Description

Leading experts present the current state of knowledge of the subject of magnetoconvection from the viewpoint of applied mathematics. Here, leading experts present the current state of knowledge of the subject of magnetoconvection: the study of the interplay between magnetic fields and convection. The book covers all aspects of the subject from the viewpoint of applied mathematics, and as a branch of astrophysical (or geophysical) fluid dynamics. Here, leading experts present the current state of knowledge of the subject of magnetoconvection: the study of the interplay between magnetic fields and convection. The book covers all aspects of the subject from the viewpoint of applied mathematics, and as a branch of astrophysical (or geophysical) fluid dynamics. The last thirty years have seen great leaps forward in the subject of magnetoconvection. Computational techniques can now explain exotic nonlinear behaviour, transition to chaos and the formation of structures that can be observed on the surface of the Sun. Here, two leading experts present the current state of knowledge of the subject. They provide a mathematical and numerical treatment of the interactions between electrically conducting fluids and magnetic fields that lead to the complex structures and rich behaviour observed on the Sun and other stars, as well as in the interiors of planets like the Earth. The authors' combined analytical and computational approach provides a model for the study of a wide range of related problems. The discussion includes bifurcation theory, chaotic behaviour, pattern formation in two and three dimensions, and applications to geomagnetism and to the properties of sunspots and other features at the solar surface. Preface; 1. Introduction; 2. Basic MHD; 3. Linearized Boussinesq magnetoconvection; 4. The nonlinear regime; 5. 2D Boussinesq magnetoconvection; 6. 3D Boussinesq magnetoconvection; 7. Magnetoconvection, rotation and the dynamo; 8. Compressible magnetoconvection; 9. Solar and stellar magnetic fields; Appendix A. The Boussinesq and anelastic approximations; Appendix B. Chaotic systems; Appendix C. Double-diffusive convection; Appendix D. Magnetic buoyancy and the magneto-Boussinesq approximation; References; Index.