@article{RuedigerSchultzHollerbach2021,
  author    = {R{\"u}diger, G{\"u}nther and Schultz, Manfred and Hollerbach, Rainer},
  title     = {Destabilization of super-rotating Taylor-Couette flows by current-free helical magnetic fields},
  series = {Journal of plasma physics},
  volume    = {87},
  journal   = {Journal of plasma physics},
  number    = {2},
  publisher = {Cambridge University Press},
  address   = {London},
  issn      = {1469-7807},
  doi       = {10.1017/S0022377821000295},
  pages     = {19},
  year      = {2021},
  abstract  = {In an earlier paper we showed that the combination of azimuthal magnetic fields and super-rotation in Taylor-Couette flows of conducting fluids can be unstable against non-axisymmetric perturbations if the magnetic Prandtl number of the fluid is Pm not equal 1. Here we demonstrate that the addition of a weak axial field component allows axisymmetric perturbation patterns for Pm of order unity depending on the boundary conditions. The axisymmetric modes only occur for magnetic Mach numbers (of the azimuthal field) of order unity, while higher values are necessary for the non-axisymmetric modes. The typical growth time of the instability and the characteristic time scale of the axial migration of the axisymmetric mode are long compared with the rotation period, but short compared with the magnetic diffusion time. The modes travel in the positive or negative z direction along the rotation axis depending on the sign of B phi Bz. We also demonstrate that the azimuthal components of flow and field perturbations travel in phase if vertical bar B phi vertical bar >> vertical bar B-z vertical bar, independent of the form of the rotation law. Within a short-wave approximation for thin gaps it is also shown (in an appendix) that for ideal fluids the considered helical magnetorotational instability only exists for rotation laws with negative shear.},
  language  = {en}
}
@article{FeudelTuckermanZaksetal.2017,
  author    = {Feudel, Fred and Tuckerman, Laurette S. and Zaks, Michael and Hollerbach, Rainer},
  title     = {Hysteresis of dynamos in rotating spherical shell convection},
  series = {Physical review fluids / American Physical Society},
  volume    = {2},
  journal   = {Physical review fluids / American Physical Society},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2469-990X},
  doi       = {10.1103/PhysRevFluids.2.053902},
  pages     = {11},
  year      = {2017},
  abstract  = {Bifurcations of dynamos in rotating and buoyancy-driven spherical Rayleigh-Benard convection in an electrically conducting fluid are investigated numerically. Both nonmagnetic and magnetic solution branches comprised of rotating waves are traced by path-following techniques, and their bifurcations and interconnections for different Ekman numbers are determined. In particular, the question of whether the dynamo branches bifurcate super- or sub-critically and whether a direct link to the primary pure convective states exists is answered.},
  language  = {en}
}
@book{RuedigerKitchatinovHollerbach2013,
  author    = {R{\"u}diger, G{\"u}nther and Kitchatinov, Leonid L. and Hollerbach, Rainer},
  title     = {Magnetic processes in astrophysics : theory, simulations, experiments},
  publisher = {Wiley-VCH},
  address   = {Weinheim, Bergstr.},
  isbn      = {978-3-527-41034-7},
  pages     = {346 S.},
  year      = {2013},
  language  = {en}
}
@article{FeudelBergemannTuckermanetal.2011,
  author    = {Feudel, Fred and Bergemann, Kay and Tuckerman, Laurette S. and Egbers, C. and Futterer, B. and Gellert, Marcus and Hollerbach, Rainer},
  title     = {Convection patterns in a spherical fluid shell},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {83},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {4},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.83.046304},
  pages     = {8},
  year      = {2011},
  abstract  = {Symmetry-breaking bifurcations have been studied for convection in a nonrotating spherical shell whose outer radius is twice the inner radius, under the influence of an externally applied central force field with a radial dependence proportional to 1/r(5). This work is motivated by the GeoFlow experiment, which is performed under microgravity condition at the International Space Station where this particular central force can be generated. In order to predict the observable patterns, simulations together with path-following techniques and stability computations have been applied. Branches of axisymmetric, octahedral, and seven-cell solutions have been traced. The bifurcations producing them have been identified and their stability ranges determined. At higher Rayleigh numbers, time-periodic states with a complex spatiotemporal symmetry are found, which we call breathing patterns.},
  language  = {en}
}