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- Olaf Schmidtmann, Fred Feudel, Norbert Seehafer
- 1997

The usage of nonlinear Galerkin methods for the numerical solution of partial diieren-tial equations is demonstrated by treating an example. We desribe the implementation of a nonlinear Galerkin method based on an approximate inertial manifold for the 3D magneto-hydrodynamic equations and compare its eeciency with the linear Galerkin approximation. Special… (More)

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 These results give quantitative support to the… (More)

The Roberts flow, a helical flow in the form of convectionlike rolls, is known to be capable of both kinematic and nonlinear dynamo action. We study the Roberts dynamo with particular attention being paid to the spatial structure of the generated magnetic field and its back-reaction on the flow. The dynamo bifurcation is decisively determined by the… (More)

- V. V. Pipin, N. Seehafer
- 2008

Context. The standard dynamo model for the solar and stellar magnetic fields is based on the αΩ mechanism, namely, an interplay between differential rotation (the Ω effect) and a mean electromotive force generated by helical turbulent convection flows (the α effect). There are, however, a number of problems with the α effect and αΩ dynamo models. Two of… (More)

We have studied bifurcation phenomena for the incompressible Navier-Stokes equations in two space dimensions with periodic boundary conditions. Fourier representations of velocity and pressure have been used to transform the original partial diierential equations into systems of ordinary diierential equations (ODE), to which then numerical methods for the… (More)

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… (More)

Received (Day Month Year) Revised (Day Month Year) 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… (More)

- N Seehafer
- 2007

It is shown that the eeect of mean-eld magnetohydrodynamics, which consists in the generation of a mean electromotive force along the mean magnetic eld by turbulently uctuating parts of velocity and magnetic eld, is equivalent to the simultaneous generation of both turbulent and mean-eld magnetic helicities, the generation rates being equal in magnitude and… (More)

- Fred Feudel, Norbert Seehafer, Olaf Schmidtmann
- 2007

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 eld have been used to transform the original partial diierential equations into systems of ordinary… (More)

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