摘要:

In the parameter space of a fluid subject to triple convection, there is a critical hypersurface on which three growth rates of linear theory vanish and all the rest are distinctly negative. When parameter values are chosen to place the system very near to this polycritical condition, the temporal behavior of the system may be complicated and even chaotic. This remark, based on rather general considerations (Arneodoet al., 1984), is here illustrated by an example from GFD (Arneodoet al., 1982): two-dimensional Boussinesq thermohaline convection (or semi-convection) in a planeparallel layer rotating about a vertical axis and subject to mathematically convenient boundary conditions. The treatment is made in terms that show why the results may apply to many fluid dynamical systems or indeed to other kinds of triply unstable systems and, using both amplitude equations and mappings, we discuss the chaos that can arise.

ISSN:0309-1929    

DOI:10.1080/03091928508219264

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

The behavior of Rossby waves on a shear flow in the presence of a nonlinear critical layer is studied, with particular emphasis on the role played by the critical layer in a Rossby wave resonance mechanism. Previous steady analyses are extended to the resonant case and it is found that the forced wave dominates the solution, provided the flow configuration is not resonant for the higher harmonics induced by the critical layer. Numerical simulations for the forced initial value problem show that the solution evolves towards the analysed steady state when conditions are resonant for the forced wave, and demonstrate some of the complications that arise when they are resonant for higher harmonics. In relating the initial value and steady problems, it is argued that the time dependent solution does not require the large mean flow distortion that Haberman (1972) found to be necessary outside the critical layer in the steady case.

ISSN:0309-1929    

DOI:10.1080/03091928508219265

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

Simple analytical solutions are presented for nondivergent topographic waves (rotational modes) in a certain type of elliptical basin. Under the assumption that the basin's depth contours form a family of confocal ellipses, the governing potential vorticity equation in elliptic cylindrical coordinates reduces to a Cartesian form, independent of the coordinate scale factors. As a consequence, for the exponential depth profileh=e−bξ, where ξ is the radial coordinate, the radial eigenfunctions for elliptically travelling waves in a basin with a partial vertical barrier along the centerline can be expressed in terms of elementary functions. For a lake without a barrier, approximate analytical solutions are obtained by the Rayleigh-Ritz (variational) method. The periods and streamline patterns of the first few modes of the variational solutions are compared with those due to Ball (1965) for an elliptic paraboloid.

ISSN:0309-1929    

DOI:10.1080/03091928508219266

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

We describe numerical simulations of giant-cell solar convection and magnetic field generation. Nonlinear, three-dimensional, time-dependent solutions of the anelastic magnetohydrodynamic equations are presented for a stratified, rotating, spherical shell of ionized gas. The velocity, magnetic field, and thermodynamic variables are solved simultaneously and self-consistently with full nonlinear feedback. Convection, driven in the outer part of this shell by a superadiabatic gradient, penetrates into the inner, subadiabatic part. Previous dynamic dynamo sjmulations have demonstrated that, when the dynamo operates in the convection zone, the magnetic fields propagate away from the equator in the opposite direction inferred from the solar butterfly diagram. Our simulations suggest that the solar dynamo may be operating at the base of the convection zone in the transition region between the stable interior and the turbulent convective region. There our simulated angular velocity decreases with depth, as it does in the convection zone; but the simulated helicity has the opposite sign compared to its convection zone value. As a result, our simulated magnetic fields in this transition region initially propagated toward the equator. However, due to our limited numerical resolution of the small amplitude helical fluid motions in this dense, stable region, only the initial phase propagation could be simulated, not a complete magnetic cycle.

ISSN:0309-1929    

DOI:10.1080/03091928508219267

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

The effects of compressibility on the stability of internal oscillations in the Earth's fluid core are examined in the context of the subseismic approximation for the equations of motion describing a rotating, stratified, self-gravitating, compressible fluid in a thick shell. It is shown that in the case of a bounded fluid the results are closely analogous to those derived under the Boussinesq approximation.

ISSN:0309-1929    

DOI:10.1080/03091928508219268

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor