摘要:

We apply a two-dimensional Cartesian finite element treatment to investigate infinite Prandtl number thermal convection with temperature, strain rate and yield stress dependent rheology using parameters in the range estimated for the mantles of the terrestrial planets. To handle the strong viscosity variations that arise from such nonlinear rheology in solving the momentum equation, we exploit a multigrid method based on matrix-dependent intergrid transfer and the Galerkin coarse grid approximation. We observe that the matrix-dependent transfer algorithm provides an exceptionally robust and efficient means for solving convection problems with extreme viscosity gradients. Our algorithm displays a convergence rate per multigrid cycle about five times better than what other published methods (e.g., CITCOM of Moresi and Solomatov, 1995) offer for cases with similar extreme viscosity variation. The algorithm is explained in detail in this paper.

ISSN:0309-1929    

DOI:10.1080/03091920008203715

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Non-Markovian closure theories are compared with ensemble averaged direct numerical simulations (DNS) for decaying two-dimensional turbulence at large scale Reynolds numbers ranging from ≈ 50 to ≈ 4000. The closures, as well as DNS, are formulated for discrete wave numbers relevant to flows on the doubly periodic domain and are compared with the results of continuous wave number closures. The direct interaction approximation (DIA), self-consistent field theory (SCFT) and local energy-transfer theory (LET) closures are also compared with cumulant update versions of these closures (CUDIA, CUSCFT, CULET). The cumulant update closures are shown to have comparable performance to the standard closures but are much more efficient allowing long time integrations.

ISSN:0309-1929    

DOI:10.1080/03091920008203716

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

In this paper we use the CASL method to explore the role of boundary conditions in determining the long-time behaviour of rotating, stratified, quasi-geostrophic turbulence. We find that initially two-dimensional (sufficiently tall) columns of potential vorticity (PV) break down through three-dimensional instability to give a fully three-dimensional flow consisting of ellipsoidal structures. This is the case both for rigid-lid (isothermal) vertical boundary conditions and for vertically periodic boundaries. However, the rigid boundary case gives rise to semi-ellipsoids at both the top and bottom boundaries, and, for sufficient domain depths, preferred depths for the formation of ellipsoids in the interior. By contrast, in the vertically periodic case, the distribution of ellipsoids is homogeneous in depth.

ISSN:0309-1929    

DOI:10.1080/03091920008203717

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Dynamic interaction between magnetic field and fluid motion is studied through a numerical experiment of nonlinear three-dimensional magnetoconvection in a rapidly rotating spherical fluid shell to which a uniform magnetic field parallel to its spin axis is applied. The fluid shell is heated by internal heat sources to maintain thermal convection. The mean value of the magnetic Reynolds number in the fluid shell is 22.4 and 10 pairs of axially aligned vortex rolls are stably developed. We found that confinement of magnetic flux into anti-cyclonic vortex rolls was crucial on an abrupt change of the mode of magnetoconvection which occurred at Δ = 1 ∼ 2, where A is the Elsasser number. After the mode change, the fluid shell can store a large amount of magnetic flux in itself by changing its convection style, and the magnetostrophic balance among the Coriolis, Lorentz and pressure forces is established. Furthermore, the toroidal/poloidal ratio of the induced magnetic energy becomes less than unity, and the magnetized anti-cyclones are enlarged due to the effect of the magnetic force. Using these key ideas, we investigated the causes of the mode change of magnetoconvection. Considering relatively large magnetic Reynolds number and a rapid rotation rate of this model, we believe that these basic ideas used to interpret the present numerical experiment can be applied to the dynamics in the Earth's and other planetary cores.

ISSN:0309-1929    

DOI:10.1080/03091920008203718

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

This paper develops further a convection model that has been studied several times previously as a very crude idealization of planetary core dynamics. A plane layer of electrically-conducting fluid rotates about the vertical in the presence of a magnetic field. Such a field can be created spontaneously, as in the Childress—Soward dynamo, but here it is uniform, horizontal and externally-applied. The Prandtl number of the fluid is large, but the Ekman, Elsasser and Rayleigh numbers are of order unity, as is the ratio of thermal to magnetic diffusivity. Attention is focused on the onset of convection as the temperature difference applied across the layer is increased, and on the preferred mode,i.e., the planform and time-dependence of small amplitude convection. The case of main interest is the layer confined between electrically-insulating no-slip walls, but the analysis is guided by a parallel study based on illustrative boundary conditions that are mathematically simpler.

ISSN:0309-1929    

DOI:10.1080/03091920008203719

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor