摘要:

We discuss numerical solutions of nonlinear equations that model magnetic field generation in a thin layer beneath the convection zone of a late type star. The model equations were derived previously in Paper I (DeLuca and Gilman, 1986b). Three main results are found: first, the oscillating, dynamo wave solutions discussed in DeLuca and Gilman (1986a) are shown to be a result of the severe truncation used in those calculations; second, the induced velocity feld is shown to have an important role in determining the spatial structure of the magnetic field solutions; time dependent solutions have been found. These are not wave-like solutions, rather the amplitude of different horizontal wave modes vary in time. Further, we show that the exact solutions found in Paper I are generally unstable, with the exception of those that are independent of ŷ (latitude in our Cartesian geometry), which are stable if the transient induced velocity field remains small. We conclude that the induced velocity fields are an important ingredient in any model of dynamo action below the solar convection zone.

ISSN:0309-1929    

DOI:10.1080/03091928808213622

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

We employ the method of ordered cumulants to calculate corrections to the first order smoothing approximations of the transport coefficients α and β appearing in the mean-field dynamo equation. Special results are derived for the case of stationary, isotropic Gaussian turbulence, and explicit formulae are given for α(4)and β(4), the terms arising when fourth order correlations are involved. The order of these terms, relative to the usual second order correlation terms, isS2, whereS=uθτc/λc, is the Strouhal number. Two particular examples demonstrate that the corrections can dominate the original terms, and even change the sign of α and (or) β. The coefficient β(4)strongly depends on the helicity of the turbulent flow.

ISSN:0309-1929    

DOI:10.1080/03091928808213623

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

The equations for a relativistic perfect fluid result from the requirement that the total mass-energy be stationary with respect to variations δxα(a, b, c, s) in the space-time location of the fluid particle identified by Lagrangian labels (a, b, c) at the pointson its world-line. By considering variations of the Lagrangian labels that leave the specific volume and entropy unchanged, we obtain a general covariant statement of vorticity conservation. The conservation laws for circulation, potential vorticity, and helicity are simple corollaries. This Noether-theorem derivation shows that the vorticity laws have no analogues in particle mechanics, where the corresponding particle labels cannot be continuously vaned.

ISSN:0309-1929    

DOI:10.1080/03091928808213624

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

We investigate the evolution of a parallel shear flow which has embedded within it a thin, symmetrically positioned layer of stable density stratification. The primary instability of this flow may deliver either Kelvin-Helmholtz waves or Holmboe waves, depending on the strength of the stratification. In this paper we describe a sequence of numerical simulations which reveal for the first time the behavior of the Holmboe wave at finite amplitude and clarify its structural relationship to the Kelvin-Helmholtz wave.

ISSN:0309-1929    

DOI:10.1080/03091928808213625

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

We describe nonlinear time-dependent numerical simulations of whole mantle convection for a Newtonian, infinite Prandtl number, anelastic fluid in a three-dimensional spherical shell for conditions that approximate the Earth's mantle. Each dependent variable is expanded in a series of 4,096 spherical harmonics to resolve its horizontal structure and in 61 Chebyshev polynomials to resolve its radial structure. A semiimplicit time-integration scheme is used with a spectral transform method. In grid space there are 61 unequally-spaced Chebyshev radial levels, 96 Legendre colatitudinal levels, and 192 Fourier longitudinal levels. For this preliminary study we consider four scenarios, all having the same radially-dependent reference state and no internal heating. They differ by their radially-dependent linear viscous and thermal diffusivities and by the specified temperatures on their isothermal, impermeable, stress-free boundaries. We have found that the structure of convection changes dramatically as the Rayleigh number increases from 105to 106to 107. The differences also depend on how the Rayleigh number is increased. That is, increasing the superadiabatic temperature drop, δT, across the mantle produces a greater effect than decreasing the diffusivities. The simulation with a Rayleigh number of 107is approximately 10,000 times critical, close to estimates of that for the Earth's mantle. However, although the velocity structure for this highest Rayleigh number scenario may be adequately resolved, its thermodynamic structure requires greater horizontal resolution. The velocity and thermodynamic structures of the scenarios at Rayleigh numbers of 105and 106appear to be adequately resolved. The 105Rayleigh number solution has a small number of broad regions of warm upflow embedded in a network of narrow cold downflow regions; whereas, the higher Rayleigh number solutions (with large δT) have a large number of small hot upflow plumes embedded in a broad weak background of downflow. In addition, as would be expected, these higher Rayleigh number solutions have thinner thermal boundary layers and larger convective velocities, temperatures perturbations, and heat fluxes. These differences emphasize the importance of developing even more realistic models at realistic Rayleigh numbers if one wishes to investigate by numerical simulation the type of convection that occurs in the Earth's mantle.

ISSN:0309-1929    

DOI:10.1080/03091928808213626

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor