A Fourier-spectral element algorithm for thermal convection in rotating axisymmetric containers

Fournier, Alexandre; Bunge, Hans‐Peter; Hollerbach, Rainer; Vilotte, Jean‐Pierre

doi:10.1016/j.jcp.2004.10.020

Cited by 38 publications

(21 citation statements)

References 62 publications

(110 reference statements)

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“…A spectral element code is used, based on the hydrodynamic code of Fournier et al (2005). The solutions are expanded into Fourier modes in the azimuthal direction.…”

Section: Discussionmentioning

confidence: 99%

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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“…A spectral element code is used, based on the hydrodynamic code of Fournier et al (2005). The solutions are expanded into Fourier modes in the azimuthal direction.…”

Section: Discussionmentioning

confidence: 99%

The angular momentum transport by unstable toroidal magnetic fields

Rüdiger

Gellert

Spada

et al. 2014

A&A

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“…Galerkin methods are applied to each individual cell, expanding the unknowns in linear (Matsui and Okuda, 2004), quadratic (Chan et al, 2001), or higher-order functions. Hybrid solutions, using Fourier expansions in longitude and a spectral element decompositions in the meridional plane (Fournier et al, 2005), have been implemented for thermal convection in a rotating sphere, and can be extended to the dynamo problem. Using higher-order spectral representation within the meridional cells defines the so-called spectral element schemes (Fournier et al, 2004(Fournier et al, , 2005.…”

Section: Local Methodsmentioning

confidence: 99%

Numerical Dynamo Simulations

Christensen

Wicht

2007

Treatise on Geophysics

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“…The material of the cylinders is assumed as made from perfect conductors, or in some other cases made from an expansion of the solution in Fourier modes in the azimuthal direction generating a sample of meridional problems each of which is solved using a Legendre spectral element method 21,22 .…”

Section: Equationsmentioning

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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A Fourier-spectral element algorithm for thermal convection in rotating axisymmetric containers

Cited by 38 publications

References 62 publications

The angular momentum transport by unstable toroidal magnetic fields

The angular momentum transport by unstable toroidal magnetic fields

Numerical Dynamo Simulations

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

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