Experimental Evidence for a Transient Tayler Instability in a Cylindrical Liquid-Metal Column

Seilmayer, Martin; Stefani, Frank; Gundrum, Thomas; Weier, Tom; Gerbeth, Günter; Gellert, M.; Rüdiger, G.

doi:10.1103/physrevlett.108.244501

Cited by 99 publications

(111 citation statements)

References 22 publications

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“…which is fulfilled by the magnetic field generated by a homogeneous axial electric current, for which B φ ∝ R. If an electric current flows unbounded in the axial direction, the critical Hartmann number Ha out = B out R 0 / √ μ 0 ρνη is about 20, which has indeed been realized in an experiment (Seilmayer et al 2012;Rüdiger et al 2012). Numerical simulations of this magnetic configuration showed, however, that the eddy viscosity resulting from this instability remains small compared with its microscopic value.…”

Section: Numerical Setup and The Calculation Of The Effective Viscositymentioning

confidence: 94%

The angular momentum transport by unstable toroidal magnetic fields

Rüdiger

Gellert

Spada

et al. 2014

A&A

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We demonstrate with a nonlinear magnetohydrodynamic (MHD) code that angular momentum can be transported because of the magnetic instability of toroidal fields under the influence of differential rotation, and that the resulting effective viscosity may be high enough to explain the almost rigid-body rotation observed in radiative stellar cores. We only consider stationary, current-free fields, and only those combinations of rotation rates and magnetic field amplitudes which provide maximal numerical values of the viscosity. We find that the dimensionless ratio of the effective over molecular viscosity, ν T /ν, linearly grows with the Reynolds number of the rotating fluid multiplied by the square-root of the magnetic Prandtl number, which is approximately unity for the considered red subgiant star KIC 7341231. For the interval of magnetic Reynolds numbers considered -which is restricted by numerical constraints of the nonlinear MHD code -the magnetic Prandtl number has a remarkable influence on the relative importance of the contributions of the Reynolds stress and the Maxwell stress to the total viscosity, which is magnetically dominated only for Pm > ∼ 0.5. We also find that the magnetized plasma behaves as a non-Newtonian fluid, i.e., the resulting effective viscosity depends on the shear in the rotation law. The decay time of the differential rotation thus depends on its shear and becomes longer and longer during the spin-down of a stellar core.

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Section: Numerical Setup and The Calculation Of The Effective Viscositymentioning

confidence: 94%

The angular momentum transport by unstable toroidal magnetic fields

Rüdiger

Gellert

Spada

et al. 2014

A&A

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“…of the growth rate is adopted (with Γ as a dimensionless numerical factor which only depends on the gap width and the magnetic Prandtl number), which has been derived for the nonrotating pinch and which has been experimentally realized 15,16 , then for the strongest super-rotation the …”

Section: B Growth Ratesmentioning

confidence: 99%

“…Both AMRI and (resting) TI have recently been realized in the MHD laboratory using the liquid eutectic alloy GaInSn with Pm = 1.4 · 10 −6 as the conducting fluid 16,17 . If the results shall be applied to turbulent media like the stellar convection zones then the magnetic Prandtl number must be replaced by its turbulence-induced values which are much larger 18 .…”

Section: Introductionmentioning

confidence: 99%

Subcritical excitation of the current-driven Tayler instability by super-rotation

et al. 2016

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It is known that in a hydrodynamic Taylor-Couette system uniform rotation or a rotation law with positive shear ('super-rotation') are linearly stable. It is also known that a conducting fluid under the presence of a sufficiently strong axial electric-current becomes unstable against nonaxisymmetric disturbances. It is thus suggestive that a cylindric pinch formed by a homogeneous axial electric-current is stabilized by rotation laws with dΩ /dR ≥ 0. However, for magnetic Prandtl number Pm = 1 and for slow rotation also rigid rotation and super-rotation support the instability by lowering their critical Hartmann numbers. For super-rotation in narrow gaps and for modest rotation rates this double-diffusive instability even exists for toroidal magnetic fields with rather arbitrary radial profiles, the current-free profile B φ ∝ 1/R included. -For rigid rotation and for super-rotation the sign of the azimuthal drift of the nonaxisymmetric hydromagnetic instability pattern strongly depends on the magnetic Prandtl number. The pattern counterrotates with the flow for Pm ≪ 1 and it corotates for Pm ≫ 1 while for rotation laws with negative shear the instability pattern migrates in the direction of the basic rotation for allPm.An axial electric-current of minimal 3.6 kAmp flowing inside or outside the inner cylinder suffices to realize the double-diffusive instability for super-rotation in experiments using liquid sodium as the conducting fluid between the rotating cylinders. The limit is 11 kAmp if a gallium alloy is used.

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“…Although the occurrence of MRI under the influence of a purely azimuthal magnetic field had been studied much earlier (see Hawley et al 1995;Ogilvie & Pringle 1996;Papaloizou & Terquem 1997), the crucial effect arose again for the particular combination of low Pm and slightly steeper than Keplerian shear profiles. It has to be noticed that this azimuthal MRI (AMRI), as we call it now, works for azimuthal magnetic fields that are current-free in the considered fluid, quite in contrast to the Tayler instability (Tayler 1973;Seilmayer et al 2012), which is a pinch-type instability in a current-carrying conducting medium.…”

Section: Introductionmentioning

confidence: 99%

A Unifying Picture of Helical and Azimuthal Magnetorotational Instability, and the Universal Significance of the Liu Limit

Kirillov

Stefani

Fukumoto

2012

ApJ

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The magnetorotational instability (MRI) plays a key role for cosmic structure formation by triggering turbulence in the rotating flows of accretion disks that would be otherwise hydrodynamically stable. In the limit of small magnetic Prandtl number, the helical and the azimuthal versions of MRI are known to be governed by a quite different scaling behavior than the standard MRI with a vertical applied magnetic field. Using the short-wavelength approximation for an incompressible, resistive, and viscous rotating fluid, we present a unified description of helical and azimuthal MRI, and we identify the universal character of the Liu limit 2(1 − √ 2) ≈ −0.8284 for the critical Rossby number. From this universal behavior we are also led to the prediction that the instability will be governed by a mode with an azimuthal wavenumber that is proportional to the ratio of axial to azimuthal applied magnetic field, when this ratio becomes large and the Rossby number is close to the Liu limit.

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Experimental Evidence for a Transient Tayler Instability in a Cylindrical Liquid-Metal Column

Cited by 99 publications

References 22 publications

The angular momentum transport by unstable toroidal magnetic fields

The angular momentum transport by unstable toroidal magnetic fields

Subcritical excitation of the current-driven Tayler instability by super-rotation

A Unifying Picture of Helical and Azimuthal Magnetorotational Instability, and the Universal Significance of the Liu Limit

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