摘要:

An analytical theory of purely baroclinic two-layer singular vortices is presented. The evolution of the vortex structure and the vortex tracks are calculated. It is found that four mechanisms govern the motion of the vortex: (i) barotropic beta gyres, (ii) baroclinic beta gyres, (iii) the interactim between the lower-layer and upper-layer vortices, (iv) Rossby wave radiation. The role of each of these mechanisms and their joint influence upon the baroclinic vortex dynamics are analysed.

ISSN:0309-1929    

DOI:10.1080/03091929708245455

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

The motion of fluid contained between two concentric spherical surfaces is analysed in the limit of strong rotation appropriate to large scale flows and arbitrary gap width. To do so, the dynamical equations are written in the natural cylindrical co-ordinate system that gives a central role to the axis of rotation. The case of a homogeneous fluid allows us to give a general solution of the inviscid, steady flow when sources and sinks have prescribed boundary distributions. Fluid can cross the equatorial plane without breaking rotational constraints provided the source-sink forcing is antisymmetric. However the cylindrical surface tangent to the inner sphere at the equator is singular and calls for higher order inertial and/or viscous effects. No specific solution is obtained in the stratified case, instead a number of integral constraints along the axis of rotation are derived allowing us to relate the interior motion to the surface forcing distributions. The unsteady low frequency waves with Taylor column-like motions are obtained exactly and we extend the non dispersive limit of classical Rossby wave theory in concentric spheres of arbitrary gap width. In the stratified case, a new mode that has no counterpart in the classical, shallow fluid theory is found at the equator.

ISSN:0309-1929    

DOI:10.1080/03091929708245456

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

Separable solutions of the Poincari equation are obtained for a rotating annulus of heightLand side wall radiiriandro. On perturbing solutions of the Poincaré equation and adopting Ekman boundary layersof O(E1/2), where appropriate, analaytical convective solutions are obtained for the rapidly rotating annulus, in the limit of the Ekman numberEand the Prandtl numberPrtending to zero for three different sets of velocity boundary conditions. The convective problem is also solved numerically with exactly the same parameters as used for the analytical analysis, for the most complicated boundary condition set, non-slip on both the side walls and ends, which is shown to be in good agreement with the asymptotic theory.

ISSN:0309-1929    

DOI:10.1080/03091929708245457

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

The problem of magnetic field generation by fluid motions driven by thermal buoyancy in a rotating spherical shell is considered. In extension of earlier work on this problem particular attention is devoted to questions of numerical convergence and of sequences of bifurcations. Finite amplitude convection and nonlinear dynamo solutions are found at Rayleigh numbers below the critical value for the onset of convection. Chaotic solutions appear to be preferred in large regions of the parameter space of the problem.

ISSN:0309-1929    

DOI:10.1080/03091929708245458

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

We study the propagation of nonlinear MHD waves in a highly magnetized dissipative plasma cavity forced at its boundaries. This interacting wave system is analyzed by Galerkin and multiple-scale analyses leading to a simple dynamical system which shares the properties of both the van der Pol and the Duffing oscillator. The system is separated into a Hamiltonian part — possessing a double homoclinic loop to a saddle - and a perturbation. By means of the Melnikov function technique, we show that the saddle's stable and unstable manifolds intersect for suitable values of the forcing amplitude, provided the forcing frequency exceeds a critical value. Saddle-node and period-doubling sequences of bifurcations of periodic orbits (notably a period-three orbit) set in near the homoclinic intersection; these accumulate from below to the same critical value of the control parameter, at which a chaotic limit set appears with fractal dimension ≃ 2.25. Beyond this critical value chaos unfolds into periodic orbits, via saddlenode-bifurcations. Near one of these, the Alfvén wave's amplitude has an, intermittent behaviour over long time-scales with a power chute of about 90% at the intermissions.

ISSN:0309-1929    

DOI:10.1080/03091929708245459

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

The finite-amplitude evolution of neutral perturbations to the Cushman-Roisin frontal geostrophic model for a simple upwelling front with spatially varying potential vorticity is determined. It is shown that the sinuous and varicose modes are governed by the “bright” and “dark” NLS equations, respectively. This implies that the sinuous modes can exhibit Benjamin-Feir instability (while the varicose modes do not), suggesting the possibility that envelope solitons can form on a frontal outcropping. Exploiting the underlying Hamiltonian structure, it is nevertheless shown that all monotomc parallel front solutions of the Cushman-Roisin model are nonlinearly stable in the sense of Liapunov.

ISSN:0309-1929    

DOI:10.1080/03091929708245460

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

In rapidly rotating systems, a (and, in certain circumstances, the) most important nonlinear effect is the geostrophic flowVg(s)1φ associated with Taylor's (1963) constraint. Its role has been extensively studied in the context of α2−and αω-dynamos, and, to a lesser extent in magnetoconvection problems. Here, we investigate its role in the magnetic stability problem, using a cylindrical geometry. First, we investigate the influence of a representative variety of arbitrarily prescribed flowsVg(s)1φ, withV(s) =sω(s), and find that there can be a significant reduction in the critical field strength for flows having a negative outward gradient (dω/ds< 0). We then choose a typical such flow (V= -Rms2) and focus attention on the interaction between the magnetic instability present (or not) when the flow is absent (Rm=0) and the instability driven by differential rotation when the flow is stronger. It is found that instability (even when driven only by the differential rotation) exists only above a minimum field strength. Finally, having gained an understanding of the roles that differential rotation can play, we investigate the nonlinear magnetic stability problem, where the nonlinear effect is the geostrophic flow. We find cases where the geostrophic flow has the property of destabilising the system. This can happen for the most unstable mode, so the nonlinear effect of the geostrophic flow can be subcritical. Corresponding nonlinear calculations at finite Ekman numberE(Hutcheson and Feam, 1995a, b) did not find subcriticality so there must be some value ofE <10−4below which the geostrophic flow dominates the other nonlinear effects and subcriticality becomes possible. What that value is may influence how lowEmust be taken in full geodynamo simulations to correctly qualitatively describe the dynamics of the core.

ISSN:0309-1929    

DOI:10.1080/03091929708245461

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

A plane layer of electrically conducting Boussinesq fluid betweenz = ± d/2rotating with constant angular velocity ω = ωz under a vertical gravitational field g = -gzis examined. In order to simulate the Earth's toroidal field, an imposed non-uniform magnetic field of the form

ISSN:0309-1929    

DOI:10.1080/03091929708245462

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

Following earlier suggestions to replace the ensemble average used in the mean-field electrodynamics by an averaging over the azimuthal coordinate, we consider the basic coefficients in the turbulent electromotive force (EMF) as time-dependent functions. The well-known dynamo coefficients α and ηT- both in the relevant tensorial formulations - are derived from one and the same turbulence field with maximal helicity so that in a local formulation the total turbulent EMF is described as a time series. The (kinematic) turbulence models have always the same intensity of ≃ 100 ms−1and the number of the eddies in the unit length is varied. The EMF-coefficients α and ηTare evaluated within the limit of high (microscopic) conductivity.

ISSN:0309-1929    

DOI:10.1080/03091929708245463

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

A nonlinear αω-dynamo wave propagating equator-wards along a thin differentially rotating convective shell is considered. Nonlinearity arises from α-quenching, while an asymptotic solution is based on the small aspect ratio ε of the shell. Wave modulation is linked to a latitudinal θ-dependent local dynamo numberD(θ); the crucial effects of radial diffusion are incorporated and characterid by a parameter μ. A truncated representation of the solution is obtained. A Parker wave is confined to a latitude belt θ2> θ > θ1>. It is triggered with finite amplitude at a high latitude θ2, whereDachieves a threshold valueDT; that fixes the dynamo wave frequency in terns of the constant μ alone. At lower latitudes θ < θ2, the magnetic field amplitude depends onD(θ), which unlike μ may evolve over a time scale large compared with the cycle period. Eventually, the wave evaporates at a low latitude θ1, whereDdrops to the linear Parker wave valueDp(<DT). The model has two remarkable features. Firstly, whereas the field amplitude is sensitive to variations of dynamo parameters via the dynamo number, the frequency is relatively stable independent ofD. Secondly, the Parker wave is fully nonlinear, because DT-Dp= O(Dp), and is not accessible through weakly nonlinear theory. The key feature of the solution is the novel resolution of the finite amplitude wave stimulation at θ2. It is also argued that the Parker wave is stable, except where it has small amplitude at low latitude θ above but close to θ1. Numerical solutions of the complete governing equations are reported, which support the analytic results for the truncated system.

ISSN:0309-1929    

DOI:10.1080/03091929708245464

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor