- Dynamical systems (1) (remove)
- Convection and Magnetic Field Generation in Rotating Spherical Fluid Shells (2004)
- The dissertation reports results from numerical and analytical studies of convection and dynamo action in rotating fluid spheres and spherical shells. This research is motivated by the geophysical problem of the origin and properties of the Earth's magnetism. Extensive numerical simulations are performed in order to advance the understanding of the basic physical components and mechanisms believed to be responsible for the generation and the variations in time of the main geomagnetic field. Questions such as linear onset and nonlinear finite-amplitude properties of rotating convection, generation and equilibration of magnetic fields in electrically conducting fluids, nonlinear feedback effects of the generated magnetic fields on convection, spatio-temporal structures of magnetic and velocity fields, oscillations and coherent processes in turbulent regimes and other questions are studied in dependence on all basic parameters of the problem, as well as for various choices of the magnetic, thermal and velocity boundary conditions and for some secondary assumptions such as a finitely-conducting inner core and various basic temperature profiles. Because of the lack of knowledge of the properties of the Earth's core and the uncertain details of the processes that take place there, this research is necessary in order to provide the tools for extrapolation to realistic models of the geodynamo. Of particular interest are various types of oscillations of dipolar fields. In contrast to quadrupolar and hemispherical dynamos dipolar dynamos have been originally considered to be non-oscillatory. But the six different types of dipolar oscillations, among which is the ``invisible'' one, reported in this dissertation alter this view. Generation of magnetic fields by convection shows a strong dependence on the Prandtl number P of the fluid. But this fact has received little attention in the past. Convection-driven dynamo action at Prandtl numbers larger than unity is studied with the goal to test the validity of the magnetostrophic approximation. The latter is found to be poorly satisfied for P < 300. Dynamos in this regime require magnetic Prandtl numbers Pm which increase with P. The same trend continues to hold for values of P less then unity and this regime thus seems to be best suited to reach the goal of minimal values of Pm. For Pm=P=0.1 a hemispherical dynamo is obtained in the case of a rotation parameter tau=10**5. A further reduction of Pm leads to a decay of magnetic field irrespective of the Rayleigh numbers used. Apart from numerical simulations and parameter studies of basic physical mechanisms, the dissertation includes an analytical study of inertial convection in rotating spheres in the limit of small Prandtl numbers and large rotation rates. Explicit expressions for the dependence of the Rayleigh number on the azimuthal wavenumber and on the product of P tau are derived and new results for the case of a nearly thermally insulating boundary are obtained. Limited comparisons with actually observed features of the geomagnetic field are also presented. An example are the torsional Alfven waves found in the numerical simulations of this dissertation. They are geophysically relevant as a possible cause for the observed secular variation impulses of the Earth's magnetic field. Reversals of the magnetic field polarity have also been observed in our simulations. Dynamo intermittency and interaction between dipolar and quadrupolar components are preconditions for aperiodic dipolar reversals similar to those of the Earth's main field. However, the opportunities for quantitative comparisons with geophysical observations are rather limited by the complexity of the self-consistent dynamo problem and by the computational restrictions of our numerical simulations.