Hydromagnetics of rotating fluids

Acheson, D. J.; Hide, R.

doi:10.1088/0034-4885/36/2/002

Cited by 237 publications

(139 citation statements)

References 133 publications

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“…The magneto-rotational instability could operate in regions of the Sun where angular velocity decreases outward from the rotation axis (as it does in the polar regions). Balbus & Hawley (1994) showed that the strong local stratification of the tachocline limits displacements to horizontal surfaces, as expected; this could provide a source of unaccounted for latitudinal momentum mixing in the polar regions.…”

Section: Stability Of the Slow Tachocline Modelssupporting

confidence: 66%

“…But the situation may in fact be much worse. In the tachocline, the magnetic Prandtl number is of the order of ν/η ∼ 10 −2 ; if a small-scale dynamo indeed operates at these values of the magnetic Prandtl number (Boldyrev & Cattaneo 2004) magnetic energy accumulates somewhere on the turbulent inertial range and reaches equipartition well before the larger scale field does. This process could quench the turbulent magnetic diffusivity for much lower field strengths (Cattaneo & Vainshtein 1991).…”

Section: Discussion and Prospect For The Dynamo Confinement Modelmentioning

confidence: 99%

“…A boundary analysis provides useful quantitative estimates of the tachocline properties in both open and confined geometries: viscous effects are only important in a thin Ekman-Hartmann boundary layer (see the review by Acheson & Hide 1973) of width (9.6) where the field of amplitude B 0 is assumed to be mostly parallel to the outer boundary (as in the case of the confined field) and is measured in Tesla. The usual Ekman numbers are defined as…”

Section: First Modelsmentioning

confidence: 99%

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Magnetic confinement of the solar tachocline

Garaud¹

2007

The Solar Tachocline

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Two distinct classes of magnetic confinement models exist for the solar tachocline. The "slow tachocline" models are associated with a large-scale primordial field embedded in the radiative zone. The "fast tachocline" models are associated with an overlying dynamo field. I describe the results obtained in each case, their pros and cons, and compare them with existing solar observations. I conclude by discussing new lines of investigation that should be pursued, as well as some means by which these models could be unified or reconciled.

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Section: Stability Of the Slow Tachocline Modelssupporting

confidence: 66%

Section: Discussion and Prospect For The Dynamo Confinement Modelmentioning

confidence: 99%

Section: First Modelsmentioning

confidence: 99%

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Magnetic confinement of the solar tachocline

Garaud¹

2007

The Solar Tachocline

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“…In order to familiarize the reader with it, we first demonstrate that they easily yield a number of classical results, see e.g. (Acheson & Hide 1973;Acheson 1978).…”

Section: Connection To Known Stability and Instability Criteriamentioning

confidence: 99%

Local instabilities in magnetized rotational flows: a short-wavelength approach

Kirillov

Stefani

Fukumoto³

2014

J. Fluid Mech.

189

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We perform a local stability analysis of rotational flows in the presence of a constant vertical magnetic field and an azimuthal magnetic field with a general radial dependence. Employing the short-wavelength approximation we develop a unified framework for the investigation of the standard, the helical, and the azimuthal version of the magnetorotational instability, as well as of current-driven kink-type instabilities. Considering the viscous and resistive setup, our main focus is on the case of small magnetic Prandtl numbers which applies, e.g., to liquid metal experiments but also to the colder parts of accretion disks. We show that the inductionless versions of MRI that were previously thought to be restricted to comparably steep rotation profiles extend well to the Keplerian case if only the azimuthal field slightly deviates from its current-free (in the fluid) profile. We find an explicit criterion separating the pure azimuthal inductionless magnetorotational instability from the regime where this instability is mixed with the Tayler instability. We further demonstrate that for particular parameter configurations the azimuthal MRI originates as a result of a dissipation-induced instability of the Chandrasekhar's equipartition solution of ideal magnetohydrodynamics.

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“…It should further be noted that the ratio of the magnetic to kinetic energy for slow MC waves scales like (Acheson and Hide 1973)…”

Section: Magnetic-coriolis Wavesmentioning

confidence: 99%

Short Timescale Core Dynamics: Theory and Observations

Finlay¹,

Dumberry²,

Chulliat³

et al. 2010

Terrestrial Magnetism

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Fluid motions in the Earth's core produce changes in the geomagnetic field (secular variation) and are also an important ingredient in the planet's rotational dynamics. In this article we review current understanding of core dynamics focusing on short timescales of years to centuries. We describe both theoretical models and what may be inferred from geomagnetic and geodetic observations. The kinematic concepts of frozen flux and magnetic diffusion are discussed along with relevant dynamical regimes of magnetostrophic balance, tangential geostrophy, and quasi-geostrophy. An introduction is given to free modes and waves that are expected to be present in Earth's core including axisymmetric torsional oscillations and non-axisymmetric Magnetic-Coriolis waves. We focus on important recent developments and promising directions for future investigations.

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Hydromagnetics of rotating fluids

Cited by 237 publications

References 133 publications

Magnetic confinement of the solar tachocline

Magnetic confinement of the solar tachocline

Local instabilities in magnetized rotational flows: a short-wavelength approach

Short Timescale Core Dynamics: Theory and Observations

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