摘要:

A numerical model is used to study the transition between various types of periodic and chaotic behavior in a two-layer baroclinic circumferential flow. At small supercriticalityF−Fcand low friction Γ, a type of chaos similar to that predicted by low-order or weakly-nonlinear models is found. However, contrary to the predictions of these relatively simple models, this type of aperiodic behavior, first discovered by E. N. Lorenz in his classic study of thermal convection, occupies only a small bubble in theF− Γ parameter-space. As the supercriticality is increased the aperiodic regime terminates abruptly and a broad band of periodic motions separates the weakly-nonlinear chaotic region from a higher-dimensional type of chaos that occurs at largerF−FcWave-wave vacillation is predicted near the crossing of the wavenumber −1 and wavenumber −2 neutral curves. The calculations are in qualitative agreement with experiments, especially in that the transition to chaos at moderateF−Fc, as Γ is decreased, involves both period-doubling and quasi-periodicity.

ISSN:0309-1929    

DOI:10.1080/03091928608210090

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

In this study, the equations of the three-dimensional convective motion of an infinite Prandtl number fluid are solved in spherical geometry, for Rayleigh numbers up to 15 times the critical number. An iterative method is used to find stationary solutions. The spherical parts of the operators are treated using a Galerkin collocation method while the radial and time dependences are expressed using finite difference methods. A systematic search for stationary solutions has led to eight different stream patterns for a low Rayleigh number (1.28 times the critical number). They can be classified as:

ISSN:0309-1929    

DOI:10.1080/03091928608210091

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

In this paper we derive a set of equations which model magnetic field generation and maintenance in a thin region, (∼ 104)km thick, below the solar convection zone, and present some simple exact solutions. Energy to drive the dynamo is assumed to come from helical convection that overshoots into this region. Differential rotation and meridional circulation result only from feedbacks by the induced fields. The equations are derived for a homogeneous incompressible fluid in Cartesian geometry. The momentum equation, magnetic induction equation, and the continuity equation are included in the analysis. We assume velocity and magnetic field patterns have an aspect ratio of ∼1/10 (radial to horizontal scale), that the large scale velocities are smaller than the convection zone velocities, a few meters per sec, and the large scale magnetic fields are of the order of 104Gauss. Finally we assume that the time scale of interest is the advective time scale. Using these assumptions, we derive governing equations in which the Coriolis force balances the Lorentz force, the pressure gradient force, and the viscosity, and in which the magnetic fields are maintained by the α effect but significantly modified by the above velocity fields. The results of this model will be discussed in following papers.

ISSN:0309-1929    

DOI:10.1080/03091928608210092

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The viscous flow past a right circular cylinder on a β-plane is numerically studied. The basic flow, unbounded laterally, is assumed to be uniform. The explored parameter space isRo<O(1),Ek≪O(1),∼O(1) and δ=2, whereRois the Rossby number,Ekthe Ekman number,the beta parameter, and δ the aspect ratio. Under these conditions, the quasigeostrophic potential vorticity equation is integrated numerically.

ISSN:0309-1929    

DOI:10.1080/03091928608210093

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Recently Merkine, Mo and Kalnay (1985) have re-examined the possible existence of Fofonoff's (1954) steady free inertial solution and the role of Fofonoff's mode in numerical circulation models after Veronis (1966). Merkineet al. conclude that the Fofonoff mode does not occur, that such a mode would be barotropically unstable and that resemblances between numerical circulations and Fofonoff's mode are more dependent upon the natures of forcing and dissipation. On the contrary, I suggest that Fofonoff's mode very naturally does emerge and that forcing and dissipation only impede the full realization of Fofonoff's mode. Moreover, statistical mechanical arguments from Salmon, Holloway and Hendershott (1976) show that the Fofonoff mode is expected to co-exist with a transient eddy field whose statistics are in equilibrium with the mode; thus bartotropic instability does not argue for non-realization of Fofonoff's mode.

ISSN:0309-1929    

DOI:10.1080/03091928608210094

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor