Showing papers by "Friedrich H. Busse published in 1998"

Evolution of spontaneous structures in dissipative continuous systems

Abstract: Mathematical Tools for Pattern Formation.- Formation of Dynamical Structures in Axisymmetric Fluid Systems.- Pattern Formation in Binary Fluid Convection and in Systems with Throughflow.- Dynamical Structures in Open Fluid Systems.- Theoretical and Experimental Investigations of the Faraday Instability.- Pattern Formation in an Inhomogeneous Environment.- Electrically Driven Instabilities in Smectic Liquid Crystal Films.- Electrohydrodynamic Convection in Nematics.- Dynamics of Patterns of Chemical Reactions on Surfaces.- Convection and Pattern Formation Induced by Autocatalytic Chemical Reactions.- Formation of Spatio-Temporal Structures in Semiconductors.- Formation of Patterns in Granular Materials.- Spontaneous Generation of Magnetic Fields in the Laboratory.- From Single Cells to a Multicellular Organism: The Development of the Social Amoebae Dictyostelium Discoideum.

On Convection Driven Dynamos in Rotating Spherical Shells

Abstract: Solutions for chaotic dynamos driven by thermal convection in a rotating spherical shell are obtained numerically for different Prandtl numbers. The influence of this parameter which is usually suppressed in the magnetostrophic approximation is emphasized in the present analysis.

Transitions to complex flows in the Ekman–Couette layer

Abstract: Secondary and tertiary states of fluid flow in a layer between two plates in relative motion and rotating about a normal axis of rotation are studied numerically for a wide range of parameters. Plane Couette flow without rotation and the single Ekman layer at a rigid plate above a quiescent fluid half-space are obtained as limiting cases. A Galerkin method is used for the investigation of the bifurcation structures of the problem. A Chebyshev collocation scheme is used for following the evolution of time-dependent states of the flow

Asymmetric Squares as an Attracting Set in Rayleigh-Bénard Convection

Abstract: Properties of asymmetric square convection in a horizontal fluid layer heated from below are studied numerically with a Galerkin method. Since the Boussinesq approximation is used and symmetric rigid boundaries are assumed, both types of asymmetric square convection---those with rising and those with descending motion in the center---are physically equivalent. It is shown that asymmetric square convection becomes stable with respect to arbitrary three-dimensional infinitesimal disturbances for Rayleigh numbers in excess of 3 to 4 times the critical value.

Stationary and time dependent convection in the rotating cylindrical annulus with modulated height

Abstract: The onset of convection driven by centrifugal buoyancy in the annular region between two coaxial corotating cylinders is investigated when the height of the annular region not only depends on the distance from the axis as in most previous works on the problem but on the azimuthal coordinate as well. The onset of convection in the form of stationary flows or in the form of thermal Rossby waves is investigated in dependence on the parameters of the problem. The evolution of the various modes with increasing amplitude of motion is followed through integrations in time of the fully nonlinear basic equations. Various forms of periodic, quasiperiodic and aperiodic time dependence are found.

The kinematic dynamo action of spiralling convective flows

Abstract: We consider the kinematic production of magnetic fields in a sphere by velocity fields dominated by differential rotation and spiralling convective cells. The high magnetic Reynolds number limit of Braginsky (1964) is considered and formulae are derived allowing an α-effect parametrization of such flows to be easily calculated. This permits an axisymmetric system to be investigated in parallel with the direct 3-D numerical computations. Good agreement between the asymptotic and 3-D calculations is found. The ‘spiralling’ property typical of convective motion in rotating spheres is important in terms of dynamo action; the differential rotation coexisting with this feature is also vital. Indeed, it is the presence of both features which allows the analysis of Braginsky to be employed. With flows approximating the columnar form anticipated for rapidly rotating convection, dynamo action is relatively easily achieved for all azimuthal wavenumbers; modes of differing wavenumbers interact almost by a simple superposition. With flows of more complex latitudinal form, the mutual interactions between modes become more complicated. For columnar-type flows, dipole magnetic fields are favoured when the sense of outward spiralling is prograde and the zonal flow is eastwards, as is physically preferred.

Spontaneous Generation of Magnetic Fields in the Laboratory

Abstract: An introduction to the dynamo effect as a bifurcation phenomenon in moving, electrically conducting fluids is given and its importance as the origin of cosmic magnetic field is pointed out. The second part of this article is devoted to the planned experimental realization of the dynamo effect in the laboratory. Since liquid sodium must be pumped for this purpose through helical pipes at rates of about 100m 3/h, the planned experiment has required several years of preparation. First results are expected after this article has gone to print.