摘要:

Under consideration are interfaces between two media of different densities and which arise from the interaction between theMth andNth harmonics of the motion where 1 ≤N<M. By means of the method of multiple scales in both space and time a pair of nonlinear coupled partial differential equations is derived which model the progression of the interface. The equations contain a detuning parameter [sgrave] which allow imperfections in the resonance to be taken into account. Stokes-type sinusoidal solutions to the equations were sought. It was found that solutions exist for all values of the interaction ratioM/N. In some situations interfaces exist at both exact and near resonance; while in others they are destroyed by amplifications in the detuning. In yet others, a quantity of detuning is actually necessary for the profiles to exist. In all cases, even when the parameters are fixed, a very large class of interface profiles is possible. Finally, the stability of the profiles is studied. It is found that some are quite stable, even to perturbations with wavenumbers close to the main flow.

ISSN:0309-1929    

DOI:10.1080/03091920008204123

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 unit order. In Part I of this series, it was also supposed that the ratio thermal diffusivity diffusivity/magnetic diffusivity is O(1), but here we suppose that this ratio is large. The character of the solution is changed in this limit. In the case of main interest, when the layer is confined between electrically-insulating no-slip walls, the solution is significantly different from the solution when the mathematically simpler, illustrative boundary conditions also considered in Part I are employed. As in Part I, attention is focussed 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.

ISSN:0309-1929    

DOI:10.1080/03091920008204124

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

The annulus model considers convection between concentric cylinders with sloping endwalls. It is used as a simplified model of convection in a rapidly rotating sphere. Large azimuthal wavenumbers are preferred in this problem, and this has been exploited to develop an asymptotic approach to nonlinear convection in the annulus. The problem is further reduced because the Taylor-Proudman constraint simplifies the dependence in the direction of the rotation vector, so that a nonlinear system dependent only on the radial variable and time results. As Rayleigh number is increased a sequence of bifurcations is found, from steady solutions to periodic solutions and 2-tori, typically ending in chaotic behaviour. Both the magnetic (MHD convection) and non-magnetic problem has been considered, and in the non-magnetic case our bifurcation sequence can be compared with those found by previous two-dimensional numerical simulations.

ISSN:0309-1929    

DOI:10.1080/03091920008204125

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Radiative transfer through a model plane-parallel grey atmosphere is investigated. For the purposes of this study the atmosphere is considered to consist of a stationary, inviscid and incompressible fluid. A definitive description of this state is essential for an analysis of the convective instability of such an atmosphere, which will be considered in later papers. The fluid is assumed to be in local thermodynamic equilibrium (LTE) and the treatment of the radiation field is simplified through the use of the Eddington approximation. This results in a pair of simultaneous equations for the temperature and mean radiative intensity. It is shown that the structure of the atmosphere, under the assumption of convective stability, depends on two dimensionless parameters which can be related to the ratio of radiative to conductive heat transfer and the ratio of layer depth to photon mean free path. Analysis reveals that when the bulk of the atmosphere is in radiative equilibrium boundary layers are required at the upper and lower surfaces in order to satisfy the appropriate boundary conditions. The structure of these boundary layers is analyzed through the method of asymptotic matching. These results predict structure of the temperature and mean intensity at the parameter extremes appropriate for both planetary and stellar applications.

ISSN:0309-1929    

DOI:10.1080/03091920008204126

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

The convective instability of a model plane-parallel grey layer of radiating fluid which is heated from below and bounded above by a vacuum is investigated numerically. Both thermal conductivity and radiative transfer of energy are included. The equation governing the transfer of radiation through the steady, incompressible fluid can be simplified by using the Eddington approximation. The linearized equations of marginal stability are solved for a wide range of values of the optical depth of the layer and of the ratio of radiative conductivity to thermal conductivity. Limiting cases are observed for various parameter extremes and considered analytically. A radiative limit is found with a conventionally sized minimum Rayleigh number and horizontal wave number in a suitable scaling. The correct boundary conditions in this limit are found to be Dirichlet for the perturbation mean intensity or perturbation temperature fields.

ISSN:0309-1929    

DOI:10.1080/03091920008204127

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

by John Green (Cambridge University Press), 1999, 213 pp., £42.50 (hardbound; ISBN 0 5212 49759).

ISSN:0309-1929    

DOI:10.1080/03091920008204128

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor