TY - JOUR A1 - Pipin, Valerij V. A1 - Seehafer, Norbert T1 - Stellar dynamos with Omega x J effect N2 - 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. Y1 - 2009 UR - http://www.aanda.org/index.php?option=article&access=doi&doi=10.1051/0004-6361:200810766 U6 - https://doi.org/10.1051/0004-6361:200810766 SN - 0004-6361 ER - TY - THES A1 - Seehafer, Norbert A1 - Pipin, Valerij V. T1 - An advective solar-type dynamo without the alpha effect N2 - Context: Most solar and stellar dynamo models use the alpha-Omega scenario where the magnetic field is generated by the interplay between differential rotation (the Omega effect) and a mean electromotive force due to helical turbulent convection flows (the alpha effect). There are, however, turbulent dynamo mechnisms that may complement the alpha effect or may be an alternative to it. Aims: We investigate models of solar-type dynamos where the alpha effect is completely replaced by two other turbulent dynamo mechanisms, namely the Omega x J effect and the shear- current effect, which both result from an inhomogeneity of the mean magnetic field. Methods: We studied axisymmetric mean-field dynamo models containing differential rotation, the Omega x J and shear-current effects, and a meridional circulation. 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. Results: Without meridional flow, no satisfactory agreement of the models with the solar observations can be obtained. With a sufficiently strong meridional circulation included, however, the main properties of the large-scale solar magnetic field, namely, its oscillatory behavior, its latitudinal drift towards the equator within each half cycle, and its dipolar parity with respect to the equatorial plane, are correctly reproduced. Conclusions: We have thereby constructed the first mean-field models of solar-type dynamos that do not use the alpha effect. Y1 - 2009 UR - http://www.aanda.org/ U6 - https://doi.org/10.1051/0004-6361/200912614 SN - 0004-6361 ER - TY - JOUR A1 - Seehafer, Norbert T1 - Relaxation to equilibrium and inverse energy cascades in solar active regions Y1 - 1994 SN - 1-563-47099-3 SN - 0079-6050 ER - TY - JOUR A1 - Feudel, Fred A1 - Seehafer, Norbert T1 - On the bifurcation phenomena in truncations of the 2D Navier-Stokes equations Y1 - 1995 ER - TY - JOUR A1 - Seehafer, Norbert T1 - Current helicity and the turbulent electromotive force Y1 - 1994 ER - TY - JOUR A1 - Seehafer, Norbert T1 - Alpha effect in the solar atmosphere Y1 - 1994 ER - TY - JOUR A1 - Feudel, Fred A1 - Seehafer, Norbert A1 - Tuckerman, Laurette S. T1 - Multistability in rotating spherical shell convection Y1 - 2013 UR - http://link.aps.org/doi/10.1103/PhysRevE.87.023021 (9.9.2013) SN - 1539-3755 ER - TY - JOUR A1 - Feudel, Fred A1 - Rüdiger, Sten A1 - Seehafer, Norbert T1 - Bifurcation phenomena and dynamo effect in electrically conducting fluids N2 - 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. Y1 - 2001 ER - TY - JOUR A1 - Demircan, Ayhan A1 - Scheel, S. A1 - Seehafer, Norbert T1 - Heteroclinic behavior in rotating Rayleigh-Benard convection N2 - 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. Y1 - 2000 UR - http://link.springer.de/link/service/journals/10051/bibs/0013004/00130765.htm ER - TY - JOUR A1 - Schumacher, Jörg A1 - Seehafer, Norbert T1 - Bifurcation analysis of the plane sheet pinch N2 - 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. Y1 - 2000 UR - http://publish.aps.org/abstract/PRE/v61/p2695 ER - TY - JOUR A1 - Demircan, Ayhan A1 - Seehafer, Norbert T1 - Dynamos in rotating and nonrotating convection in the form of asymmetric squares N2 - 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. Y1 - 2001 ER - TY - JOUR A1 - Seehafer, Norbert A1 - Demircan, Ayhan A1 - Feudel, Fred T1 - Fluid helicity and dynamo effect N2 - 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. Y1 - 2001 ER - TY - JOUR A1 - Demircan, Ayhan A1 - Seehafer, Norbert T1 - Nonlinear square patterns in Rayleigh-Benard convection N2 - 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. Y1 - 2001 UR - http://www.edpsciences.com/articles/euro/full/2001/02/6376/6376.html ER - TY - JOUR A1 - Demircan, Ayhan A1 - Seehafer, Norbert T1 - Dynamo in asymmetric square convection Y1 - 2002 SN - 0309-1929 ER - TY - JOUR A1 - Seehafer, Norbert A1 - Gellert, Marcus A1 - Kuzanyan, Kirill M. A1 - Pipin, V. V. T1 - Helicity and the solar dynamo Y1 - 2003 ER - TY - JOUR A1 - Seehafer, Norbert A1 - Demircan, Ayhan T1 - Dynamo action in cellular convection Y1 - 2003 ER - TY - JOUR A1 - Rust, David M. A1 - Crooker, N. U. A1 - Gold, R. E. A1 - Golub, Leon A1 - Hundhausen, A. J. A1 - Lanzerotti, L. J. A1 - Lazarus, A. J. A1 - Seehafer, Norbert A1 - Zanetti, L. J. T1 - Heliospheric lins explorer (HELIX) Y1 - 1996 ER - TY - JOUR A1 - Seehafer, Norbert A1 - Galanti, B. A1 - Feudel, Fred A1 - Rüdiger, Sten T1 - Symmetry breaking bifurcations for the magnetohydrodynamic equations with helical forcing Y1 - 1996 ER - TY - JOUR A1 - Seehafer, Norbert A1 - Zienicke, Egbert A1 - Feudel, Fred T1 - Absence of magnetohydrodynamic activity in the voltage-driven sheet pinch Y1 - 1996 ER - TY - JOUR A1 - Feudel, Fred A1 - Seehafer, Norbert T1 - Bifurcations and pattern formation in two-dimensional Navier-Stokes fluid Y1 - 1995 ER -