摘要:

This paper considers oceanic buoyancy driven flow using the linearised equations for a continuously stratified, incompressible, inviscid, Boussinesq fluid. The ocean is unbounded horizontally, infinitely deep and has a linear sloping bottom of arbitrary orientation. Initially the fluid is at rest with uniform buoyancy frequency. Then a point mass source, located on the sea floor, is switched-on and maintained. Using quasigeostrophic theory, explicit analytical solutions are found for the case of (a) a mid-latitude β-plane when the bottom is flat, or (b) anf-plane in the presence of a sloping bottom. In the former case the solutions complement those obtained by McDonald (1992) while in the latter case a two-dimensional bottom trapped wave response is generated.

ISSN:0309-1929    

DOI:10.1080/03091929508229061

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We study spin-up of a viscous electrically conducting Boussinesq fluid in a circular cylinder subject to thermal stratification and uniform axial magnetic field. The cylinder is a perfect conductor of electricity and of heat. Physical parameters are chosen to be consistent with those of planetary interiors:Em∼ E ≤ 1, β ∼ E½, ò ∼ E−1, S ∼ 1, whereE, Em'β, òandSare, respectively, the Ekman number, the magnetic Ekman number, the reciprocal square of the Alfvén Mach number, the Prandtl number and the stratification number [see definitions just after (2.22)]. The linearized basic equations for axisymmetric fluid motion are solved by boundary layer analysis. Three kinds of end-plate boundary layers and two kinds of side-wall boundary layers are found to exist. The non-diffusive interior flow is solved by Fourier-Bessel expansion method combined with Laplace transformation. The Laplace transform solution is inverted numerically by the use of residue theorem combined withMathematica(Wolfram Res., 1992). Results show that the spin-up process is finished within the homogeneous non-magnetic spin-up timet = (L2/ νΩ)½even for cases with non-negligible stratification in accordance with those of Loper's conjecture (Loper, 1976b,c).

ISSN:0309-1929    

DOI:10.1080/03091929508229062

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

This paper presents the first attempt to examine the stability of a poloidal magnetic field in a rapidly rotating spherical shell of electrically conducting fluid. We find that a steady axisymmetric poloidal magnetic field loses its stability to a non-axisymmetric perturbation when the Elsasser number A based on the maximum strength of the field exceeds a value about 20. Comparing this with observed fields, we find that, for any reasonable estimates of the appropriate parameters in planetary interiors, our theory predicts that all planetary poloidal fields are stable, with the possible exception of Jupiter. The present study therefore provides strong support for the physical relevance of magnetic stability analysis to planetary dynamos. We find that the fluid motions driven by magnetic instabilities are characterized by a nearly two-dimensional columnar structure attempting to satisfy the Proudman-Taylor theorm. This suggests that the most rapidly growing perturbation arranges itself in such a way that the geostrophic condition is satisfied to leading order. A particularly interesting feature is that, for the most unstable mode, contours of the non-axisymmetric azimuthal flow are closely aligned with the basic axisymmetric poloidal magnetic field lines. As a result, the amplitude of the azimuthal component of the instability is smaller than or comparable with that of the poloidal component, in contrast with the instabilities generated by toroidal decay modes (Zhang and Fearn, 1994). It is shown, by examining the same system with and without fluid inertia, that fluid inertia plays a secondary role when the magnetic Taylor numberTm≳ 105. We find that the direction of propagation of hydromagnetic waves driven by the instability is influenced strongly by the size of the inner core.

ISSN:0309-1929    

DOI:10.1080/03091929508229063

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

ISSN:0309-1929    

DOI:10.1080/03091929508229064

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

In a rapidly rotating, electrically conducting fluid we investigate the thermal stability of the fluid in the presence of an imposed toroidal magnetic field and an imposed toroidal differential rotation. We choose a magnetic field profile that is stable. The familiar role of differential rotation is a stabilising one. We wish to examine the less well known destabilising effect that it can have. In a plane layer model (for which we are restricted to Roberts numberq= 0) with differential rotation,U=sΩ(z)1ø, no choice of Ω(z) led to a destabilising effect. However, in a cylindrical geometry (for which our model permits all values ofq) we found that differential rotationsU=sΩ(s)1øwhich include a substantial proportion of negative gradient (dΩ/ds≤ 0) give a destabilising effect which is largest when the magnetic Reynolds numberRm= O(10); the critical Rayleigh number,Rac, is about 7% smaller at minimum than atRm= 0 forq= 106. We also find that asqis reduced, the destabilising effect is diminished and atq= 10−6, which may be more appropriate to the Earth's core, the effect causes a dip in the critical Rayleigh number of only about 0.001%. This suggests that we see no dip in the plane layer results because of theq= 0 condition. In the above results, the Elsasser number A = 1 but the effect of differential rotation is also dependent on A. Earlier work has shown a smooth transition from thermal to differential rotation driven instability at high A [A = O(100)]. We find, at intermediate A [A = O(10)], a dip in theRacvs.Rmcurve similar to the A = 1 case. However, it hasRac≤ 0 at its minimum and unlike the results for high A, larger values ofRmresult in a restabilisation.

ISSN:0309-1929    

DOI:10.1080/03091929508229065

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Motivated by the problems of magnetic flux storage and dynamo action in stars with convection zones, we study the equilibrium and stability of magnetic flux tubes under the influence of differential rotation and stratification. The formalism developed in the first paper in this series is applied to axisymmetric, toroidal flux tubes (flux rings) lying in planes parallel to the equator at an arbitrary latitude. We assume mechanical force equilibrium, which requires neutral buoyancy of the flux tube and a longitudinal internal flow in the direction of stellar rotation. Stability against isentropic perturbations is investigated by considering both axisymmetric and non-axisymmetric, three-dimensional displacements of the equilibrium configuration. For axisymmetric modes, we find qualitative differences between the stability criteria for flux tubes within and outside the equatorial plane, where instability is generally easier to excite and overstable modes appear. In the case of non-axisymmetric perturbations, the results of a numerical study with parameter values corresponding to the bottom of the solar convection zone are discussed. The stability properties depend in a complicated way on the various parameters (e.g., latitude, magnetic field, superadiabaticity of the stratification, angular velocity and its gradient). While the magnetic field value for the onset of undulatory (Parker) instability with large growth rates is mainly determined by the stratification and the rotation rate, instabilities at somewhat lower field strengths with relatively small growth rates depend strongly on the sign and the value of the angular velocity gradient.

ISSN:0309-1929    

DOI:10.1080/03091929508229066

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor