摘要:

Nonlinear axisymmetric convective motions of self-gravitating, infinite Prandtl number fluids in spheres and thick spherical shells are determined for a variety of shell sizes and for different modes of heating. For one combination of heating from within and from below the onset of convection is governed by a self-adjoint system of equations and boundary conditions. For two other heating modes, heating only from within or only from below, the linearized equations and boundary conditions are not self-adjoint. The properties of the self-adjoint solutions together with a parameter which quantifies the departure from self-adjointness provide a theoretical framework for organizing, understanding, and generalizing the heat transfer characteristics of the non-self-adjoint cases. The variations in heating and shell size that are considered yield 6 different patterns of steady convection—flows with 1 and 3 meridional cells, and pairs of oppositely rotating flows with 2 and 4 meridional cells. The heat transport properties of the different convection patterns and the stability of the flows to general axisymmetric and nonaxisymmetric disturbances are ascertained.

ISSN:0309-1929    

DOI:10.1080/03091928308209038

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

A general method is presented for deriving complex eigenvalue bounds for linear second order systems. It is applied to the problem of stratified horizontal magnetohydrodynamic shear flow, and it is found that, if the system is convectively stable, the imaginary part of the eigenfrequency is bounded by ½∣ú'0∣max, whereu0is the flow velocity. In the absence of a magnetic field, the classical Miles–Howard–Chimonas result is recovered, but with more detail about the growth rates of individual modes. These results are shown to hold for free as well as rigid boundaries.

ISSN:0309-1929    

DOI:10.1080/03091928308209039

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

A method discussed in Paper I (Cally, 1983) for determining complex eigenvalue bounds for second-order ordinary differential systems is applied to an isothermal, perfectly conducting, compressible, stratified medium permeated by a horizontal magnetic field and aligned shear flow. The magnetic field is chosen such that the Alfvén velocity is everywhere constant. For this particular system, the eigenvalue bounds obtained are generally tighter than those obtained in Paper I, and an additional feature is that the bound on the maximum growth rate peaks at a finite value of horizontal wavenumberk, not ask→∞, as is found in Paper I.

ISSN:0309-1929    

DOI:10.1080/03091928308209040

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The effect of rigid body rotations on the structure of turbulence correlations for incompressible two-dimensional turbulent flow is examined. It is proven that the usual turbulence correlations that are constructed from the fluctuating velocity are invariant under rigid body rotations of the fluid while those that are constructed from the fluctuating pressure are not. An explicit transformation rule for rigid body rotations is developed for an important class of turbulence correlations that are built up from the fluctuating pressure. It is shown how these results can serve as a powerful tool in the development of turbulent closure models that are suitable for the study of atmospheric turbulence in the stratosphere.

ISSN:0309-1929    

DOI:10.1080/03091928308209041

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor