Confinement of rotating convection by a laterally varying magnetic field

Sreenivasan, Binod; Gopinath, Venkatesh

doi:10.1017/jfm.2017.286

Cited by 13 publications

(5 citation statements)

References 39 publications

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“…ref. 45), this process would tend to generate a relatively smooth polar minimum that would be predominantly axisymmetric in structure (e.g., case S2 in ref. 24), unlike the strongly nonaxisymmetric magnetic minima observed at the Earth's CMB (Fig.…”

Section: Summary and Discussionmentioning

confidence: 99%

Geomagnetic polar minima do not arise from steady meridional circulation

Cao

Yadav

Aurnou

2018

Proc. Natl. Acad. Sci. U.S.A.

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Observations of the Earth’s magnetic field have revealed locally pronounced field minima near each pole at the core–mantle boundary (CMB). The existence of the polar magnetic minima has long been attributed to the supposed large-scale overturning circulation of molten metal in the outer core: Fluid upwells within the inner core tangent cylinder toward the poles and then diverges toward lower latitudes when it reaches the CMB, where Coriolis effects sweep the fluid into anticyclonic vortical flows. The diverging near-surface meridional circulation is believed to advectively draw magnetic flux away from the poles, resulting in the low intensity or even reversed polar magnetic fields. However, the interconnections between polar magnetic minima and meridional circulations have not to date been ascertained quantitatively. Here, we quantify the magnetic effects of steady, axisymmetric meridional circulation via numerically solving the axisymmetric magnetohydrodynamic equations for Earth’s outer core under the magnetostrophic approximation. Extrapolated to core conditions, our results show that the change in polar magnetic field resulting from steady, large-scale meridional circulations in Earth’s outer core is less than 3% of the background field, significantly smaller than the ∼ 100% polar magnetic minima observed at the CMB. This suggests that the geomagnetic polar minima cannot be produced solely by axisymmetric, steady meridional circulations and must depend upon additional tangent cylinder dynamics, likely including nonaxisymmetric, time-varying processes.

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Section: Summary and Discussionmentioning

confidence: 99%

Geomagnetic polar minima do not arise from steady meridional circulation

Cao

Yadav

Aurnou

2018

Proc. Natl. Acad. Sci. U.S.A.

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“…This clustering of roots of Chebyshev polynomials proved useful for exploring the steady two-dimensional amagnetic convection in the plane layer at high Rayleigh numbers by Chebyshev collocations [16,17] and for tackling the magnetic dynamo problem [18] for a uniform shear flow between a solid plate sliding over another one, both having anisotropic electrical conductivity. (It can be exploited directly: for instance, finite differences in the radial direction were used in [19] with the nodes located at the roots of Chebyshev polynomials. )…”

Section: Introductionmentioning

confidence: 99%

Algorithmic Aspects of Simulation of Magnetic Field Generation by Thermal Convection in a Plane Layer of Fluid

2023

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We present an algorithm for numerical solution of the equations of magnetohydrodynamics describing the convective dynamo in a plane horizontal layer rotating about an arbitrary axis under geophysically sound boundary conditions. While in many respects we pursue the general approach that was followed by other authors, our main focus is on the accuracy of simulations, especially in the small scales. We employ the Galerkin method. We use products of linear combinations (each involving two to five terms) of Chebyshev polynomials in the vertical Cartesian space variable and Fourier harmonics in the horizontal variables for space discretisation of the toroidal and poloidal potentials of the flow (satisfying the no-slip conditions on the horizontal boundaries) and magnetic field (for which the boundary conditions mimick the presence of a dielectric over the fluid layer and an electrically conducting bottom boundary), and of the deviation of temperature from the steady-state linear profile. For the chosen coefficients in the linear combinations, the products satisfy the respective boundary conditions and constitute non-orthogonal bases in the weighted Lebesgue space. Determining coefficients in the expansion of a given function in such a basis (for instance, for computing the time derivatives of these coefficients) requires solving linear systems of equations for band matrices. Several algorithms for determining the coefficients, which are exploiting algebraically precise relations, have been developed, and their efficiency and accuracy have been numerically investigated for exponentially decaying solutions (encountered when simulating convective regimes which are spatially resolved sufficiently well). For the boundary conditions satisfied by the toroidal component of the flow, our algorithm outperforms the shuttle method, but the latter proves superior when solving the problem for the conditions characterising the poloidal component. While the conditions for the magnetic field on the horizontal boundaries are quite specific, our algorithms for the no-slip boundary conditions are general-purpose and can be applied for treating other boundary-value problems in which the zero value must be admitted on the boundary.

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“…They considered linear magnetoconvection in a spherical shell in the rapidly rotating limit E → 0, where E is the Ekman number that gives the ratio of viscous to Coriolis forces. Although the spatially varying magnetic field in a nonlinear dynamo does not substantially lower the threshold for convective onset relative to that in the nonmagnetic system (Sreenivasan and Gopinath, 2017), there is a substantial enhancement of helical convection in the neighbourhood of the length scale of energy injection (Sreenivasan and Kar, 2018). The growth of convection is notably absent in a kinematic dynamo, which fails to produce the axial dipole with the same parameters and initial conditions.…”

Section: Introductionmentioning

confidence: 91%

The role of slow magnetostrophic waves in the formation of the axial dipole in planetary dynamos

Varma¹,

Sreenivasan²

2022

Preprint

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The preference for the axial dipole in planetary dynamos is investigated through the analysis of wave motions in spherical dynamo models. Our study focuses on the role of slow magnetostrophic waves, which are generated from localized balances between the Lorentz, Coriolis and buoyancy (MAC) forces. Since the slow waves are known to intensify with increasing field strength, simulations in which the field grows from a small seed towards saturation are useful in understanding the role of these waves in dynamo action. Axial group velocity measurements in the energy-containing scales show that fast inertial waves slightly modified by the magnetic field and buoyancy are dominant under weak fields. However, the dominance of the slow waves is evident for strong fields satisfying |ω M /ω C | ∼ 0.1, where ω M and ω C are the frequencies of the Alfvén and inertial waves respectively. A MAC wave window of azimuthal wavenumbers is identified wherein helicity generation by the slow waves strongly correlates with dipole generation. Analysis of the magnetic induction equation suggests a poloidal-poloidal field conversion in the formation of the dipole. Finally, the attenuation of slow waves may result in polarity reversals in a strongly driven Earth's core.

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Confinement of rotating convection by a laterally varying magnetic field

Cited by 13 publications

References 39 publications

Geomagnetic polar minima do not arise from steady meridional circulation

Geomagnetic polar minima do not arise from steady meridional circulation

Algorithmic Aspects of Simulation of Magnetic Field Generation by Thermal Convection in a Plane Layer of Fluid

The role of slow magnetostrophic waves in the formation of the axial dipole in planetary dynamos

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