Experiments on precessing flows in the Earth's liquid core

Vanyo, James P.; Wilde, Pieter de; Cardin, Philippe; Olson, Peter

doi:10.1111/j.1365-246x.1995.tb03516.x

Cited by 109 publications

(136 citation statements)

References 40 publications

(65 reference statements)

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“…The third type is by far the most accessible to theoretical analysis and is understood best. However, early experiments conveyed the intuition that the second type is the most important (Malkus 1968;Vanyo et al 1995). Clearly, different instabilities set in Fig. 14 Sketch of the structure of unstable precession driven flow (from Lorenzani and Tilgner 2001) first depending on the control parameters and we do not know at present what to expect for planetary values.…”

Section: Tidally Driven and Precession Driven Dynamosmentioning

confidence: 99%

Theory and Modeling of Planetary Dynamos

Wicht

Tilgner

2010

Space Sci Rev

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Numerical dynamo models are increasingly successful in modeling many features of the geomagnetic field. Moreover, they have proven to be a useful tool for understanding how the observations connect to the dynamo mechanism. More recently, dynamo simulations have also ventured to explain the surprising diversity of planetary fields found in our solar system. Here, we describe the underlying model equations, concentrating on the Boussinesq approximations, briefly discuss the numerical methods, and give an overview of existing model variations. We explain how the solutions depend on the model parameters and introduce the primary dynamo regimes. Of particular interest is the dependence on the Ekman number which is many orders of magnitude too large in the models for numerical reasons. We show that a minor change in the solution seems to happen at E = 3×10 −6 whose significance, however, needs to be explored in the future. We also review three topics that have been a focus of recent research: field reversal mechanisms, torsional oscillations, and the influence of Earth's thermal mantle structure on the dynamo. Finally we discuss the possibility of tidally or precession driven planetary dynamos.

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Section: Tidally Driven and Precession Driven Dynamosmentioning

confidence: 99%

Theory and Modeling of Planetary Dynamos

Wicht

Tilgner

2010

Space Sci Rev

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“…It is estimated that there is abundant energy in rotation to sustain the generation of planetary magnetic fields [Kerswell, 1996]. It has been shown experimentally that the spatially complex flows required for dynamo action can occur in nonuniformly rotating spheroidal systems [Malkus, 1968;Vanyo et al, 2007;Noir and Cardin, 2001;Noir et al, 2003]. Recently, it has been convincingly demonstrated that precession-driven flows can indeed generate and sustain magnetic fields [Tilgner, 2005;Wu and Roberts, 2009].…”

Section: Introductionmentioning

confidence: 99%

Shapes of two‐layer models of rotating planets

2010

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[1] To first approximation the interiors of many planetary bodies consist of a core and mantle with significantly different densities. The shapes of the surface and interface between the core and the mantle are basic properties reflecting planetary structure and rotation. In addition, interface shape is an important parameter controlling the dynamics of a fluid core. We present a theory for the rotational distortion of a two-layer model of a planet (two-layer Maclaurin spheroid) that determines the shapes of both the interface and the outer free surface without treating departure from sphericity as a small perturbation. Since the interface and the outer free surface, in general, have different shapes, two different spheroidal coordinates are required in the mathematical analysis, and the transformation between them is at the heart of the complexity of the theory. Furthermore, two different cases have to be considered. In the first case, the core is sufficiently large, or the rate of rotation is sufficiently small, that the foci of the outer free surface are located within the core. In the second case, the core is sufficiently small, or the rate of rotation is sufficiently fast, that the foci of the free surface are located within the outer layer. In comparison to the classical Maclaurin solution which is explicitly analytical, the relevant multiple integrals for the equilibrium solution of a two-layer Maclaurin spheroid have to be evaluated numerically. The shape of a two-layer rotating planet is characterized by three dimensionless parameters that are explored systematically in the present study.

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“…Note that spheroidal or ellipsoidal geometry has frequently been employed by many authors to study fluid motion in geophysical and astrophysical contexts (see e.g. Vanyo et al 1995;Lorenzani & Tilgner 2001;Noir et al 2003;Wu & Roberts 2009;Le Bars et al 2010).…”

Section: Introduction and Formulationmentioning

confidence: 99%

Asymptotic theory of resonant flow in a spheroidal cavity driven by latitudinal libration

2012

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We consider a homogeneous fluid of viscosity ν confined within an oblate spheroidal cavity, x 2 /a 2 + y 2 /a 2 + z 2 /(a 2 (1 − E 2 )) = 1, with eccentricity 0 < E < 1. The spheroidal container rotates rapidly with an angular velocity Ω 0 , which is fixed in an inertial frame and defines a small Ekman number E = ν/(a 2 |Ω 0 |), and undergoes weak latitudinal libration with frequencyω|Ω 0 | and amplitude Po|Ω 0 |, where Po is the Poincaré number quantifying the strength of Poincaré force resulting from latitudinal libration. We investigate, via both asymptotic and numerical analysis, fluid motion in the spheroidal cavity driven by latitudinal libration. When |ω − 2/(2 − E 2 )| O(E 1/2 ), an asymptotic solution for E 1 and Po 1 in oblate spheroidal coordinates satisfying the no-slip boundary condition is derived for a spheroidal cavity of arbitrary eccentricity without making any prior assumptions about the spatial-temporal structure of the librating flow. In this case, the librationally driven flow is nonaxisymmetric with amplitude O(Po), and the role of the viscous boundary layer is primarily passive such that the flow satisfies the no-slip boundary condition. When |ω − 2/(2 − E 2 )| O(E 1/2 ), the librationally driven flow is also non-axisymmetric but latitudinal libration resonates with a spheroidal inertial mode that is in the form of an azimuthally travelling wave in the retrograde direction. The amplitude of the flow becomes O(Po/E 1/2 ) at E 1 and the role of the viscous boundary layer becomes active in determining the key property of the flow. An asymptotic solution for E 1 describing the librationally resonant flow is also derived for an oblate spheroidal cavity of arbitrary eccentricity. Three-dimensional direct numerical simulation in an oblate spheroidal cavity is performed to demonstrate that, in both the non-resonant and resonant cases, a satisfactory agreement is achieved between the asymptotic solution and numerical simulation at E 1.

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Experiments on precessing flows in the Earth's liquid core

Cited by 109 publications

References 40 publications

Theory and Modeling of Planetary Dynamos

Theory and Modeling of Planetary Dynamos

Shapes of two‐layer models of rotating planets

Asymptotic theory of resonant flow in a spheroidal cavity driven by latitudinal libration

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