Related papers: The integral equation approach to kinematic dynamo…
The induction equation of kinematic magnetohydrodynamics is mathematically equivalent to a system of integral equations for the magnetic field in the bulk of the fluid and for the electric potential at its boundary. We summarize the recent…
With only a few exceptions, the numerical simulation of cosmic and laboratory hydromagnetic dynamos has been carried out in the framework of the differential equation method. However, the integral equation method is known to provide robust…
The experimental realization of dynamo excitation as well as theoretical and numerical examinations of the induction equation have shown the relevance of boundary conditions for a self-sustaining dynamo. Within the interior of a field…
The homogeneous dynamo effect is at the root of cosmic magnetic field generation. With only a very few exceptions, the numerical treatment of homogeneous dynamos is carried out in the framework of the differential equation approach. The…
We present an elegant method of determining the eigensolutions of the induction and the dynamo equation in a fluid embedded in a vacuum. The magnetic field is expanded in a complete set of functions. The new method is based on the…
The paper deals with the integral equation approach to steady kinematic dynamo models in finite domains based on Biot-Savart's law. The role of the electric potential at the boundary is worked out explicitly. As an example, a modified…
Numerical studies of a kinematic dynamo based on von Karman type flows between two counterrotating disks in a finite cylinder are reported. The flow has been optimized using a water model experiment, varying the driving impellers…
We study numerically the induction mechanisms generated from an array of helical motions distributed along a cylinder. Our flow is a very idealized geometry of the columnar structure that has been proposed for the convective motion inside…
We numerically examine dynamo action generated by a flow of an electrically conducting fluid in a precessing cylindrical cavity. We compare a simplified kinematic approach based on the solution of the magnetic induction equation with a…
Kinematic simulations of the induction equation are carried out for different setups suitable for the von-K\'arm\'an-Sodium (VKS) dynamo experiment. Material properties of the flow driving impellers are considered by means of high…
A numerical study of the magnetic induction equation has been performed on von Karman type flows. These flows are generated by two co-axial counter-rotating propellers in cylindrical containers. Such devices are currently used in the von…
Planetary magnetic fields are generated by motions of electrically conducting fluids in their interiors. The dynamo problem has thus received much attention in spherical geometries, even though planetary bodies are non-spherical. To go…
The magnetohydrodynamic dynamo equation is derived within general relativity, using the covariant 1+3 approach, for a plasma with finite electric conductivity. This formalism allows for a clear division and interpretation of plasma and…
The VKS experiment has evidenced dynamo action in a highly turbulent liquid sodium von K\'arm\'an flow [R. Monchaux et al., Phys. Rev. Lett. {\bf 98}, 044502 (2007)]. However, the existence and the onset of a dynamo happen to depend on the…
We present results from consistent dynamo simulations, where the electrically conducting and incompressible flow inside a cylinder vessel is forced by moving impellers numerically implemented by a penalization method. The numerical scheme…
Hydrodynamic and magnetohydrodynamic numerical studies of a mechanically forced two-vortex flow inside a sphere are reported. The simulations are performed in the intermediate regime between the laminar flow and developed turbulence where a…
The solar surface dynamo has become an active area of research in an attempt to understand the origin of a variety of magnetic field structures on the sun. The major modification that needs to be incorporated in the standard dynamo process…
The intention of the ''von Karman sodium'' (VKS) experiment is to study the hydromagnetic dynamo effect in a highly turbulent and unconstrained flow. Much effort has been devoted to the optimization of the mean flow and the lateral boundary…
Mean-field dynamo equations are addressed with the aid of the path-integral method. The evolution of magnetic field is treated as a three-dimensional Wiener random process, and the mean magnetic-field equations are obtained with the Wiener…
Hydromagnetic dynamo theory provides the prevailing theoretical description for the origin of magnetic fields in the universe. Here we consider the problem of kinematic, small-scale dynamo action driven by a random, incompressible,…