Some Unusual Properties of Turbulent Convection and Dynamos in Rotating Spherical Shells
نویسنده
چکیده
Convection of an electrically conducting fluid in a rotating system represents a basic dynamical process in planetary interiors and in stars. Astrophysicists and geophysicists have long been interested in the mechanisms that govern the convective heat transport and the generation of magnetic fields by convection in those systems. The availability in recent years of large scale computer capacities has permitted numerical simulations of detailed models for those processes. Only the larger length scales can be taken into account in those computations, of course, and eddy diffusivities are usually introduced to model the influence of the smaller unresolved scales of the turbulent flows. A difficulty arises from the fact that it can not generally be assumed that all eddy diffusivities are equal. First, they apply to scalar as well as to vector quantities, such as temperature and magnetic fields. Secondly, the diffusivities in the absence of turbulence differ enormously such that the turbulence may not be sufficiently strong to equalize them. In the Earth’s liquid core, for instance, the magnetic diffusivity is large enough to be taken into account without the consideration of an eddy contribution while a comparable eddy viscosity would have to exceed the probable molecular viscosity value by a factor of at least 106. As has been demonstrated in the past [11] the dynamics of convection in rotating spherical shells and its dynamo action are very sensitive to ratios of diffusivities, especially to the Prandtl number around its usually assumed value of unity. More complex methods for treating effects of turbulence could eventually be used, such as k− ε-models, and the undoubtedly important anisotropy of turbulent
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