Homomorphisms of some function lattices

Jensen, Gerd

doi:10.1007/bf01376219

Cited by 5 publications

(5 citation statements)

References 4 publications

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“…The fluid pressurep must therefore be somewhat smaller inside the tube (where B =+ 0) than just outside, the same is therefore true of the density, and the tube tends to rise, This mechanism of 'magnetic buoyancy' was pointed out by Parker (1955) and Jensen (1955)) and has subsequently been much discussed in connexion with the dynamics of the upper layers of the sun (see, for example, Parker 1976). Note that our assumption here of infinitely fast diffusion of heat has filtered out conventional buoyancy forces that would otherwise arise owing to the vertical entropy gradient.…”

Section: Introductionmentioning

confidence: 97%

Magnetic instabilities of a rotating gas

Acheson

Gibbons

1978

J. Fluid Mech.

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We explore two types of instability which may develop when a highly conducting gas rotates rapidly in the presence of a radial gravitational force and an azimuthal magnetic field. Beyond a critical radius (equal to twice the isothermal scale height) a decrease of magnetic flux (per unit mass) outwards leads to the appearance of eastward-propagating waves by the mechanism of ‘magnetic buoyancy’. Within the critical radius an increase of magnetic flux outwards leads to westward-propagating waves by a totally different mechanism. Provided that the effects of Ohmic dissipation are not too large, either instability may set in for quite modest magnetic flux gradients, even when the magnetic energy of the system is very much smaller than the rotational energy.

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Section: Introductionmentioning

confidence: 97%

Magnetic instabilities of a rotating gas

Acheson

Gibbons

1978

J. Fluid Mech.

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“…Cowling (1946) envisaged flux tubes running as girdles around the Sun and suggested that loops were carried upwards by convection to emerge as sunspot pairs. Soon after, the idea of magnetic buoyancy was put forward as the mechanism by which flux tubes journey from the base of the convection zone to the photosphere (Parker 1955;Jensen 1955). Parker demonstrated that an isolated magnetic flux tube in a stratified plasma under gravity must be buoyant, provided that it is close to thermal equilibrium with its surroundings.…”

Section: Introductionmentioning

confidence: 99%

On the emergence of toroidal flux tubes: general dynamics and comparisons with the cylinder model

MacTaggart¹,

Hood²

2009

A&A

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Aims. In this paper we study the dynamics of toroidal flux tubes emerging from the solar interior, through the photosphere and into the corona. Many previous theoretical studies of flux emergence use a twisted cylindrical tube in the solar interior as the initial condition. Important insights can be gained from this model, however, it does have shortcomings. The axis of the tube never fully emerges as dense plasma becomes trapped in magnetic dips and restrains its ascent. Also, since the entire tube is buoyant, the main photospheric footpoints (sunspots) continually drift apart. These problems make it difficult to produce a convincing sunspot pair. We aim to address these problems by considering a different initial condition, namely a toroidal flux tube. Methods. We perform numerical experiments and solve the 3D MHD equations. The dynamics are investigated through a range of initial field strengths and twists.Results. The experiments demonstrate that the emergence of toroidal flux tubes is highly dynamic and exhibits a rich variety of behaviour. In answer to the aims, however, if the initial field strength is strong enough, the axis of the tube can fully emerge. Also, the sunspot pair does not continually drift apart. Instead, its maximum separation is the diameter of the original toroidal tube.

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“…The preceding Proposition is a reformulation of Theorem 3.1 from [8] (see also Lemma 1.1 in [12]) stated for semi-affine lattices. Its proof is the same as that in [9] (Proposition 2.7)-unlike the proof in [8] no ultrafilters are used.…”

Section: Proposition 3 the Functors C And X Are Adjointmentioning

confidence: 92%