摘要:

The linear problem of the onset of convection in rotating spherical shells is analysed numerically in dependence on the Prandtl number. The radius ratio η=ri/roof the inner and outer radii is generally assumed to be 0.4. But other values of η are also considered. The goal of the analysis has been the clarification of the transition between modes drifting in the retrograde azimuthal direction in the low Taylor number regime and modes traveling in the prograde direction at high Taylor numbers. It is shown that for a given valuemof the azimuthal wavenumber a single mode describes the onset of convection of fluids of moderate or high Prandtl number. At low Prandtl numbers, however, three different modes for a givenmmay describe the onset of convection in dependence on the Taylor number. The characteristic properties of the modes are described and the singularities leading to the separation with decreasing Prandtl number are elucidated. Related results for the problem of finite amplitude convection are also reported.

ISSN:0309-1929    

DOI:10.1080/03091928708208809

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Thermal convection in a vertically-mounted, rotating annulus of a particular design proposed by Davies and Walin (1977) is investigated. The annulus used in the present study differs from the conventional type in some important aspects: the sidewalls are finitely conducting, and the thermal conductance of the sidewalls is height-dependent. The theoretical model due to Davies and Walin is briefly recounted. The present study aims to verify the theoretical model; we have acquired numerical solutions to the governing Navier-Stokes equations. The numerical results are supportive of the theoretical contentions. The near-linear dependence of the isothermal slope on the parameterD, which is a function of Ω and ΔT, is corroborated within reasonable limits. New data on the vertical and radial structures of the meridional and azimuthal flows are presented. The numerical results also confirm that the shape of the sidewall thickness has a substantial influence on the meridional flow patterns. In the bulk of the interior flow field, the dominant azimuthal flow field and the temperature field are linked by the thermal wind relation.

ISSN:0309-1929    

DOI:10.1080/03091928708208810

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

It is shown that a systematic development of physical quantities using spherical harmonics provides analytical solutions to a whole class of linear problems of rotating fluids.

ISSN:0309-1929    

DOI:10.1080/03091928708208811

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Finite difference algorithms have been developed to solve a one-dimensional non-linear parabolic equation with one or two moving boundaries and to analyse the unsteady plane flow of ice-sheets. They are designed to investigate the response of an ice-sheet to changes in climate, and to reconstruct climatic changes implied by past ice-sheet variations inferred from glacial geological data. Two algorithms are presented and compared. The first, a fixed domain method, replaces time as an independent variable with span. The grid interval in real space is kept constant, and thus the number of grid points changes with span. The second, a moving mesh method, retains time as one of the independent variables, but normalises the spatial variable relative to the span, which now enters the diffusion and advection coeficients in the parabolic equation for the surface profile.

ISSN:0309-1929    

DOI:10.1080/03091928708208812

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor