Short Timescale Core Dynamics: Theory and Observations

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

doi:10.1007/978-1-4419-7955-1_8

Cited by 22 publications

(45 citation statements)

References 169 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As shown by Galtier (2014), an explanation can only be found when a rigorous analysis is conducted on the weak turbulence equations: the relation corresponds in fact to the finite helicity flux spectra, which are exact solutions of the equations. It has been long recognized that the Earth's magnetic field is not steady (Finlay et al 2010). Changes occur across a wide range of time scales, from secondsbecause of interactions between the solar wind and the magnetosphere -to several tens of millions of years, which is the longest timespan between polarity reversals.…”

mentioning

confidence: 99%

Weak turbulence theory for rotating magnetohydrodynamics and planetary flows

Galtier

2014

J. Fluid Mech.

View full text Add to dashboard Cite

International audienceA weak turbulence theory is derived for magnetohydrodynamics (MHD) under rapid rotation and in the presence of a uniform large-scale magnetic field which is associated with a constant Alfvén velocity . The angular velocity is assumed to be uniform and parallel to . Such a system exhibits left and right circularly polarized waves which can be obtained by introducing the magneto-inertial length . In the large-scale limit ( , with being the wavenumber) the left- and right-handed waves tend to the inertial and magnetostrophic waves, respectively, whereas in the small-scale limit ( ) pure Alfvén waves are recovered. By using a complex helicity decomposition, the asymptotic weak turbulence equations are derived which describe the long-time behaviour of weakly dispersive interacting waves via three-wave interaction processes. It is shown that the nonlinear dynamics is mainly anisotropic, with a stronger transfer perpendicular than parallel to the rotation axis. The general theory may converge to pure weak inertial/magnetostrophic or Alfvén wave turbulence when the large- or small-scale limits are taken, respectively. Inertial wave turbulence is asymptotically dominated by the kinetic energy/helicity, whereas the magnetostrophic wave turbulence is dominated by the magnetic energy/helicity. For both regimes, families of exact solutions are found for the spectra, which do not correspond necessarily to a maximal helicity state. It is shown that the hybrid helicity exhibits a cascade whose direction may vary according to the scale at which the helicity flux is injected, with an inverse cascade if and a direct cascade otherwise. The theory is relevant to the magnetostrophic dynamo, whose main applications are the Earth and the giant planets, such as Jupiter and Saturn, for which a small ( ) Rossby number is expected

show abstract

mentioning

confidence: 99%

Weak turbulence theory for rotating magnetohydrodynamics and planetary flows

Galtier

2014

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…In addition to the various references listed in this section, the interested reader will find a complete account of the theoretical and observational foundations of that knowledge in the reviews by Jackson and Finlay (2007) and Finlay et al (2010).…”

Section: Inference On Core Dynamics From Geomagnetic Observationsmentioning

confidence: 99%

“…As such, the problem is non-unique (Backus 1968). Consequently, further assumptions on u h are needed; those are reviewed in detail and discussed by Holme (2007) and Finlay et al (2010). In addition, the product of the inversion is often regularized: Intermediate-to smallscale features are damped in order to produce a flow of moderate spatial complexity.…”

Section: Inference On Core Dynamics From Geomagnetic Observationsmentioning

confidence: 99%

“…The subject of torsional oscillations is reviewed by Finlay et al (2010). Trying to fit the secular variation (or to explain time-dependent core flow) using that class of wavy motions is of great interest, since it provides in particular constraints on the strength of the cylindrical radial magnetic induction inside the core, B s .…”

Section: Inference On Core Dynamics From Geomagnetic Observationsmentioning

confidence: 99%

“…These phenomena include inertial waves (which build geostrophy), various types of magnetohydrodynamic waves, advection, and Ohmic dissipation; the corresponding time scales are roughly of order 1 day, 10 yr, 100 yr, and 10,000 yr, respectively (e.g. Gubbins and Roberts 1987;Jault 2008;Finlay et al 2010). Having those time scales in the right proportion is currently not easily achievable with three-dimensional dynamo models.…”

Section: Why Consider Geomagnetic Data Assimilationmentioning

confidence: 99%

See 2 more Smart Citations

An Introduction to Data Assimilation and Predictability in Geomagnetism

et al. 2010

View full text Add to dashboard Cite

International audienceData assimilation in geomagnetism designates the set of inverse methods for geomagnetic data analysis which rely on an underlying prognostic numerical model of core dynamics. Within that framework, the time-dependency of the magnetohydrodynamic state of the core need no longer be parameterized: The model trajectory (and the secular variation it generates at the surface of the Earth) is controlled by the initial condition, and possibly some other static control parameters. The primary goal of geomagnetic data assimilation is then to combine in an optimal fashion the information contained in the database of geomagnetic observations and in the dynamical model, by adjusting the model trajectory in order to provide an adequate fit to the data. The recent developments in that emerging field of research are motivated mostly by the increase in data quality and quantity during the last decade, owing to the ongoing era of magnetic observation of the Earth from space, and by the concurrent progress in the numerical description of core dynamics. In this article we review briefly the current status of our knowledge of core dynamics, and elaborate on the reasons which motivate geomagnetic data assimilation studies, most notably (a) the prospect to propagate the current quality of data backward in time to construct dynamically consistent historical core field and flow models, (b) the possibility to improve the forecast of the secular variation, and (c) on a more fundamental level, the will to identify unambiguously the physical mechanisms governing the secular variation. We then present the fundamentals of data assimilation (in its sequential and variational forms) and summarize the observations at hand for data assimilation practice. We present next two approaches to geomagnetic data assimilation: The first relies on a three-dimensional model of the geodynamo, and the second on a quasi-geostrophic approximation. We also provide an estimate of the limit of the predictability of the geomagnetic secular variation based upon a suite of three-dimensional dynamo models. We finish by discussing possible directions for future research, in particular the assimilation of laboratory observations of liquid metal analogs of Earth's core

show abstract

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

2014

View full text Add to dashboard Cite

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.

show abstract

Short Timescale Core Dynamics: Theory and Observations

Cited by 22 publications

References 169 publications

Weak turbulence theory for rotating magnetohydrodynamics and planetary flows

Weak turbulence theory for rotating magnetohydrodynamics and planetary flows

An Introduction to Data Assimilation and Predictability in Geomagnetism

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

Contact Info

Product

Resources

About