摘要:

We examine two-layer geostrophic flows over a flat bottom on the β-plane. If the displacement of the interface is of the order of the depth of the upper layer, the dynamics of the flow depends on the following non-dimensional parameters:(i)the Rossby number ε,(ii)the ratio δ of the depth of the upper layer to the total depth of the fluid,(iii)the “β-effect number” α = Ro/Recot , where Rois the deformation radius, Re, is the earth's radius and is the latitude. In this paper

ISSN:0309-1929    

DOI:10.1080/03091929608213627

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

An exceptional case to the model-independent theory of Knobloch (1995) is presented, by investigating a rotating cylindrical annulus of heightHand side wall radiiroandri, with non-slip, perfectly thermally conducting side walls and thermally insulating stress-free ends. Radial heating permits the possibility of either two- or three-dimensional convective solutions being the preferred mode. An analytical solution is obtained for the two-dimensional case and a numerical solution for the three-dimensional solution, which is also applied to the two-dimensional solution. It is shown that both two- and three-dimensional solutions can be realized depending on the aspect ratio, γ =H/d, whered=ro-riis the thickness of the annulus, the radii ratio λ =ri/roand the rotation rate of the model. For γ = O(1) and λ = 0.4, the preferred convective solution is three-dimensional when the Taylor number,T< 102and two-dimensional forT> 102. For small aspect ratios, γ ≪ 1, the preferred mode is two-dimensional for all rotation rates.

ISSN:0309-1929    

DOI:10.1080/03091929608213628

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We address the possibility for the core flows that generate the geomagnetic field to contribute significantly to the decade variations of the mean pole position (generally called the Markowitz wobble). This assumption is made plausible by the observation that the flow at the surface of the core-estimated from the geomagnetic secular variation models-experiences important changes on this time scale. We discard the viscous and electromagnetic core-mantle couplings and consider only the pressure torque γpfresulting from the fluid flow overpressure acting on the non-spherical core-mantle boundary (CMB) at the bottom of the mantle, and the gravity torque γgfdue to the density heterogeneity driving the core flow. We show that forces within the core balance each other on the time scale considered and, using global integrals over the core, the mantle and the whole Earth, we write Euler's equation for the mantle in terms of two more useful torques γPgeoand γ. The “geostrophic torque”, γPgeoincorporates γpfand part of γgf, while γ is another fraction of γgf. We recall how the geostrophic pressurepgeo, and thus γPgeofor a given topography, can be derived from the flow at the CMB and compute the motion of the mean pole from 1900 to 1990, assuming in a first approach that the unknown γ can be neglected. The amplitude of the computed pole motion is three to ten times less than the observed one and out of the phase with it. In order to estimate the possible contribution of γ we then use a second approach and consider the case in which the reference state for the Earth is assumed to be the classical axisymmetric ellipsoidal figure with an almost constant ellipticity within the core. We show that (γPgeo+ γ) is then equal to a pseudo-electromagnetic torque γL3, the torque exerted on the core by the component of the Lorentz force along the axis of rotation (this torque exists even though the mantle is assumed insulating). This proves that, at least in this case and probably in the more general case of a bumpy CMB, γ is not negligible compared with γPgeo. Eventually, we estimate the order of magnitude of γL3, show that it is likely to be small and conclude with further possibilities for the Markowitz wobble to be excited from within the core.

ISSN:0309-1929    

DOI:10.1080/03091929608213629

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Hydrodynamical stability of steady flows of two-phase media with a domination of cloud evaporation is studied. Steady state flows dominated by evaporation effects are demonstrated to be intrinsically nonuni-form with characteristic spatial scale inversely proportional to the evaporation mass rate gain. In the short-wavelength limit small perturbations are shown to be stable in subsonic regions of such flows and unstable in supersonic ones. The bulk hydrodynamical motion in broad-absorption line regions of QSOs and in the interstellar medium of the Galaxy are estimated to be influenced considerably by evaporating clouds. As a consequence, stability of these motions is argued to be affected by evaporation effects.

ISSN:0309-1929    

DOI:10.1080/03091929608213630

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The Maximally Efficient Generation Approach (MEGA) is a method to find approximate solutions in a region where strong differential rotation (ω-effect) and helicity (α-effect) coexist (Ruzmaikinet al., 1990). In this paper, new general MEGA-type solutions were obtained in the form of simple analytical formulas. It is shown that MEGA gives a WKBJ type solution to αω-dynamo problem with turning point at the maximum of the product of α- and ω-effects. MEGA attains a higher accuracy if there is a clear maximum of this product in real space far from the boundaries, which is the most usual case in real situations. The approximated eigenvalue depends crucially on the distribution of the product of α- and ω-effects, but not much on the particular distributions of the individual effects. The predicted eigenvalues and eigenfunctions were compared with the solutions from numerical analysis. It was found that the critical Reynolds numbers and oscillation frequencies predicted by the MEGA method are very close to the numerically obtained results for models with reasonable parameters. This gives strong support for MEGA estimations as simple and effective means for finding the region of parameters responsible for the astrophysical dynamos. However, the difference between the MEGA and numerical results become large when the maximum of generation is located near the outer boundary or when there is very small overlap of α- and ω-effects. For successful MEGA predictions, the difference between the MEGA and numerical critical Reynolds numbers (of dipole or quadrupole family, whichever is the smaller) is similar to the difference between the numerical solutions for the dipole and quadrupole modes.

ISSN:0309-1929    

DOI:10.1080/03091929608213631

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Bayly (1993) introduced and investigated the equation (ϑt+v·▽-η ▽2)S=RSas a scalar analogue of the magnetic induction equation. Here,S(r,t) is a scalar function and the flow fieldv(r,t) and “stretching” functionR(r,t) are given independently. This equation is much easier to handle than the corresponding vector equation and, although not of much relevance to the (vector) kinematic dynamo problem, it helps to study some features of the fast dynamo problem. In this note the scalar equation is considered for linear flow and a harmonic potential as stretching function. The steady equation separates into one-dimensional equations, which can be completely solved and therefore allow one to monitor the behaviour of the spectrum in the limit of vanishing diffusivity. For more general homogeneous flows a scaling argument is given which ensures fast dynamo action for certain powers of the harmonic potential. Our results stress the singular behaviour of eigenfunctions in the limit of vanishing diffusivity and the importance of stagnation points in the flow for fast dynamo action.

ISSN:0309-1929    

DOI:10.1080/03091929608213632

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor