@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{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{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{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{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{DemircanSeehafer2002, author = {Demircan, Ayhan and Seehafer, Norbert}, title = {Dynamo in asymmetric square convection}, issn = {0309-1929}, year = {2002}, 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{DemircanSeehafer1999, author = {Demircan, Ayhan and Seehafer, Norbert}, title = {Bifurcation to oscillations and chaos in rotating convection}, year = {1999}, language = {en} } @article{DonnerFeudelSeehaferetal.2007, author = {Donner, Reik Volker and Feudel, Fred and Seehafer, Norbert and Sanjuan, Miguel Angel Fernandez}, title = {Hierarchical modeling of a forced Roberts Dynamo}, issn = {0218-1274}, doi = {10.1142/S021812740701941X}, year = {2007}, abstract = {We investigate the dynamo effect in a flow configuration introduced by G. O. Roberts in 1972. Based on a clear energetic hierarchy of Fourier components on the steady-state dynamo branch, an approximate model of interacting modes is constructed covering all essential features of the complete system but allowing simulations with a minimum amount of computation time. We use this model to study the excitation mechanism of the dynamo, the transition from stationary to time-dependent dynamo solutions and the characteristic properties of the latter ones.}, language = {en} } @article{DonnerSeehaferSanjuanetal.2006, author = {Donner, Reik Volker and Seehafer, Norbert and Sanjuan, Miguel Angel Fernandez and Feudel, Fred}, title = {Low-dimensional dynamo modelling and symmetry-breaking bifurcations}, series = {Physica. D, Nonlinear phenomena}, volume = {223}, journal = {Physica. D, Nonlinear phenomena}, number = {2}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0167-2789}, doi = {10.1016/j.physd.2006.08.022}, pages = {151 -- 162}, year = {2006}, abstract = {Motivated by the successful Karlsruhe dynamo experiment, a relatively low-dimensional dynamo model is proposed. It is based on a strong truncation of the magnetohydrodynamic (MHD) equations with an external forcing of the Roberts type and the requirement that the model system satisfies the symmetries of the full MHD system, so that the first symmetry-breaking bifurcations can be captured. The backbone of the Roberts dynamo is formed by the Roberts flow, a helical mean magnetic field and another part of the magnetic field coupled to these two by triadic mode interactions. A minimum truncation model (MTM) containing only these energetically dominating primary mode triads is fully equivalent to the widely used first-order smoothing approximation. However, it is shown that this approach works only in the limit of small wave numbers of the excited magnetic field or small magnetic Reynolds numbers (\$Rm ll 1\$). To obtain dynamo action under more general conditions, secondary mode}, 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{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{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{FeudelSeehaferSchmidtmann1995, author = {Feudel, Fred and Seehafer, Norbert and Schmidtmann, Olaf}, title = {Fluid helicity and dynamo bifurcations}, year = {1995}, 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{FeudelSeehaferTuckerman2013, author = {Feudel, Fred and Seehafer, Norbert and Tuckerman, Laurette S.}, title = {Multistability in rotating spherical shell convection}, issn = {1539-3755}, year = {2013}, language = {en} } @article{FeudelSeehaferTuckermanetal.2013, author = {Feudel, Fred and Seehafer, Norbert and Tuckerman, Laurette S. and Gellert, Marcus}, title = {Multistability in rotating spherical shell convection}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {87}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {2}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.87.023021}, pages = {8}, year = {2013}, abstract = {The multiplicity of stable convection patterns in a rotating spherical fluid shell heated from the inner boundary and driven by a central gravity field is presented. These solution branches that arise as rotating waves (RWs) are traced for varying Rayleigh number while their symmetry, stability, and bifurcations are studied. At increased Rayleigh numbers all the RWs undergo transitions to modulated rotating waves (MRWs) which are classified by their spatiotemporal symmetry. The generation of a third frequency for some of the MRWs is accompanied by a further loss of symmetry. Eventually a variety of MRWs, three-frequency solutions, and chaotic saddles and attractors control the dynamics for higher Rayleigh numbers.}, language = {en} } @article{FeudelTuckermanGellertetal.2015, author = {Feudel, Fred and Tuckerman, L. S. and Gellert, M. and Seehafer, Norbert}, title = {Bifurcations of rotating waves in rotating spherical shell convection}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {92}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {5}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.92.053015}, pages = {7}, year = {2015}, abstract = {The dynamics and bifurcations of convective waves in rotating and buoyancy-driven spherical Rayleigh-Benard convection are investigated numerically. The solution branches that arise as rotating waves (RWs) are traced by means of path-following methods, by varying the Rayleigh number as a control parameter for different rotation rates. The dependence of the azimuthal drift frequency of the RWs on the Ekman and Rayleigh numbers is determined and discussed. The influence of the rotation rate on the generation and stability of secondary branches is demonstrated. Multistability is typical in the parameter range considered.}, language = {en} } @article{FeudelTuckermanGellertetal.2015, author = {Feudel, Fred and Tuckerman, L. S. and Gellert, Marcus and Seehafer, Norbert}, title = {Bifurcations of rotating waves in rotating spherical shell convection}, series = {Physical Review E}, volume = {92}, journal = {Physical Review E}, number = {5}, publisher = {American Physical Society}, address = {Woodbury}, issn = {1539-3755}, doi = {10.1103/PhysRevE.92.053015}, year = {2015}, abstract = {The dynamics and bifurcations of convective waves in rotating and buoyancy-driven spherical Rayleigh-Benard convection are investigated numerically. The solution branches that arise as rotating waves (RWs) are traced by means of path-following methods, by varying the Rayleigh number as a control parameter for different rotation rates. The dependence of the azimuthal drift frequency of the RWs on the Ekman and Rayleigh numbers is determined and discussed. The influence of the rotation rate on the generation and stability of secondary branches is demonstrated. Multistability is typical in the parameter range considered.}, language = {en} } @article{FuhrmannSeehaferValori2007, author = {Fuhrmann, Marcel and Seehafer, Norbert and Valori, Gherardo}, title = {Preprocessing of solar vector magnetograms for force-free magnetic field extrapolation}, issn = {0004-6361}, doi = {10.1051/0004-6361:20078454}, year = {2007}, abstract = {Context. Reliable measurements of the solar magnetic field are restricted to the phoptosphere. As an alternative to measurements, the field in the higher layers of the atmosphere is calculated from the measured photospheric field, mostly under the assumption that it is force-free. However, the magnetic field in the photosphere is not force-free. Moreover, most methods for the extrapolation of the photospheric magnetic field into the higher layers prescribe the magnetic vector on the whole boundary of the considered volume, which overdetermines the force-free field. Finally, the extrapolation methods are very sensitive to small-scale noise in the magnetograph data, which, however, if sufficienly resolved numerically, should affect the solution only in a thin boundary layer close to the photosphere. Aims. A new method for the preprocessing of solar photospheric vector magnetograms has been developed that, by improving their compatibility with the condition of force- freeness and removing small-scale noise, makes them more suitable for extrapolations into three- dimensional nonlinear force-free magnetic fields in the chromosphere and corona. Methods. A functional of the photospheric field values is minimized whereby the total magnetic force and the total magnetic torque on the considered volume above the photosphere, as well as a quantity measuring the degree of small-scale noise in the photospheric boundary data, are simultaneously made small. For the minimization, the method of simulated annealing is used and the smoothing of noisy magnetograph data is attained by windowed median averaging. Results. The method was applied to a magnetogram derived from a known nonlinear force-free test field to which an artificial noise had been added. The algorithm recovered all main structures of the magnetogram and removed small- scale noise. The main test was to extrapolate from the noisy photospheric vector magnetogram before and after the preprocessing. The preprocessing was found to significantly improve the agreement of the extrapolated with the exact field.}, language = {en} } @article{FuhrmannSeehaferValorietal.2011, author = {Fuhrmann, Marcel and Seehafer, Norbert and Valori, Gherardo and Wiegelmann, T.}, title = {A comparison of preprocessing methods for solar force-free magnetic field extrapolation}, series = {Astronomy and astrophysics : an international weekly journal}, volume = {526}, journal = {Astronomy and astrophysics : an international weekly journal}, publisher = {EDP Sciences}, address = {Les Ulis}, issn = {0004-6361}, doi = {10.1051/0004-6361/201015453}, pages = {12}, year = {2011}, abstract = {Context. Extrapolations of solar photospheric vector magnetograms into three-dimensional magnetic fields in the chromosphere and corona are usually done under the assumption that the fields are force-free. This condition is violated in the photosphere itself and a thin layer in the lower atmosphere above. The field calculations can be improved by preprocessing the photospheric magnetograms. The intention here is to remove a non-force-free component from the data. Aims. We compare two preprocessing methods presently in use, namely the methods of Wiegelmann et al. (2006, Sol. Phys., 233, 215) and Fuhrmann et al. (2007, A\&A, 476, 349). Methods. The two preprocessing methods were applied to a vector magnetogram of the recently observed active region NOAA AR 10 953. We examine the changes in the magnetogram effected by the two preprocessing algorithms. Furthermore, the original magnetogram and the two preprocessed magnetograms were each used as input data for nonlinear force-free field extrapolations by means of two different methods, and we analyze the resulting fields. Results. Both preprocessing methods managed to significantly decrease the magnetic forces and magnetic torques that act through the magnetogram area and that can cause incompatibilities with the assumption of force-freeness in the solution domain. The force and torque decrease is stronger for the Fuhrmann et al. method. Both methods also reduced the amount of small-scale irregularities in the observed photospheric field, which can sharply worsen the quality of the solutions. For the chosen parameter set, the Wiegelmann et al. method led to greater changes in strong-field areas, leaving weak-field areas mostly unchanged, and thus providing an approximation of the magnetic field vector in the chromosphere, while the Fuhrmann et al. method weakly changed the whole magnetogram, thereby better preserving patterns present in the original magnetogram. Both preprocessing methods raised the magnetic energy content of the extrapolated fields to values above the minimum energy, corresponding to the potential field. Also, the fields calculated from the preprocessed magnetograms fulfill the solenoidal condition better than those calculated without preprocessing.}, language = {en} } @article{FuhrmannSeehaferValorietal.2011, author = {Fuhrmann, Marcel and Seehafer, Norbert and Valori, Gherardo and Wiegelmann, Thomas}, title = {A comparison of preprocessing methods for solar force-free magnetic field extrapolation}, issn = {0004-6361}, year = {2011}, language = {en} } @article{HassaninKliemSeehafer2016, author = {Hassanin, Alshaimaa and Kliem, Bernhard and Seehafer, Norbert}, title = {Helical kink instability in the confined solar eruption on 2002 May 27}, series = {Astronomische Nachrichten = Astronomical notes}, volume = {337}, journal = {Astronomische Nachrichten = Astronomical notes}, publisher = {Wiley-VCH}, address = {Weinheim}, issn = {0004-6337}, doi = {10.1002/asna.201612446}, pages = {1082 -- 1089}, year = {2016}, language = {en} } @article{HassaninKliemSeehaferetal.2022, author = {Hassanin, Alshaimaa and Kliem, Bernhard and Seehafer, Norbert and T{\"o}r{\"o}k, Tibor}, title = {A model of homologous confined and ejective eruptions involving kink instability and flux cancellation}, series = {The astrophysical journal : an international review of spectroscopy and astronomical physics}, volume = {929}, journal = {The astrophysical journal : an international review of spectroscopy and astronomical physics}, number = {2}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {2041-8205}, doi = {10.3847/2041-8213/ac64a9}, pages = {7}, year = {2022}, abstract = {In this study, we model a sequence of a confined and a full eruption, employing the relaxed end state of the confined eruption of a kink-unstable flux rope as the initial condition for the ejective one. The full eruption, a model of a coronal mass ejection, develops as a result of converging motions imposed at the photospheric boundary, which drive flux cancellation. In this process, parts of the positive and negative external flux converge toward the polarity inversion line, reconnect, and cancel each other. Flux of the same amount as the canceled flux transfers to a flux rope, increasing the free magnetic energy of the coronal field. With sustained flux cancellation and the associated progressive weakening of the magnetic tension of the overlying flux, we find that a flux reduction of approximate to 11\% initiates the torus instability of the flux rope, which leads to a full eruption. These results demonstrate that a homologous full eruption, following a confined one, can be driven by flux cancellation.}, language = {en} } @article{KliemRustSeehafer2010, author = {Kliem, Bernhard and Rust, S. and Seehafer, Norbert}, title = {Helicity transport in a simulated coronal mass ejection}, series = {Proceedings of the International Astronomical Union}, journal = {Proceedings of the International Astronomical Union}, publisher = {International Astronomical Union}, address = {Cambridge}, issn = {1743-9213}, doi = {10.1017/S1743921311006715}, pages = {125 -- 128}, year = {2010}, language = {en} } @article{KliemSeehafer2022, author = {Kliem, Bernhard and Seehafer, Norbert}, title = {Helicity shedding by flux rope ejection}, series = {Astronomy and astrophysics : an international weekly journal}, volume = {659}, journal = {Astronomy and astrophysics : an international weekly journal}, publisher = {EDP Sciences}, address = {Les Ulis}, issn = {0004-6361}, doi = {10.1051/0004-6361/202142422}, pages = {9}, year = {2022}, abstract = {We quantitatively address the conjecture that magnetic helicity must be shed from the Sun by eruptions launching coronal mass ejections in order to limit its accumulation in each hemisphere. By varying the ratio of guide and strapping field and the flux rope twist in a parametric simulation study of flux rope ejection from approximately marginally stable force-free equilibria, different ratios of self- and mutual helicity are set and the onset of the torus or helical kink instability is obtained. The helicity shed is found to vary over a broad range from a minor to a major part of the initial helicity, with self helicity being largely or completely shed and mutual helicity, which makes up the larger part of the initial helicity, being shed only partly. Torus-unstable configurations with subcritical twist and without a guide field shed up to about two-thirds of the initial helicity, while a highly twisted, kink-unstable configuration sheds only about one-quarter. The parametric study also yields stable force-free flux rope equilibria up to a total flux-normalized helicity of 0.25, with a ratio of self- to total helicity of 0.32 and a ratio of flux rope to external poloidal flux of 0.94. These results numerically demonstrate the conjecture of helicity shedding by coronal mass ejections and provide a first account of its parametric dependence. Both self- and mutual helicity are shed significantly; this reduces the total initial helicity by a fraction of ∼0.4--0.65 for typical source region parameters.}, 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{KuzanyanPipinSeehafer2005, author = {Kuzanyan, Kirill M. and Pipin, V. V. and Seehafer, Norbert}, title = {On the alpha effect and current helicity of solar magnetic fields}, isbn = {92-9092-911-1}, year = {2005}, language = {en} } @article{KuzanyanPipinSeehafer2006, author = {Kuzanyan, Kirill M. and Pipin, Valerij V. and Seehafer, Norbert}, title = {The alpha effect and the observed twist and current helicity of solar magnetic fields}, issn = {0038-0938}, doi = {10.1007/s11207-006-1636-6}, year = {2006}, abstract = {We present a straightforward comparison of model calculations for the alpha-effect, helicities, and magnetic field line twist in the solar convection zone with magnetic field observations at atmospheric levels. The model calculations are carried out in a mixing-length approximation for the turbulence with a profile of the solar internal rotation rate obtained from helioseismic inversions. The magnetic field data consist of photospheric vector magnetograms of 422 active regions for which spatially-averaged values of the force-free twist parameter and of the current helicity density are calculated, which are then used to determine latitudinal profiles of these quantities. The comparison of the model calculations with the observations suggests that the observed twist and helicity are generated in the bulk of the convection zone, rather than in a layer close to the bottom. This supports two-layer dynamo models where the large-scale toroidal field is generated by differential rotation in a thin layer at the bottom while the alpha-effect is operating in the bulk of the convection zone. Our previous observational finding was that the moduli of the twist factor and of the current helicity density increase rather steeply from zero at the equator towards higher latitudes and attain a certain saturation at about 12 - 15 degrees. In our dynamo model with algebraic nonlinearity, the increase continues, however, to higher latitudes and is more gradual. This could be due to the neglect of the coupling between small-scale and large-scale current and magnetic helicities and of the latitudinal drift of the activity belts in the model}, language = {en} } @article{MirandaRempelChianetal.2013, author = {Miranda, Rodrigo A. and Rempel, Erico L. and Chian, Abraham C.-L. and Seehafer, Norbert and Toledo, Benjamin A.}, title = {Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations}, year = {2013}, language = {en} } @article{MirandaRempelChianetal.2013, author = {Miranda, Rodrigo A. and Rempel, Erico L. and Chian, Abraham C.-L. and Seehafer, Norbert and Toledo, Benjamin A. and Munoz, Pablo R.}, title = {Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {23}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {3}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.4811297}, pages = {13}, year = {2013}, abstract = {We study a transition to hyperchaos in the two-dimensional incompressible Navier-Stokes equations with periodic boundary conditions and an external forcing term. Bifurcation diagrams are constructed by varying the Reynolds number, and a transition to hyperchaos (HC) is identified. Before the onset of HC, there is coexistence of two chaotic attractors and a hyperchaotic saddle. After the transition to HC, the two chaotic attractors merge with the hyperchaotic saddle, generating random switching between chaos and hyperchaos, which is responsible for intermittent bursts in the time series of energy and enstrophy. The chaotic mixing properties of the flow are characterized by detecting Lagrangian coherent structures. After the transition to HC, the flow displays complex Lagrangian patterns and an increase in the level of Lagrangian chaoticity during the bursty periods that can be predicted statistically by the hyperchaotic saddle prior to HC transition.}, language = {en} } @article{PalusKurthsSchwarzetal.2007, author = {Palus, Milan and Kurths, J{\"u}rgen and Schwarz, Udo and Seehafer, Norbert and Novotna, Dagmar and Charvatova, Ivanka}, title = {The solar activity cycle is weakly synchronized with the solar inertial motion}, doi = {10.1016/j.physleta.2007.01.039}, year = {2007}, abstract = {We study possible interrelations between the 300-year record of the yearly sunspot numbers and the solar inertial motion (SIM) using the recently developed technique of synchronization analysis. Phase synchronization of the sunspot cycle and the SIM is found and statistically confirmed in three epochs (1734-1790, 1855-1875 and 1907-1960) of the whole period 1700-2000. These results give quantitative support to the hypothesis that there is a weak interaction between the solar activity and the SIM.}, language = {en} } @article{PipinSeehafer2009, author = {Pipin, Valerij V. and Seehafer, Norbert}, title = {Stellar dynamos with Omega x J effect}, issn = {0004-6361}, doi = {10.1051/0004-6361:200810766}, year = {2009}, abstract = {Context. The standard dynamo model for the solar and stellar magnetic fields is based on the \$alphaOmega\$ mechanism, namely, an interplay between differential rotation (the \$Omega\$ effect) and a mean electromotive force generated by helical turbulent convection flows (the \$alpha\$ effect). There are, however, a number of problems with the \$alpha\$ effect and \$alphaOmega\$ dynamo models. Two of them are that, in the case of the Sun, the obtained cycle periods are too short and the magnetic activity is not sufficiently concentrated at low latitudes. Aims. We explore the role of turbulent induction effects that may appear in addition to the \$alpha\$ effect. The additional effects result from the combined action of rotation and an inhomogeneity of the large-scale magnetic field. The best known of them is the \$vec{Omega} imesvec{J}\$ effect. We also include anisotropic diffusion and a new dynamo term that is of third order in the rotation vector \$vec{Omega}\$. Methods. We studied axisymmetric mean-field dynamo models containing differential rotation, the \$alpha\$ effect, and the additional turbulent induction effects. The model calculations were carried out using the rotation profile of the Sun as obtained from helioseismic measurements and radial profiles of other quantities according to a standard model of the solar interior. In addition, we consider a dynamo model for a full sphere that is based solely on the joint induction effects of rotation and an inhomogeneity of the large-scale magnetic field, without differential rotation and the \$alpha\$ effect (a \$delta^{2}\$ dynamo model). This kind of dynamo model may be relevant for fully convective stars. Results. With respect to the solar dynamo, the inclusion of the additional turbulent induction effects increases the period of the dynamo and brings the large-scale toroidal field closer to the equator, thus improving the agreement of the models with the observations. For the \$delta^{2}\$ dynamo working in a full sphere, we find dynamo modes that are steady if the effect of anisotropic diffusion is not included. The inclusion of anisotropic diffusion yields a magnetic field oscillating with a period close to the turbulent magnetic diffusion time.}, 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{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{ScheelSeehafer1997, author = {Scheel, S. and Seehafer, Norbert}, title = {Bifurcation to oscillations in three-dimensional Rayleigh-B{\´e}nard convection}, year = {1997}, 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{SchmidtmannFeudelSeehafer1997, author = {Schmidtmann, Olaf and Feudel, Fred and Seehafer, Norbert}, title = {Nonlinear Galerkin methods for the 3D magnetohydrodynamic equations}, year = {1997}, 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{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{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} } @article{Seehafer1995, author = {Seehafer, Norbert}, title = {The turbulent electromotive force in the high-conductivity limit}, year = {1995}, language = {en} } @article{Seehafer1996, author = {Seehafer, Norbert}, title = {Nature of the alpha effect in magnetohydrodynamics}, year = {1996}, language = {en} } @article{Seehafer1998, author = {Seehafer, Norbert}, title = {Filaments and the solar dynamo}, isbn = {1-88673-370-8}, year = {1998}, language = {en} } @article{SeehaferDemircan2003, author = {Seehafer, Norbert and Demircan, Ayhan}, title = {Dynamo action in cellular convection}, year = {2003}, 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{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{SeehaferFeudelSchmidtmann1996, author = {Seehafer, Norbert and Feudel, Fred and Schmidtmann, Olaf}, title = {Nonlinear dynamo with ABC forcing}, year = {1996}, language = {en} } @article{SeehaferFuhrmannValorietal.2007, author = {Seehafer, Norbert and Fuhrmann, M. and Valori, Gherardo and Kliem, Bernhard}, title = {Force-free magnetic fields in the solar atmosphere}, year = {2007}, 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{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{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{SeehaferSchumacher1998, author = {Seehafer, Norbert and Schumacher, J{\"o}rg}, title = {Resistivity profile and instability of the plane sheet pinch}, year = {1998}, 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{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{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{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} }