@article{SeehaferGellertKuzanyanetal.2003,
  author    = {Seehafer, Norbert and Gellert, Marcus and Kuzanyan, Kirill M. and Pipin, V. V.},
  title     = {Helicity and the solar dynamo},
  year      = {2003},
  language  = {en}
}
@article{SeehaferDemircan2003,
  author    = {Seehafer, Norbert and Demircan, Ayhan},
  title     = {Dynamo action in cellular convection},
  year      = {2003},
  language  = {en}
}
@article{ZienickeSeehaferLietal.2003,
  author    = {Zienicke, Egbert and Seehafer, Norbert and Li, B.-W. and Schumacher, J{\"o}rg and Politano, H. and Thess, H.},
  title     = {Voltage-driven instability of electrically conducting fluids},
  year      = {2003},
  language  = {en}
}
@article{FeudelGellertRuedigeretal.2003,
  author    = {Feudel, Fred and Gellert, Marcus and R{\"u}diger, Sten and Witt, Annette and Seehafer, Norbert},
  title     = {Dynamo effect in a driven helical flow},
  year      = {2003},
  language  = {en}
}
@article{DemircanSeehafer2002,
  author    = {Demircan, Ayhan and Seehafer, Norbert},
  title     = {Dynamo in asymmetric square convection},
  issn      = {0309-1929},
  year      = {2002},
  language  = {en}
}
@article{FeudelRuedigerSeehafer2001,
  author    = {Feudel, Fred and R{\"u}diger, Sten and Seehafer, Norbert},
  title     = {Bifurcation phenomena and dynamo effect in electrically conducting fluids},
  year      = {2001},
  abstract  = {Electrically conducting fluids in motion can act as self-excited dynamos. The magnetic fields of celestial bodies like the Earth and the Sun are generated by such dynamos. Their theory aims at modeling and understanding both the kinematic and dynamic aspects of the underlying processes. Kinematic dynamo models, in which for a prescribed flow the linear induction equation is solved and growth rates of the magnetic field are calculated, have been studied for many decades. But in order to get consistent models and to take into account the back-reaction of the magnetic field on the fluid motion, the full nonlinear system of the magnetohydrodynamic (MHD) equations has to be studied. It is generally accepted that these equations, i.e. the Navier-Stokes equation (NSE) and the induction equation, provide a theoretical basis for the explanation of the dynamo effect. The general idea is that mechanical energy pumped into the fluid by heating or other mechanisms is transferred to the magnetic field by nonlinear interactions. For two special helical flows which are known to be effective kinematic dynamos and which can be produced by appropriate external mechanical forcing, we review the nonlinear dynamo properties found in the framework of the full MHD equations. Specifically, we deal with the ABC flow (named after Arnold, Beltrami and Childress) and the Roberts flow (after G.~O. Roberts). The appearance of generic dynamo effects is demonstrated. Applying special numerical bifurcation-analysis techniques to high-dimensional approximations in Fourier space and varying the Reynolds number (or the strength of the forcing) as the relevant control parameter, qualitative changes in the dynamics are investigated. We follow the bifurcation sequences until chaotic states are reached. The transitions from the primary flows with vanishing magnetic field to dynamo-active states are described in particular detail. In these processes the stagnation points of the flows and their heteroclinic connections play a promoting role for the magnetic field generation. By the example of the Roberts flow we demonstrate how the break up of the heteroclinic lines after the primary bifurcation leads to a complicated intersection of stable and unstable manifolds forming a chaotic web which is in turn correlated with the spatial appearance of the dynamo.},
  language  = {en}
}
@article{DemircanSeehafer2001,
  author    = {Demircan, Ayhan and Seehafer, Norbert},
  title     = {Dynamos in rotating and nonrotating convection in the form of asymmetric squares},
  year      = {2001},
  abstract  = {We study the dynamo properties of asymmetric square patterns in Boussinesq Rayleigh-B'enard convection in a plane horizontal layer. Cases without rotation and with weak rotation about a vertical axis are considered. There exist different types of solutions distinguished by their symmetry, among them such with flows possessing a net helicity and being capable of kinematic dynamo action in the presence as well as in the absence of rotation. In the nonrotating case these flows are, however, always only kinematic, not nonlinear dynamos. Nonlinearly the back-reaction of the magnetic field then forces the solution into the basin of attraction of a roll pattern incapable of dynamo action. But with rotation added parameter regions are found where the Coriolis force counteracts the Lorentz force in such a way that the asymmetric squares are also nonlinear dynamos.},
  language  = {en}
}
@article{SeehaferDemircanFeudel2001,
  author    = {Seehafer, Norbert and Demircan, Ayhan and Feudel, Fred},
  title     = {Fluid helicity and dynamo effect},
  year      = {2001},
  abstract  = {Using the incompressible magnetohydrodynamic equations, we have numerically studied the dynamo effect in electrically conducting fluids. The necessary energy input into the system was modeled either by an explicit forcing term in the Navier-Stokes equation or fully selfconsistently by thermal convection in a fluid layer heated from below. If the fluid motion is capable of dynamo action, the dynamo effect appears in the form of a phase transition or bifurcation at some critical strength of the forcing. Both the dynamo bifurcation and subsequent bifurcations that occur when the strength of the forcing is further raised were studied, including the transition to chaotic states. Special attention was paid to the helicity of the flow as well as to the symmetries of the system and symmetry breaking in the bifurcations. The magnetic field tends to be accumulated in special regions of the flow, notably in the vicinity of stagnation points or near the boundaries of convection cells.},
  language  = {en}
}
@article{DemircanSeehafer2001,
  author    = {Demircan, Ayhan and Seehafer, Norbert},
  title     = {Nonlinear square patterns in Rayleigh-Benard convection},
  year      = {2001},
  abstract  = {We numerically investigate nonlinear asymmetric square patterns in a horizontal convection layer with up-down reflection symmetry. As a novel feature we find the patterns to appear via the skewed varicose instability of rolls. The time-independent nonlinear state is generated by two unstable checkerboard (symmetric square) patterns and their nonlinear interaction. As the bouyancy forces increase the interacting modes give rise to bifurcations leading to a periodic alternation between a nonequilateral hexagonal pattern and the square pattern or to different kinds of standing oscillations.},
  language  = {en}
}
@article{DemircanScheelSeehafer2000,
  author    = {Demircan, Ayhan and Scheel, S. and Seehafer, Norbert},
  title     = {Heteroclinic behavior in rotating Rayleigh-Benard convection},
  year      = {2000},
  abstract  = {We investigate numerically the appearance of heteroclinic behavior in a three-dimensional, buoyancy-driven fluid layer with stress-free top and bottom boundaries, a square horizontal periodicity with a small aspect ratio, and rotation at low to moderate rates about a vertical axis. The Prandtl number is 6.8. If the rotation is not too slow, the skewed-varicose instability leads from stationary rolls to a stationary mixed-mode solution, which in turn loses stability to a heteroclinic cycle formed by unstable roll states and connections between them. The unstable eigenvectors of these roll states are also of the skewed-varicose or mixed-mode type and in some parameter regions skewed-varicose like shearing oscillations as well as square patterns are involved in the cycle. Always present weak noise leads to irregular horizontal translations of the convection pattern and makes the dynamics chaotic, which is verified by calculating Lyapunov exponents. In the nonrotating case the primary rolls lose, depending on the aspect ratio, stability to traveling waves or a stationary square pattern. We also study the symmetries of the solutions at the intermittent fixed points in the heteroclinic cycle.},
  language  = {en}
}
@article{SchumacherSeehafer2000,
  author    = {Schumacher, J{\"o}rg and Seehafer, Norbert},
  title     = {Bifurcation analysis of the plane sheet pinch},
  year      = {2000},
  abstract  = {A numerical bifurcation analysis of the electrically driven plane sheet pinch is presented. The electrical conductivity varies across the sheet such as to allow instability of the quiescent basic state at some critical Hartmann number. The most unstable perturbation is the two-dimensional tearing mode. Restricting the whole problem to two spatial dimensions, this mode is followed up to a time-asymptotic steady state, which proves to be sensitive to three- dimensional perturbations even close to the point where the primary instability sets in. A comprehensive three- dimensional stability analysis of the two-dimensional steady tearing-mode state is performed by varying parameters of the sheet pinch. The instability with respect to three-dimensional perturbations is suppressed by a sufficiently strong magnetic field in the invariant direction of the equilibrium. For a special choice of the system parameters, the unstably perturbed state is followed up in its nonlinear evolution and is found to approach a three-dimensional steady state.},
  language  = {en}
}
@article{SeehaferSchumacher2000,
  author    = {Seehafer, Norbert and Schumacher, J{\"o}rg},
  title     = {Patterns in an electrically driven conducting fluid layer},
  year      = {2000},
  abstract  = {The equilibrium states of electrically conducting fluids or plasmas have been a subject of intense study for a long time, motivated in particular by the interest in controlled thermonuclear fusion, as well as that in space and astrophysical phenomena such as plasma loops in the solar corona. If high temperatures prohibit solid walls, a conducting fluid can be held together by the action of an electric current passing through it with the pressure gradients being balanced by the Lorentz force. The resultant configuration is known as a pinch. In this paper we report on studies of the pinch in the geometry of a plane sheet.},
  language  = {en}
}
@article{SeehaferSchumacher2000,
  author    = {Seehafer, Norbert and Schumacher, J{\"o}rg},
  title     = {Bifurcation analysis of an electrically driven fluid layer},
  year      = {2000},
  abstract  = {The equilibrium states of electrically conducting fluids or plasmas have been a subject of intense study for a long time, motivated in particular by the interest in controlled thermonuclear fusion, as well as that in space and astrophysical phenomena such as plasma loops in the solar corona. If high temperatures prohibit solid walls, a conducting fluid can be held together by the action of an electric current passing through it with the pressure gradients being balanced by the Lorentz force. The resultant configuration is known as a pinch. In this paper we report on studies of the pinch in the geometry of a plane sheet.},
  language  = {en}
}
@article{DemircanSeehafer2000,
  author    = {Demircan, Ayhan and Seehafer, Norbert},
  title     = {Heteroclinic behavior in rotating Rayleigh-B{\´e}nard convection},
  year      = {2000},
  abstract  = {We investigate numerically the appearance of heteroclinic behavior in a three-dimensional, buoyancy-driven, rotating fluid layer. Periodic boundary conditions in the horizontal directions and stress-free boundary conditions at the top and bottom are assumed.},
  language  = {en}
}
@article{SchumacherKliemSeehafer2000,
  author    = {Schumacher, J{\"o}rg and Kliem, Bernhard and Seehafer, Norbert},
  title     = {Three-dimensional spontaneous magnetic reconnection in neutral current sheets},
  year      = {2000},
  language  = {en}
}
@article{KurthsSeehaferSpahn1999,
  author    = {Kurths, J{\"u}rgen and Seehafer, Norbert and Spahn, Frank},
  title     = {Nichtlineare Dynamik in der Physik : Forschungsbeispiele und Forschungstrends},
  isbn      = {3-540-65329- 5},
  year      = {1999},
  language  = {de}
}
@article{BrownCanfieldFieldetal.1999,
  author    = {Brown, M. R. and Canfield, R. C. and Field, G. and Kulsrud, R. and Pevtsov, A. A. and Rosner, R. and Seehafer, Norbert},
  title     = {Magnetic helicity in space and laboratory plasmas: Editorial summary},
  year      = {1999},
  language  = {en}
}
@article{DemircanSeehafer1999,
  author    = {Demircan, Ayhan and Seehafer, Norbert},
  title     = {Bifurcation to oscillations and chaos in rotating convection},
  year      = {1999},
  language  = {en}
}
@article{RuedigerFeudelSeehafer1998,
  author    = {R{\"u}diger, Sten and Feudel, Fred and Seehafer, Norbert},
  title     = {Dynamo bifurcations in an array of driven convectionlike rolls},
  year      = {1998},
  language  = {en}
}
@article{SeehaferFeudelGalanti1998,
  author    = {Seehafer, Norbert and Feudel, Fred and Galanti, B.},
  title     = {Bifurcations in a magnetofluid with helical forcing},
  isbn      = {1-563-47284-8},
  year      = {1998},
  language  = {en}
}
@article{Seehafer1998,
  author    = {Seehafer, Norbert},
  title     = {Filaments and the solar dynamo},
  isbn      = {1-88673-370-8},
  year      = {1998},
  language  = {en}
}
@article{SchmidtmannFeudelSeehafer1998,
  author    = {Schmidtmann, Olaf and Feudel, Fred and Seehafer, Norbert},
  title     = {Nonlinear Galerkin methods based on the concept of determining modes for the magnetohydrodynamic equations},
  year      = {1998},
  language  = {en}
}
@article{ZienickeSeehaferFeudel1998,
  author    = {Zienicke, Egbert and Seehafer, Norbert and Feudel, Fred},
  title     = {Bifurcations in two-dimensional Rayleigh-B{\´e}nard convection},
  year      = {1998},
  language  = {en}
}
@article{SeehaferSchumacher1998,
  author    = {Seehafer, Norbert and Schumacher, J{\"o}rg},
  title     = {Resistivity profile and instability of the plane sheet pinch},
  year      = {1998},
  language  = {en}
}
@article{ScheelSeehafer1997,
  author    = {Scheel, S. and Seehafer, Norbert},
  title     = {Bifurcation to oscillations in three-dimensional Rayleigh-B{\´e}nard convection},
  year      = {1997},
  language  = {en}
}
@article{BraunFeudelSeehafer1997,
  author    = {Braun, Robert and Feudel, Fred and Seehafer, Norbert},
  title     = {Bifurcations and chaos in an array of forced vortices},
  year      = {1997},
  language  = {en}
}
@article{SchmidtmannFeudelSeehafer1997,
  author    = {Schmidtmann, Olaf and Feudel, Fred and Seehafer, Norbert},
  title     = {Nonlinear Galerkin methods for the 3D magnetohydrodynamic equations},
  year      = {1997},
  language  = {en}
}
@article{SeehaferSchumacher1997,
  author    = {Seehafer, Norbert and Schumacher, J{\"o}rg},
  title     = {Squire's theorem for the magnetohydrodynamic sheet pinch},
  year      = {1997},
  language  = {en}
}
@article{RustCrookerGoldetal.1996,
  author    = {Rust, David M. and Crooker, N. U. and Gold, R. E. and Golub, Leon and Hundhausen, A. J. and Lanzerotti, L. J. and Lazarus, A. J. and Seehafer, Norbert and Zanetti, L. J.},
  title     = {Heliospheric lins explorer (HELIX)},
  year      = {1996},
  language  = {en}
}
@article{SeehaferGalantiFeudeletal.1996,
  author    = {Seehafer, Norbert and Galanti, B. and Feudel, Fred and R{\"u}diger, Sten},
  title     = {Symmetry breaking bifurcations for the magnetohydrodynamic equations with helical forcing},
  year      = {1996},
  language  = {en}
}
@article{SeehaferZienickeFeudel1996,
  author    = {Seehafer, Norbert and Zienicke, Egbert and Feudel, Fred},
  title     = {Absence of magnetohydrodynamic activity in the voltage-driven sheet pinch},
  year      = {1996},
  language  = {en}
}
@article{SeehaferFeudelSchmidtmann1996,
  author    = {Seehafer, Norbert and Feudel, Fred and Schmidtmann, Olaf},
  title     = {Nonlinear dynamo with ABC forcing},
  year      = {1996},
  language  = {en}
}
@article{Seehafer1996,
  author    = {Seehafer, Norbert},
  title     = {Nature of the alpha effect in magnetohydrodynamics},
  year      = {1996},
  language  = {en}
}
@article{FeudelSeehaferSchmidtmann1996,
  author    = {Feudel, Fred and Seehafer, Norbert and Schmidtmann, Olaf},
  title     = {Bifurcation phenomena of the magnetofluid equations},
  year      = {1996},
  abstract  = {We report on bifurcation studies for the incompressible magnetohydrodynamic equations in three space dimensions with periodic boundary conditions and a temporally constant external forcing. Fourier representations of velocity, pressure and magnetic field have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then special numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. In a part of the calculations, in order to reduce the number of modes to be retained, the concept of approximate inertial manifolds has been applied. For varying (increasing from zero) strength of the imposed forcing, or varying Reynolds number, respectively, time-asymptotic states, notably stable stationary solutions, have been traced. A primary non- magnetic steady state loses, in a Hopf bifurcation, stability to a periodic state with a non-vanishing magnetic field, showing the appearance of a generic dynamo effect. From now on the magnetic field is present for all values of the forcing. The Hopf bifurcation is followed by further, symmetry-breaking, bifurcations, leading finally to chaos. We pay particular attention to kinetic and magnetic helicities. The dynamo effect is observed only if the forcing is chosen such that a mean kinetic helicity is generated; otherwise the magnetic field diffuses away, and the time-asymptotic states are non-magnetic, in accordance with traditional kinematic dynamo theory.},
  language  = {en}
}
@article{FeudelSeehafer1995,
  author    = {Feudel, Fred and Seehafer, Norbert},
  title     = {On the bifurcation phenomena in truncations of the 2D Navier-Stokes equations},
  year      = {1995},
  language  = {en}
}
@article{FeudelSeehafer1995,
  author    = {Feudel, Fred and Seehafer, Norbert},
  title     = {Bifurcations and pattern formation in two-dimensional Navier-Stokes fluid},
  year      = {1995},
  language  = {en}
}
@article{Seehafer1995,
  author    = {Seehafer, Norbert},
  title     = {The turbulent electromotive force in the high-conductivity limit},
  year      = {1995},
  language  = {en}
}
@article{FeudelSeehaferSchmidtmann1995,
  author    = {Feudel, Fred and Seehafer, Norbert and Schmidtmann, Olaf},
  title     = {Fluid helicity and dynamo bifurcations},
  year      = {1995},
  language  = {en}
}
@article{Seehafer1994,
  author    = {Seehafer, Norbert},
  title     = {Relaxation to equilibrium and inverse energy cascades in solar active regions},
  isbn      = {1-563-47099-3},
  issn      = {0079-6050},
  year      = {1994},
  language  = {en}
}
@article{Seehafer1994,
  author    = {Seehafer, Norbert},
  title     = {Current helicity and the turbulent electromotive force},
  year      = {1994},
  language  = {en}
}
@article{Seehafer1994,
  author    = {Seehafer, Norbert},
  title     = {Alpha effect in the solar atmosphere},
  year      = {1994},
  language  = {en}
}