, tells us that dynamo action is an inherent property of magnetohydrodynamic (MHD) turbulence, depending essentially on magnetic helicity. Here, we model the tachocline as a rotating, thin spherical shell containing MHD turbulence. Using this model, we find an expression for the entropy and from this develop the thermodynamics of MHD turbulence. This allows us to introduce the macroscopic parameters that affect magnetic self-organization and dynamo action, parameters that include magnetic helicity, as well as tachocline thickness and turbulent energy.

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Helical mode interactions and spectral transfer processes in magnetohydrodynamic turbulence

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.43 ◽

2016 ◽

Vol 791 ◽

pp. 61-96 ◽

Cited By ~ 14

Author(s):

Moritz Linkmann ◽

Arjun Berera ◽

Mairi McKay ◽

Julia Jäger

Keyword(s):

Energy Transfer ◽

Magnetic Fields ◽

Magnetic Helicity ◽

Asymmetric Effect ◽

Mhd Turbulence ◽

Dynamo Action ◽

Reverse Transfer ◽

Transfer Processes ◽

Inverse Cascade ◽

Mode Interactions

Spectral transfer processes in homogeneous magnetohydrodynamic (MHD) turbulence are investigated analytically by decomposition of the velocity and magnetic fields in Fourier space into helical modes. Steady solutions of the dynamical system which governs the evolution of the helical modes are determined, and a stability analysis of these solutions is carried out. The interpretation of the analysis is that unstable solutions lead to energy transfer between the interacting modes while stable solutions do not. From this, a dependence of possible interscale energy and helicity transfers on the helicities of the interacting modes is derived. As expected from the inverse cascade of magnetic helicity in 3-D MHD turbulence, mode interactions with like helicities lead to transfer of energy and magnetic helicity to smaller wavenumbers. However, some interactions of modes with unlike helicities also contribute to an inverse energy transfer. As such, an inverse energy cascade for non-helical magnetic fields is shown to be possible. Furthermore, it is found that high values of the cross-helicity may have an asymmetric effect on forward and reverse transfer of energy, where forward transfer is more quenched in regions of high cross-helicity than reverse transfer. This conforms with recent observations of solar wind turbulence. For specific helical interactions the relation to dynamo action is established. The present analysis provides new theoretical insights into physical processes where inverse cascade and dynamo action are involved, such as the evolution of cosmological and astrophysical magnetic fields and laboratory plasmas.

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Buckling of radially constrained thin spherical shell under edge load

10.2514/6.1968-106 ◽

1968 ◽

Author(s):

T. PIAN

Keyword(s):

Spherical Shell ◽

Thin Spherical Shell

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Inverse cascade in simulated MHD turbulence driven by small scale source of magnetic helicity

Magnetohydrodynamics ◽

10.22364/mhd.52.1.29 ◽

2016 ◽

Vol 52 (1) ◽

pp. 261-268

Author(s):

R. Stepanov ◽

◽

V. Titov ◽

◽

Keyword(s):

Magnetic Helicity ◽

Small Scale ◽

Mhd Turbulence ◽

Inverse Cascade

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A fast approach for acoustic source localization on a thin spherical shell

Structural Health Monitoring ◽

10.1177/14759217211041902 ◽

2021 ◽

pp. 147592172110419

Author(s):

Zixian Zhou ◽

Zhiwen Cui ◽

Tribikram Kundu

Keyword(s):

Velocity Profile ◽

Spherical Shell ◽

Source Localization ◽

Pressure Vessels ◽

Solution Technique ◽

Acoustic Source ◽

Spherical Shells ◽

Fast Approach ◽

Acoustic Source Localization ◽

Thin Spherical Shell

Thin spherical shell structures are wildly used as pressure vessels in the industry because of their property of having equal in-plane normal stresses in all directions. Since very large pressure difference between the inside and outside of the wall exists, any formation of defects in the pressure vessel wall has a huge safety risk. Therefore, it is necessary to quickly locate the area where the defect maybe located in the early stage of defect formation and make repair on time. The conventional acoustic source localization techniques for spherical shells require either direction-dependent velocity profile knowledge or a large number of sensors to form an array. In this study, we propose a fast approach for acoustic source localization on thin isotropic and anisotropic spherical shells. A solution technique based on the time difference of arrival on a thin spherical shell without the prior knowledge of direction-dependent velocity profile is provided. With the help of “L”-shaped sensor clusters, only 6 sensors are required to quickly predict the acoustic source location for anisotropic spherical shells. For isotropic spherical shells, only 4 sensors are required. Simulation and experimental results show that this technique works well for both isotropic and anisotropic spherical shells.

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Solar Internal Rotation, the Boundary Layer Dynamo and Latitude Distribution of Activity Belts

International Astronomical Union Colloquium ◽

10.1017/s0252921100079689 ◽

1991 ◽

Vol 130 ◽

pp. 237-240

Author(s):

G. Belvedere ◽

M.R.E. Proctor ◽

G. Lanzafame

Keyword(s):

Boundary Layer ◽

Internal Rotation ◽

Radial Profile ◽

Active Regions ◽

Dynamo Model ◽

Main Sequence Stars ◽

Dynamo Action ◽

Latitude Distribution ◽

Thin Spherical Shell ◽

And Migration

Abstract We suggest that the latitude distribution of solar activity belts and the related equatorward or poleward migration of different tracers of the solar cycle are a natural consequence of the internal radial profile of angular velocity via the working of a dynamo in the boundary layer beneath the convection zone. This has been confirmed by the results of a non-linear dynamo model in a very thin spherical shell which show that dynamo action may reasonably take place in the boundary layer and reproduce the observed surface phenomenology.Extending the argument to late main-sequence stars, it is reasonable to think that observations of the latitude distribution and migration of stellar active regions by current sophisticated techniques may make it possible to infer their internal rotation profile in a simple and direct way.

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