摘要:

The evolution of the marginally stable neutral modes on a plane parallel flow is studied in the limit of infinite wavelength. The amplitude of such modes is shown to satisfy a complicated integro-differential equation which is coupled through the velocity jump to the equation for the vorticity in the critical layer. For such length and time scales on which the system may be regarded as linear the mode is shown to be stable but not to decay so rapidly as to make a study of the longer time scales inappropriate. On the longer time scales the disturbance spreads out and the main objective of the paper is the determination of the conditions under which the vorticity can become quasi-steady and the mode a solitary wave.

ISSN:0309-1929    

DOI:10.1080/03091927908244530

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

This paper reports a study of slow motions produced mechanically in a rapidly rotating homogeneous liquid when the side-wall of the container is a circular cylinder of radius b′, one of the two plane end-walls is inclined at an angle ½π – α to the axis of the cylinder (which is also the axis of basic rotation with angular speed Ω) and the other end-wall is perpendicular to the rotation axes and is split at a distance a from the axis so that the inner part of the end-wall can be rotated with relative angular speed ϵΩ. The investigation thus extends to cases when α ≠ 0 and a ≠ b′ extensive previous studies of detached shear layers in systems having α = 0 and a ≠ b′ and of western boundary currents in systems having α ≠ 0 and a = b′ (sliced cylinder). A full account of the experiments outlined in this paper (see Section 4)-which covered a wide range of Rossby number |ϵ| and Ekman number E ≅ v/Ωa2-wherevis the coefficient of kinematic viscosity-will be deferred until a numerical study of the non-linear governing equations has been completed. The subsequent analytical study of the linear case (when |ϵ| ≪ E1/2) presented in Section 3 shows how the general flow pattern changes as α increases, revealing three flow regimes typified by the limiting cases tan α ≪ E1/2, E1/2≪ tan α ≪ E1/4and E1/4≪ tan α ≪ 1. It also provides some information on nonlinear effects, including the magnitude of |sϵ| at which linear theory should break down in each flow regime and the relative importance of non-linear effects in different parts of the flow.

ISSN:0309-1929    

DOI:10.1080/03091927908244531

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

A broad shelf is separated from deep water by the sudden change in gradient at the shelf break. The flow is driven by a surface shear stress and a shear layer forms at the edge of the shelf. The transport in the current over the shelf is proportional to the strength of the surface shear stress and to the change in gradient at the shelf break but inversely proportional to the depth of the shelf. The flow is described in terms of a shallow shelf sea driven by wind stress.

ISSN:0309-1929    

DOI:10.1080/03091927908244532

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

The ratio,C, of the dynamical time-scale to the thermal time-scale of a star is small. This fact is used to develop an asymptotic theory of stellar pulsations, valid in the limitC→ 0. The method is demonstrated in four planar models: a polytrope, a polytrope with an isothermal atmosphere, a layer containing a single ionization zone of finite thickness, and a layer in which there is an ionization front. In each case there is a thermal boundary layer associated with the oscillation. When it lies within the isothermal atmosphere of the second model, it is strongly destabilizing. If an ionization zone or front is to drive a layer towards instability, it must lie within the thermal boundary layer. The results for all four are compared with numerical work, and the agreement is shown to be qualitatively good. Only pulsations of infinitesimal amplitude are considered, except for the fourth model in which the so-called “saturation effect” is examined.

ISSN:0309-1929    

DOI:10.1080/03091927908244533

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

A linear analysis is used to study the stability of a rapidly rotating, electrically-conducting, self-gravitating fluid sphere of radiusr0, containing a uniform distribution of heat sources and under the influence of an azimuthal magnetic field whose strength is proportional to the distance from the rotation axis. The Lorentz force is of a magnitude comparable with that of the Coriolis force and so convective motions are fully three-dimensional, filling the entire sphere. We are primarily interested in the limit where the ratioqof the thermal diffusivityκto the magnetic diffusivity η is much smaller than unity since this is possibly of the greatest geophysical relevance.

ISSN:0309-1929    

DOI:10.1080/03091927908244534

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

A magnetohydrodynamic, dynamo driven by convection in a rotating spherical shell is supposed to have averages that are independent of time. Two cases are considered, one driven by a fixed temperature differenceRand the other by a given internal heating rateQ.It is found that whenq, the ratio of thermal conductivity to magnetic diffusivity, is small,Rmust be of orderq−4/3andQof orderq−2for dynamo action to be possible;qis small in the Earth's core, so it is hoped that the criteria will prove useful in practical as well as theoretical studies of dynamic dynamos. The criteria can be further strengthened when the ohmic dissipation of the field is significant in the energy balance. The development includes the derivation of two necessary conditions for dynamo action, both based on the viscous dissipation rate of the velocity field that drives the dynamo.

ISSN:0309-1929    

DOI:10.1080/03091927908244535

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

In Part I, the simple homopolar disc dynamo of Bullard (1955) is discussed, and it is shown that the conventional description is over-simplified and misleading in an important respect, in that it suggests the possibility of exponential growth of the magnetic field even in the limit of perfect disc conductivity, whereas, from fundamental considerations, it is known that the flux of magnetic field across the disc must in this limit remain constant. This contradiction is resolved through consideration of the effect of the azimuthal current distribution which is, in general, inevitably induced in the disc when the conditions for dynamo action are satisfied. By considering a refined model, it is shown that the field growth rate then tends to zero as the disc conductivity tends to infinity. The stability characteristics of this model are determined.

ISSN:0309-1929    

DOI:10.1080/03091927908244536

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

The mean field induction equation of Steenbeck, Krause and Rädler (1966) is solved for anisotropic αik-tensors of varying anisotropy. The attention is restricted to α2-dynamos in spheres with steady axisymmetric magnetic fields. The ratio of the electrical conductivity outside and inside the sphere is varied, but in all cases it is found that a steady dynamo does not exist when the anisotropy of the αik-tensor exceeds a critical value. Such a critical value does not exist in the exceptional case of the Fermi boundary condition. The results emphasize the important effect of boundaries on the existence of solutions of the dynamo problem.

ISSN:0309-1929    

DOI:10.1080/03091927908244537

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

A general expression for the rate of change with timetof the number of intersectionsN(in suitable units) of the lines of force of a magnetic fieldBwith a body of electrically-conducting fluid ℰ in which hydrodynamical motions are occurring leads directly to the result thatdN/dtcannot be positive ifBremains symmetric about an axis. This shows in a straightforward and elementary way that such a field cannot be amplified by fluid motions in ℰ. The possibility (or otherwise) of dynamo action in a perfectly-conducting fluid is also considered.

ISSN:0309-1929    

DOI:10.1080/03091927908244538

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

ISSN:0309-1929    

DOI:10.1080/03091927908244539

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor