The Surface Expression of Deep Columnar Flows

Holdenried-Chernoff, D.; Maffei, Stefano; Jackson, Andrew

doi:10.1029/2020gc009039

Cited by 2 publications

(2 citation statements)

References 24 publications

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“…The scalar quantity B r is the only quantity that is expressed in spherical coordinates [ θ , ϕ ] ∈ [0, π ] × [0, 2 π ]. The link between Ψ, which is expressed in cylindrical coordinates, and B r has been studied by [48], and exact band-limited relations can be found there.…”

Section: Evolution Equations For the Magnetic Fieldmentioning

confidence: 99%

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Plesio-geostrophy for Earth’s core: I. Basic equations, inertial modes and induction

Jackson

Maffei

2020

Proc. R. Soc. A.

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An approximation is developed that lends itself to accurate description of the physics of fluid motions and motional induction on short time scales (e.g. decades), appropriate for planetary cores and in the geophysically relevant limit of very rapid rotation. Adopting a representation of the flow to be columnar (horizontal motions are invariant along the rotation axis), our characterization of the equations leads to the approximation we call plesio-geostrophy , which arises from dedicated forms of integration along the rotation axis of the equations of motion and of motional induction. Neglecting magnetic diffusion, our self-consistent equations collapse all three-dimensional quantities into two-dimensional scalars in an exact manner. For the isothermal magnetic case, a series of fifteen partial differential equations is developed that fully characterizes the evolution of the system. In the case of no forcing and absent viscous damping, we solve for the normal modes of the system, called inertial modes. A comparison with a subset of the known three-dimensional modes that are of the least complexity along the rotation axis shows that the approximation accurately captures the eigenfunctions and associated eigenfrequencies.

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Section: Evolution Equations For the Magnetic Fieldmentioning

confidence: 99%

“…. The link between Ψ , which is expressed in cylindrical coordinates, and B r has been studied by [48], and exact band-limited relations can be found there.…”

Section: (A) Vertically Integrated Quantitiesmentioning

confidence: 99%

Plesio-geostrophy for Earth’s core: I. Basic equations, inertial modes and induction

Jackson

Maffei

2020

Proc. R. Soc. A.

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Interannual Magneto–Coriolis modes and their sensitivity on the magnetic field within the Earth’s core

Gerick,

Livermore

2024

Proc. R. Soc. A.

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Linear modes for which the Coriolis acceleration is almost entirely in balance with the Lorentz force are called Magneto–Coriolis (MC) modes. These MC modes are thought to exist in Earth’s liquid outer core and could therefore contribute to the variations observed in Earth’s magnetic field. The background state on which these waves ride is assumed here to be static and defined by a prescribed magnetic field and zero flow. We introduce a new computational tool to efficiently compute solutions to the related eigenvalue problem, and study the effect of a range of both axisymmetric and non-axisymmetric background magnetic fields on the MC modes. We focus on a hierarchy of conditions that sequentially partition the numerous computed modes into those which are: (i) in principle observable, (ii) those which match a proxy for interannual geomagnetic signal over 1999–2023, and (iii) those which align with core-flows based on recent geomagnetic data. We found that the background field plays a crucial role in determining the structure of the modes. In particular, we found no examples of axisymmetric background fields that support modes consistent with recent geomagnetic changes, but that some non-axisymmetric background fields do support geomagnetically consistent modes.

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The Surface Expression of Deep Columnar Flows

Abstract: An edited version of this paper was published by AGU. Copyright (2020) American Geophysical Union.• We present an exact band-limited relationship between a cylindrical flow representation and its spherical surface counterpart.

Cited by 2 publications

References 24 publications

Plesio-geostrophy for Earth’s core: I. Basic equations, inertial modes and induction

Plesio-geostrophy for Earth’s core: I. Basic equations, inertial modes and induction

Interannual Magneto–Coriolis modes and their sensitivity on the magnetic field within the Earth’s core

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