Short Timescale Core Dynamics: Theory and Observations

Finlay, Christopher C.; Dumberry, Mathieu; Chulliat, Arnaud; Pais, Maria Alexandra

doi:10.1007/s11214-010-9691-6

Cited by 103 publications

(82 citation statements)

References 171 publications

(233 reference statements)

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“…This point is addressed in detail in the present study considering both cases where the uniform magnetic field and the system rotation axis are either parallel (axisymmetric case) or perpendicular (asymmetric case). The latter case being the most plausible configuration inside the Earth's core [23,24]. We show that the linear spectral theory (LST) results for the Alfvén energy ratio (kinetic and magnetic, e.g., see, Matthaeus and Goldstein [25]) are in agreement with the DNS ones.…”

Section: Introductionsupporting

confidence: 76%

“…(40) yields S κ (k,t)/S m (k,t) ∝ k −2 (at large scales). Also, the analysis of the one-dimensional spectrum in the vertical (x 3 ) direction, which is parallel to the uniform magnetic field B, To end this section, we briefly address the case where the magnetic field is perpendicular to rotation axis (i.e., asymmetric case), it being the most plausible configuration inside the Earth's core [23,24]. In that case, the competition between Alfvén and inertial waves is more complex, depending not only on the scale and on the polar angle θ between k and but also on the azimuthal angle ϕ between k and V A ,…”

Section: B Spectramentioning

confidence: 99%

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Energy partition, scale by scale, in magnetic Archimedes Coriolis weak wave turbulence

et al. 2017

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Magnetic Archimedes Coriolis (MAC) waves are omnipresent in several geophysical and astrophysical flows such as the solar tachocline. In the present study, we use linear spectral theory (LST) and investigate the energy partition, scale by scale, in MAC weak wave turbulence for a Boussinesq fluid. At the scale k −1 , the maximal frequencies of magnetic (Alfvén) waves, gravity (Archimedes) waves, and inertial (Coriolis) waves are, respectively, V A k, N, and f. By using the induction potential scalar, which is a Lagrangian invariant for a diffusionless Boussinesq fluid [Salhi et al., Phys. Rev. E 85, 026301 (2012)], we derive a dispersion relation for the three-dimensional MAC waves, generalizing previous ones including that of f -plane MHD "shallow water" waves [Schecter et al., Astrophys. J. 551, L185 (2001)]. A solution for the Fourier amplitude of perturbation fields (velocity, magnetic field, and density) is derived analytically considering a diffusive fluid for which both the magnetic and thermal Prandtl numbers are one. The radial spectrum of kinetic, S κ (k,t), magnetic, S m (k,t), and potential, S p (k,t), energies is determined considering initial isotropic conditions. For magnetic Coriolis (MC) weak wave turbulence, it is shown that, at large scales such that V A k/f 1, the Alfvén ratio S κ (k,t)/S m (k,t) behaves like k −2 if the rotation axis is aligned with the magnetic field, in agreement with previous direct numerical simulations [Favier et al., Geophys. Astrophys. Fluid Dyn. (2012)] and like k −1 if the rotation axis is perpendicular to the magnetic field. At small scales, such that V A k/f 1, there is an equipartition of energy between magnetic and kinetic components. For magnetic Archimedes weak wave turbulence, it is demonstrated that, at large scales, such that (V A k/N 1), there is an equipartition of energy between magnetic and potential components, while at small scales (V A k/N 1), the ratio S p (k,t)/S κ (k,t) behaves like k −1 and S κ (k,t)/S m (k,t) = 1. Also, for MAC weak wave turbulence, it is shown that, at small scales (V A k/ N 2 + f 2 1), the ratio S p (k,t)/S κ (t) behaves like k −1 and S κ (k,t)/S m (k,t) = 1.

