摘要:

Convection in Earth's fluid core is regarded as a small deviation from a well-mixed adiabatic state of uniform chemical composition. The core is modeled as a binary alloy of iron and some lighter constituent, whose precise chemical composition is unknown but which is here assumed to be FeAd, where Ad = Si, O or S. The turbulent transport of heat and light constituent is considered, and a simple ansatz is proposed in which this is modeled by anisotropic diffusion. On this basis, a closed system of equations and boundary conditions is derived that governs core convection and the geodynamo. The dual (thermal + compositional) nature of core convection is reconsidered. It is concluded that compositional convection may not dominate thermal convection, as had previously been argued by Braginsky (Soviet Phys. Dokl., v. 149, p. 8, 1963; Geomag, and Aeron., v. 4, p. 698, 1964), but that the two mechanisms are most probably comparable in importance. The key parameters leading to this conclusion are isolated and estimated. Their uncertainties, which in some cases are large, are highlighted. The energetics and efficiency of the geodynamo are reconsidered and re-estimated. Arguments are advanced that indicate that the mass fraction of the light constituent in the solid inner core may not be small compared with that in the outer core, e.g. about 60%. This tends to favor silicon or sulfur over oxygen as the principal light alloying constituent.

ISSN:0309-1929    

DOI:10.1080/03091929508228992

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

The spherical geodynamo model of Braginsky (1978) is re-integrated. The original model of Braginsky modified the Taylor's condition to include the influence of viscous core-mantle coupling. Reinstating also the Ø-component of momentum ∂ωG(s)/∂t [where ωG(s) is the geostrophic shear] in the expression for the modified Taylor condition makes possible the investigation of solutions for small viscosities. Above a critical dynamo numberDc, the solution enters a viscously-limited branch (“Ekman” or “coupling” branch) and, eventually, asDis further increased, jumps to a strong-field branch. The original numerical solution of Braginsky belongs to the latter branch and is duplicated. But, with weak viscosities, the solution on that branch is proved inviscid. In that inviscid limit, Braginsky's model meets the Taylor's condition. The same code is used to re-investigate another αω dynamo model defined by a simpler choice of α and ω effects [α =Rα cos , ω =Rω(r– 1)]

ISSN:0309-1929    

DOI:10.1080/03091929508228993

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

A spherical αω-dynamo is studied for small values of the viscous coupling parameter ϵ ∼ v1/2, paying attention particularly to large dynamo numbers. The present study is a follow-up of the work by Hollerbachet al.(1992) with their choice of α-effect and Archimedean wind including also the constraint of magnetic field symmetry (or antisymmetry) due to equatorial plane. The magnetic field scaled by ϵ1/2is independent of ϵ in the solutions for dynamo numbers smaller than a certain value ofDb(the Ekman state) which are represented by dynamo waves running from pole to equator or vice-versa. However, for dynamo numbers larger thanDbthe solution bifurcates and subsequently becomes dependent on ϵ. The bifurcation is a consequence of a crucial role of the meridional convection in the mechanism of magnetic field generation. Calculations suggest that the bifurcation appears near dynamo number about 33500 and the solutions for larger dynamo numbers and ϵ = 0 become unstable and fail, while the solutions for small but non-zero ϵ are characterized by cylindrical layers of local maximum of magnetic field and sharp changes of geostrophic velocity. Our theoretical analysis allows us to conclude that our solution does not take the form of the usual Taylor state, where the Taylor constraint should be satisfied due to the special structure of magnetic field. We rather obtained the solution in the form of a “weak” Taylor state, where the Taylor constraint is satisfied partly due to the amplitude of the magnetic field and partly due to its structure. Calculations suggest that the roles of amplitude and structure are roughly fifty-fifty in our “weak” Taylor state solution and thus they can be called a Semi-Taylor state. Simple estimates show that also Ekman state solutions can be applicable in the geodynamo context.

ISSN:0309-1929    

DOI:10.1080/03091929508228994

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Three-dimensional models of thermal convection in a spherical shell are presented for five different cases, each characterized by a unique ratio,f, of the radii of the inner and outer bounding surfaces. These solutions are compared to comparable two-dimensional solutions in axisymmetric spherical, cylindrical and Cartesian coordinates. All solutions were obtained with a Rayleigh number of 105, stress free, isothermal boundaries and no internal heating in a constant property Boussinesq fluid of infinite Prandtl number. Similarities and differences between three-dimensional and two-dimensional curvilinear models are discussed in terms of scales and stability of the flow patterns, mean radial temperature profiles and heat transport. It is shown that diagnostic statistics such as mean temperature and Nusselt number may be scaled from one degree of curvature to another for both three- and two-dimensional curvilinear models, provided the aspect ratio and plan form of the flow solutions are comparable. The mean temperature is found to be sensitive to curvature and plan form but not to aspect ratio, while the Nusselt number is found to be sensitive to curvature and aspect ratio but not to the plan form of the flow.

ISSN:0309-1929    

DOI:10.1080/03091929508228995

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We develop a model for the behaviour of continuous releases (plumes) of fluid which, upon mixing with the ambient fluid, undergo a non-monotonic change in density. This model serves as an analogue for the behaviour of volcanic eruption clouds and hydrothermal plumes. If, at the source, the plume is initially actually a negatively buoyant jet, but has the potential on mixing to become buoyant, we identify a criterion for collapse of the plume that is verified by experiment (see Woods and Caulfield, 1992). In a stratified environment, we show that a nonlinearly mixing plume always attains a lower maximum height than a conventional, Iinearly mixing plume whose initial buoyancy flux is equal to the potential buoyancy flux of the nonlinearly mixing plume. The potential buoyancy flux is defined as the maximum buoyancy flux that the plume fluid can develop through mixing at large distances from the source, as the mass flux becomes large due to entrainment. For sufficiently small initial mass fluxes, the height of rise is predicted to decrease as the momentum flux is increased from zero, analogous to the results reported in Morton (1959). We explain this effect in terms of the behaviour of plumes in an unstratified ambient fluid. For a given buoyancy flux, increasing the initial mass flux always reduces the height of rise.

ISSN:0309-1929    

DOI:10.1080/03091929508228996

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

A model is formulated to study the underlying dynamics of observed asymmetries in laboratory experiments on sidewall boundary layer separation and vertical shear layer instability in rapidly rotating fluids. These experiments show differences in transition behavior depending on the nature, cyclonic or anticyclonic, of the gyre forcing. Such qualitative signatures cannot be explained by the standardf-plane quasi-geostrophic model that is unaffected, apart from a switching of the flow direction, under changes of the sign of the forcing. An important ingredient of the intermediate model derived here is a nonlinear Ekman suction condition, which includes products of the interior velocity and its derivatives. The potential vorticity equation is closed using this nonlinear suction condition and other ageostrophic advections. For the case of a cylindrical,f-plane, barotropic ocean bounded by a vertical wall atr = L, and with a weak bottom slope, the nonlinear Ekman layers inhibit sidewall boundary layer separation in cyclonically forced gyres. However, this effect is more than countered by the stretching of the total vorticity in the interior, leading to a net enhancement of separation in such gyres, relative to what happens for anticyclonic forcing. In vertical shear layer instability, anticyclonic shear zones are destabilized relative to cyclonic shear lines. Both these results are in qualitative agreement with laboratory observations.

ISSN:0309-1929    

DOI:10.1080/03091929508228997

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

There has been some interest recently in the dynamics of buoyant low viscosity conduits in surrounding more viscous fluids, motivated by applications to geophysical phenomena. Most studies have been concerned with axisymmetric cylindrical conduits, and have shown that these conduits can support robust solitary waves. Here we develop the wave evolution equation for the analogous two-dimensional slab conduit, and show that this case also supports solitary waves, which are apparently stable and can effectively survive collisions.

ISSN:0309-1929    

DOI:10.1080/03091929508228998

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

The dynamo action of a time-periodic two-dimensional flow close to integrability is analyzed. At fixed Reynolds numberRMand frequency ω, magnetic structures develop in the form of both eddies and filaments. The growth rate of the eddies appears to be the same for all frequencies and decreases withRM, while the growth rate of the filaments displays a strong co-dependence and, except in the limit of zero or infinite frequencies, converges to a non-zero value asRM→ ∞. Magnetic filaments develop in the widest chaotic zones located near the homoclinic or heteroclinic tangles, and their growth rate is strongly influenced by the width of these zones which is estimated using Melnikov formalism. This study illustrates quantitatively that not only a local stretching but also a sizable chaotic zone is required for fast dynamo action.

ISSN:0309-1929    

DOI:10.1080/03091929508228999

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We consider a mean magnetic induction fieldBevolving in an electrically conducting turbulently convecting fluid sphereV, where gravity acting radially is the only force imposing order. The turbulence is radially stratified and mirror-symmetric about planes through the origin. The only possible mean flow is spherically symmetric and radial. For small-scale turbulence, a large-scale mean field emf is generated that to a good approximation is linear inBandVB.This emf comprises the spherically symmetric β1, β2, γ1and δr1effects of Rädler (1980). In combination with the molecular magnetic diffusivity ηm, these effects produce anisotropic diffusion, different for poloidalSand toroidalTmagnetic fields, and characterised by generalised diffusion coefficients ηi(i= 0, 1, 2). The γ1and δr1effects also produce field generation similar to induction by a radial compressible laminar flow or equivalent (e.g. thermomagnetic) effect. Reasoning that usually ηi> 0, we prove decay of the norms max|r2Br| and ||T/r||1,v. For each of these norms, we give a bounding function that decays exponentially with a prescribed decay rate. Furthermore, the decay of each norm is strictly monotonic, regardless of time variations in the generation or diffusion terms. We infer that a self-exciting mean field dynamo cannot persist unless some mechanism, such as rotation, is present to break either the spherical or mirror symmetry of the turbulence. For low conductivity (large ηm) or strong turbulence (large β1), and relatively weak anisotropy (smaller β2, δr1) the decay occurs on the total diffusion time-scale determined by ηm+ β1In stars where β1probably dominates, the decay is therefore very fast on the molecular diffusion time-scale. In such cases rotation is an obvious choice for symmetry-breaker, and possible field maintenance.

ISSN:0309-1929    

DOI:10.1080/03091929508229000

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

A typical time evolution of the phase mixing phenomena is clarified for an idealized model from the standpoint of the local analysis. The model equations are taken from those of the Alfvén type standiing waves in a square region subject to a uni-directional magnetic field and to the effect of small diffusivity in which the Alfvén velocity changes with the magnetic lines offeree. These equations are solved by the use of the WKB method of solution combined with a small perturbation method with respect to the diffusivity. The results gives the time evolution (1) in the initial period in which mutually independent standing waves along each magnetic lines of forces are modulated by the phase mixing effect and (2) in the final period in which these modulated waves are damped off to become asymptotic steady state.

ISSN:0309-1929    

DOI:10.1080/03091929508229001

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor