Joint Instability of Latitudinal Differential Rotation and Toroidal Magnetic Fields below the Solar Convection Zone

Gilman, Peter A.; Fox, Peter

doi:10.1086/304330

Cited by 159 publications

(206 citation statements)

References 16 publications

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“…Klahr & Bodenheimer 2003;Petersen et al 2007a,b;Lesur & Papaloizou 2010;Lyra & Klahr 2011) and the Sun (Gilman & Fox 1997;Zaqarashvili et al 2010; to name only a few studies). In these analyses potential vorticity disturbances are effectively baroclinically torqued by some process that is either thermal or magnetic or, in some investigations, a combination of both.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…In those studies of magnetic Rossby waves in the Sun (e.g. Gilman & Fox 1997;Zaqarashvili et al 2010), Rossby waves will propagate along those places where there are strong gradients in the solar differential rotation. Treated as a hydrodynamic problem, these Rossby waves are not necessarily unstable on their own, especially for the differential rotation profiles inferred to be characteristic of the Sun's tachochline (Spiegel & Zahn 1992).…”

Section: Summary and Discussionmentioning

confidence: 99%

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Potential vorticity dynamics in the framework of disk shallow-water theory

Umurhan¹

2012

A&A

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Context. We consider potential vorticity dynamics for astrophysical disks. Aims. The aim of this work is to extend exploration of shear instabilities in cold astrophysical disks that are three-dimensional and whose mean states are baroclinic. In particular, we seek to demonstrate the potential existence of traditional baroclinic instabilities in meteorological studies. We show this in a simplified two-layer Philips disk model of a midplane symmetric disk. Methods. We analyze the dynamical normal-mode response of thin annular disks with two strongly localized potential vorticity gradients, one in each of two disk layers. Each disk layer is of constant but differing densities. The resulting mean azimuthal velocity profile shows a variation in the vertical direction, implying that the system is baroclinic in the mean state. The stability of the system is treated in the context of disk shallow-water theory, wherein azimuthal disturbances are much longer than the corresponding radial or vertical scales. The normal-mode problem is solved numerically using two different methods. Results. The results of a symmetric single-layer barotropic model is considered and it is found that instability persists for models in which the potential vorticity profiles are not symmetric, consistent with previous results. The instaiblity is interpreted in terms of interacting Rossby waves. For a two-layer system, in which the flow is fundamentally baroclinic, we report here that instability takes on the form of mixed barotropic-baroclinic type: instability occurs, but it qualitatively follows the pattern of instability found in the barotropic models. Instability arises because of the phase locking and interaction of the Rossby waves between the two layers. The strength of the instability weakens as the density contrast between layers increases. Conclusions. Baroclinic instability is feasible for astrophysical disks but has the character of mixed barotropic-baroclinic type. The instability as explored in this study could be present in protoplanetary disks with weak vertical density stratification.

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Section: Summary and Discussionmentioning

confidence: 99%

Section: Summary and Discussionmentioning

confidence: 99%

Potential vorticity dynamics in the framework of disk shallow-water theory

Umurhan¹

2012

A&A

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“…Moreover, the transition region itself where the differential rotation rapidly becomes uniform (the tachocline) appears to be hydrodynamically unstable (Arlt, Sule & Rüdiger 2005). For strong magnetic fields, however, there might be a magnetohydrodynamic instability which leads to an α-effect such as described by Gilman and Fox (1997) and Dikpati and Gilman (2000). Similar results for nonaxisymmetric disturbances have been found within the thin-flux tube approximation by Schüssler et al (1994) and Caligari et al (1998).…”

Section: Introductionmentioning

confidence: 99%

Advection‐dominated solar dynamo model with two‐cell meridional flow and a positive α ‐effect in the tachocline

Bonanno¹,

Elstner

Belvedère

2006

Astron Nachr

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Most probably the sunspot cycle period is ruled by a meridional flow located near the base of the convection zone (Hathaway et al. 2003). On the other hand, if the eddy diffusivity is low enough, dramatic modification of the standard α 2 Ω-dynamo by the meridional flow are expected. In this paper we shall discuss the dependence of periods, dynamo numbers and the sign of the current helicity as a function of the magnetic Reynolds number for a double cell meridional circulation and for a positive α-effect at the base of the convection zone. The dynamo action occurs at lower latitudes and its location is at the interface between equatorward and poleward motions near the base of the convection zone. In spite of the complexity of the flow pattern, our simulations show that the resulting dynamo action reproduces several observed features of the solar cycle.

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“…The tachocline is thin and its stability properties are rather peculiar. For instance, Gilman & Fox (1997) showed that the tachocline latitudinal shear is unstable to nonaxisymmetric disturbances when a toroidal magnetic field is present. Instabilities in the tachocline have been studied in detail by Dikpati et al (2009) for a wide range of rotation and toroidal field profiles.…”

Section: Introductionmentioning

confidence: 99%

Stability of the toroidal magnetic field in rotating stars

Bonanno

Урпин

2013

A&A

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The magnetic field in stellar radiation zones can play an important role in phenomena such as mixing, angular momentum transport, etc. We study the effect of rotation on the stability of a predominantly toroidal magnetic field in the radiation zone. In particular we considered the stability in spherical geometry by means of a linear analysis in the Boussinesq approximation. It is found that the effect of rotation on the stability depends on a magnetic configuration. If the toroidal field increases with the spherical radius, the instability cannot be suppressed entirely even by a very fast rotation. Rotation can only decrease the growth rate of instability. If the field decreases with the radius, the instability has a threshold and can be completey suppressed.

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Joint Instability of Latitudinal Differential Rotation and Toroidal Magnetic Fields below the Solar Convection Zone

Cited by 159 publications

References 16 publications

Potential vorticity dynamics in the framework of disk shallow-water theory

Potential vorticity dynamics in the framework of disk shallow-water theory

Advection‐dominated solar dynamo model with two‐cell meridional flow and a positive α ‐effect in the tachocline

Stability of the toroidal magnetic field in rotating stars

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