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Section: Introductionsupporting

confidence: 76%

Section: B Spectramentioning

confidence: 99%

Energy partition, scale by scale, in magnetic Archimedes Coriolis weak wave turbulence

et al. 2017

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“…This improvement can be sought on the numerical models themselves, who should ideally describe fast (interannual) core processes at work in the geomagnetic , Finlay et al 2010a). This is not a trivial task.…”

Section: Discussionmentioning

confidence: 99%

A candidate secular variation model for IGRF-12 based on Swarm data and inverse geodynamo modelling

2015

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In the context of the 12th release of the international geomagnetic reference field (IGRF), we present the methodology we followed to design a candidate secular variation model for years 2015-2020. An initial geomagnetic field model centered around 2014.3 is first constructed, based on Swarm magnetic measurements, for both the main field and its instantaneous secular variation. This initial model is next fed to an inverse geodynamo modelling framework in order to specify, for epoch 2014.3, the initial condition for the integration of a three-dimensional numerical dynamo model. The initialization phase combines the information contained in the initial model with that coming from the numerical dynamo model, in the form of three-dimensional multivariate statistics built from a numerical dynamo run unconstrained by data. We study the performance of this novel approach over two recent 5-year long intervals, 2005-2010 and 2009-2014. For a forecast horizon of 5 years, shorter than the large-scale secular acceleration time scale (∼10 years), we find that it is safer to neglect the flow acceleration and to assume that the flow determined by the initialization is steady. This steady flow is used to advance the three-dimensional induction equation forward in time, with the benefit of estimating the effects of magnetic diffusion. The result of this deterministic integration between 2015.0 and 2020.0 yields our candidate average secular variation model for that time frame, which is thus centered on 2017.5.

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“…To perform a consistent inversion of the frozen flux equation at the CMB, in addition to imposing a certain behavior to the flow and to regularizing it [see Holme, 2007;Finlay et al, 2010], every scale composing the secular variation and the magnetic field must be known. Unfortunately, in the current models describing the spatiotemporal evolution of the Earth's magnetic field derived from satellite and observatory data, the resolution of both the SV and the MF is limited.…”

Section: The Unresolved Scale Issuementioning

confidence: 99%

Bayesian inversion for the filtered flow at the Earth's core‐mantle boundary

2014

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The inverse problem of determining the flow at the Earth's core-mantle boundary according to an outer core magnetic field and secular variation model has been investigated through a Bayesian formalism. To circumvent the issue arising from the truncated nature of the available fields, we combined two modeling methods. In the first step, we applied a filter on the magnetic field to isolate its large scales by reducing the energy contained in its small scales, we then derived the dynamical equation, referred as filtered frozen flux equation, describing the spatiotemporal evolution of the filtered part of the field. In the second step, we proposed a statistical parametrization of the filtered magnetic field in order to account for both its remaining unresolved scales and its large-scale uncertainties. These two modeling techniques were then included in the Bayesian formulation of the inverse problem. To explore the complex posterior distribution of the velocity field resulting from this development, we numerically implemented an algorithm based on Markov chain Monte Carlo methods. After evaluating our approach on synthetic data and comparing it to previously introduced methods, we applied it to a magnetic field model derived from satellite data for the single epoch 2005.0. We could confirm the existence of specific features already observed in previous studies. In particular, we retrieved the planetary scale eccentric gyre characteristic of flow evaluated under the compressible quasi-geostrophy assumption although this hypothesis was not considered in our study. In addition, through the sampling of the velocity field posterior distribution, we could evaluate the reliability, at any spatial location and at any scale, of the flow we calculated. The flow uncertainties we determined are nevertheless conditioned by the choice of the prior constraints we applied to the velocity field.

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Short Timescale Core Dynamics: Theory and Observations

Cited by 103 publications

References 171 publications

Energy partition, scale by scale, in magnetic Archimedes Coriolis weak wave turbulence

Energy partition, scale by scale, in magnetic Archimedes Coriolis weak wave turbulence

A candidate secular variation model for IGRF-12 based on Swarm data and inverse geodynamo modelling

Bayesian inversion for the filtered flow at the Earth's core‐mantle boundary

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