摘要:

We study a semi-analytical model of convection in a rapidly-rotating, differentially-heated annulus with sloping top and bottom lids. Rapid rotation leads to a preservation of relatively simple, two-dimensional (2-D) structure in the experimentally-observed flow, while temporal complexity increases with the Rayleigh number. The model is, therefore, two-dimensional; it exhibits a sequence of bifurcations from steadily-drifting, azimuthally-periodic convection columns, also called thermal Rossby waves, through vacillation and a period-doubling cascade, to aperiodic, weakly-turbulent solutions.

ISSN:0309-1929    

DOI:10.1080/03091928908208896

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The lines of force of a magnetic field extending through an infinitely conducting fluid between footpoints on the planesz=0 andz=Lcan be wrapped and interwoven by bounded continuous motions of the footpoints into a random sequence of arbitrary topological patterns along the field. The sign of the topological helicity of the winding pattern of the field vanes at random along the field. On the other hand, in force-free equilibrium the relative helicity (α=B. ▿B/B2) is rigorously constant along each line of force. Indeed in the limit of an endless random sequence of independent winding patterns along the field, the helicity falls asymptotically to zero and the field becomes curl free. A field with constant helicity along each line of force is obliged to create internal tangential discontinuities (in which the sign of the curl and the helicity is arbitrary) if it is to follow the varying topological helicity imposed by the twists and turns of the succession of independent winding patterns.

ISSN:0309-1929    

DOI:10.1080/03091928908208897

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

It is shown that any stationary three-dimensional velocity field or magnetic field is a potential field in the two dimensional subspace of the Bernoulli surfacesS(Q) or isobaric surfacesS(p), respectively. From this it is shown that the streamlines and the lines of force follow the optical ray paths inS(Q) andS(p) for indices of refractionvandB, respectively. This formal analogy shows how the lines are refracted by variations of the pressure applied by the fluid and field on either side. In particular, it is shown howcontinuousvariations of the pressure producediscontinuities(bifurcations) in the field, forming tangential discontinuities.

ISSN:0309-1929    

DOI:10.1080/03091928908208898

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

We address the problem of frontal stability by making use of the geostrophic momentum approximation to the full hydrodynamic field equations. In a previous analysis of this same problem (Moore and Peltier, 1987) that was based upon use of the full hydrostatic primitive equations, we demonstrated that fronts were subject to a cyclone scale mode of baroclinic instability that had not been isolated in any previous stability analysis. Subsequent work (Moore and Peltier, 1988) demonstrated that this new source of instability was completely filtered when the analysis was performed using conventional quasi-geostrophic theory. Not only did quasi-geostrophic theory fail to account for the cyclone scale mode, however, it also rather severely distorted the long wavelength Charney-Eady mode. Our geostrophic momentum analysis of the frontal stability problem reported here shows that this higher level of approximation similarly filters the cyclone scale mode but it does completely correct the phase speed and growth rate errors for the long waves that were introduced by the quasi-geostrophic approximation. In this sense the geostrophic momentum approximation is shown to constitute a useful intermediate form of the dynamical equations. Because it filters the cyclone scale mode, however, it is nevertheless flawed in a rather fundamental way.

ISSN:0309-1929    

DOI:10.1080/03091928908208899

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The linear stability of the Bénard layer with the combined effects of a uniform magnetic field and a uniform angular velocity in the presence of a Hall current is examined using the Boussinesq approximation. Assuming the directions of the magnetic field and angular velocity to be both vertical, for time-independent motions the problem is studied for different types of boundaries using an asymptotic analysis for large Taylor and Hartmann numbersTandMrespectively. The Hall current is found to have a significant influence on the onset of convection. When the Hall constant,m, is of order unity the critical Rayleigh number (R) is found to increase withmwhenTlies in the range O(M4) ≤T≤ O(M6) for all types of boundaries. For largem, that is whenm= O(Ms), (s> O) for free insulating boundaries the Hall current is found to affectRwhenT≤ O(M3). In the case of free perfectly conducting boundaries, whenm= O(M) andT≤ O(M2), the Hall current is found to influenceRto leading order.

ISSN:0309-1929    

DOI:10.1080/03091928908208900

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A mechanism for producing long-period oscillations of both the wave and zonal-flow components in a two-layer baroclinic system is described. The mechanism hinges on two fundamental properties. First, when the planetary β-effect is sufficiently large, two fundamental linearly-unstable waves with adjacent azimuthal wavenumbers can both equilibrate to non-zero finite-amplitude. Because these adjacent wavenumbers have different frequenciesf1andf2when on the β-plane, interference between the fundamental instabilities will generate an apparent periodic fluctuation in the wave field with a lower frequencyf2-f1, but there is no direct periodic forcing of the zonal flow. Secondly, however,nonlineargeneration of higher-order sidebands by the two fundamentals, coupled with back interactions on the fundamentals themselves will generate azonal flow vacillationwith frequencyn2f1-n1f2, wheren1andn2are the fundamental wavenumbers. This vacillation mechanism is first illustrated through truncated spectral model calculations. These are then shown to successfully predict a number of laboratory experimental observations of low-frequency zonal-flow oscillations.

ISSN:0309-1929    

DOI:10.1080/03091928908208901

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor