Steady fluid flow in a precessing spheroidal shell

Busse, Friedrich H.

doi:10.1017/s0022112068001655

Cited by 214 publications

(308 citation statements)

References 8 publications

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“…It is not understood why these internal shear layers appear on top of the flow in Fig. 13 except for the strongest of them (Busse 1968), but they are a robust feature of both experiments and simulations. The third type is a consequence of the streamline geometry in Fig.…”

Section: Tidally Driven and Precession Driven Dynamosmentioning

confidence: 95%

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: 95%

Theory and Modeling of Planetary Dynamos

Wicht

Tilgner

2010

Space Sci Rev

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“…However, it is generally believed that the effect of the singularities is weak and insignificant because the mass flux from the critical regions is much smaller than that from the rest of the boundary layer (see e.g. Roberts & Stewartson 1965;Busse 1968;Tilgner & Busse 2001).…”

Section: K H Chan and X Liaomentioning

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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“…In particular the occurrence of this 'tidal' instability together with thermal or compositional convection in the molten cores of planets, such as the Earth, might be of prime importance in the generation or in the dynamics of the geomagnetic fields (Kerswell, 1994;Kerswell and Malkus, 1998). Recent measurements of magnetic fields around relatively small planets such as the Jovian moons Io and Ganymède (Kivelson et al, 1996a,b) may reinforce the interest in the study of inertial instabilities such as the elliptical or the precessional ones (Malkus, 1968;Busse, 1968;Noir et al, 2001;Kerswell, 1993;Lorenzani and Tilgner, 2003). Aldridge et al (1997), and Seyed-Mahmoud et al (2000 have performed computations and built as already mentioned, a rotating deformable shell where they observed the presence of the elliptical instability.…”

Section: Introductionmentioning

confidence: 99%

Elliptical instability of the flow in a rotating shell

Lacaze¹,

Gal²,

Dizès³

2005

Physics of the Earth and Planetary Interiors

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A theoretical and experimental study of the spin-over mode induced by the elliptical instability of a flow contained in a slightly deformed rotating spherical shell is presented. This geometrical configuration mimics the liquid rotating cores of planets when deformed by tides coming from neighboring gravitational bodies. Theoretical estimations for the growth rates and for the non linear amplitude saturations of the unstable mode are obtained and compared to experimental data obtained from Laser Döppler anemometry measurements. Visualizations and descriptions of the various characteristics of the instability are given as functions of the flow parameters.

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Steady fluid flow in a precessing spheroidal shell

Cited by 214 publications

References 8 publications

Theory and Modeling of Planetary Dynamos

Theory and Modeling of Planetary Dynamos

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

Elliptical instability of the flow in a rotating shell

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