Dynamo and Dynamics, a Mathematical Challenge

This book contains the lectures given at the workshop "Dynamo and dynamics, a mathematical challenge" held in Cargese from August 21 to 26, 2000. The workshop differed from most previous conferences on the dynamo effect in two important respects. First, it was at this international conference that the experimental observation of homogeneous fluid dynamos was first reported. Second, the conference gathered scientists from very different fields, thus showing that thepynamo problem has become an interdisciplinary subject involving not only astrophysicists and geophysicists, but also scientists working in dynamical systems theory, hydrodynamics, and numerical simulation, as well as several groups in experimental physics. This book thus reports important results on various dynamo studies in these different contexts: - Decades after the discovery of the first analytic examples of laminar fluid dynamos, the self-generation of a magnetic field by a flow ofliquid sodium has been reported by the Karlsruhe and Riga groups. Although there were no doubts concerning the self generation by the laminar Roberts-type or Ponomarenko-type flows that were used, these experiments have raised interesting questions about the influence of the turbulent fluctuations on the dynamo threshold and on the saturation level of the magnetic field.

Table of Contents:
1: Laboratory dynamos, theory and experiments.- A nonstationary dynamo experiment in a braked torus.- Riga Dynamo Experiment.- Generation of magnetic field in the Couette-Taylor system.- Dynamo action, between numercial experiments and liquid sodium devices.- MHD in von Kármán Swirling flows.- Dynamo action in a forced Taylor-Green vortex.- On the possibility of an homogeneous MHD dynamo in the laboratory.- Saturation of a Ponomarenko type fluid dynamo.- Dynamo Action due to Ekman layer Instability.- Hunting for dynamos: eight different liquid sodium flows.- Thermal flow in a rotating spherical gap with a dielectrophoretic central force field.- Preliminary Measurement of the Turbulent Magnetic Diffusivity in three dimensions.- Saturation mechanism in a model of the Karlsruhe dynamo.- 2: Planetary and stellar dynamos, hydrodynamical models and simulations.- Sheared helical turbulence and the helicity constraint in large-scale dynamos.- The inverse cascade in turbulent dynamos.- Rotating magnetoconvection in dependence on stratification, diffusive processes, and boundary conditions.- Small- and large-scale dynamo action in simple forced flows.- Convection driven dynamos in rotating spherical fluid shells.- Dynamos in rotating and nonrotating convection in the form of asymmetric squares.- Magnetoconvection.- On the application of grid-spectral method to the solution of geodynamo equations.- Super- and counter-rotating jets and vortices in strongly magnetic spherical Couette flow.- Large- and small-scale dynamo action.- Dynamo problems in spherical and nearly spherical geometries.- Anelastic planetary magnetohydrodynamics.- 3: Astrophysical dynamos, observations and theory.- The Galactic Dynamo.- Turbulent Diamagnetism and Galactic Dynamo.- Parker instability withCoriolis force and magnetic reconnection as a part of the galactic fast dynamo action.- Magnetic helicity flux and the nonlinear galactic dynamo.- Helioseismic tests of dynamo models.- Asymptotic WKBJ-studies of solar dynamo waves: 1D and 2D cases.- Dynamo effect with inertial modes in a spherical shell?.- Two types of nonlinearities in magnetic dynamo.- The solar dynamo: axial symmetry and homogeneity broken.- Alpha-quenched a2? dynamo waves in stellar shells.- Two-dimensional disk dynamos with vertical outflows into a halo.- 4: Dynamos as dynamical systems, low-order models and phenomenology.- Structurally stable heteroclinic cycles and the dynamo dynamics.- Two-component dynamical model of the solar cycle.- Symmetries of the solar dynamo: comparing theory with observation.- Suicidal and parthenogenetic dynamos.- Heteroclinic cycles and fluid motions in rotating spheres.- Convection-driven dynamos, amplitude equations and large-scale fields.- A heteroclinic model of geodynamo reversals and excursions.- Aspects of the dynamics underlying solar and stellar dynamo models.- Modulation and symmetry-breaking in low-order models of the solar dynamo.