摘要:

We describe laboratory observations of the flow of a homogeneous fluid over three-dimensional obstacles that are towed along the bottom of one vertical wall of a wide rotating channel. The behaviour of the viscous-inertial flow, for a given direction of rotation, depends strongly upon whether the wall is on the right- or left-hand side when looking downstream (in the direction of flow relative to the obstacle). There are a number of flow regimes, with a blocked region occurring above the topography at low Rossby numbers when the wall is on the right of the flow (for anticlockwise rotation), but a large blocked region developing downstream of the obstacle when the wall is on the left. Blocking on the left-hand wall occurs at larger Rossby numbers than on the right-hand wall, contrary to theoretical predictions for slowly varying topography or linearised disturbances. When the influence of viscosity is sufficiently small the blocked region against a left-hand wall gives way to a train of cyclonic eddies. No wake is seen when the wall is on the right of the flow and there are no anticyclonic eddies. At large Rossby numbers the disturbance takes the form of a system of standing inertial lee waves.

ISSN:0309-1929    

DOI:10.1080/03091928308210119

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

A study is made of the zonal-mean motions induced by a growing baroclinic wave in several contexts, under the framework of three different analysis schemes: the conventional Eulerian mean (EM), the transformed Eulerian mean (TEM), and the generalized Lagrangian mean (GLM). The effect of meridional shear in the initial jet on these induced mean motions is considered by treating the instability problem in the context of the two-layer model.

ISSN:0309-1929    

DOI:10.1080/03091928308210120

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

This paper experimentally investigates the convective planform near critical in a fluid layer whose temperature-dependent viscosity varies from top to bottom by up to a factor of 1500. Convection occurs in three different planforms: rolls, hexagons and squares. The square planform, which appears only for fluids with viscosity variation greater than about 50, replaces the hexagonal convection pattern as the Rayleigh number increases much above critical. The large amplitude of hexagonal convection with strong viscosity variation precludes studying the hexagon-square transition with perturbation methods of the type used to study the hexagon-roll transitions at smaller viscosity variations.

ISSN:0309-1929    

DOI:10.1080/03091928308210121

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

An idealised α2ω-dynamo is considered in which the α-effect is prescribed. The additional ω-effect results from a geostrophic motion whose magnitude is determined indirectly by the Lorentz forces and Ekman suction at the boundary. As the strength of the α-effect is increased, a critical value α*cis reached at which dynamo activity sets in; α*cis determined by the solution of the kinematic α2-dynamo problem. In the neighbourhood of the critical value of α* the magnetic field is weak of orderE1/4(μηρω)½due to the control of Ekman suction;E(≪1) is the Ekman number. At certain values of α*, viscosity independent solutions are found satisfying Taylor's constraint. They are identified by the bifurcation of a nonlinear eigenvalue problem. Dimensional arguments indicate that following this second bifurcation the magnetic field is strong of order (μηρω)½. The nature of the transition between the kinematic linear theory and the Taylor state is investigated for various distributions of the α-effect. The character of the transition is found to be strongly model dependent.

ISSN:0309-1929    

DOI:10.1080/03091928308210122

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

We examine by means of a local analysis the effects of an azimuthal magnetic fieldB(r) on the stability of a rapidly-rotating fluid subject to a radial temperature gradient, taking the ratio κ/η of thermal to magnetic diffusivities to be small, as in the Earth's core. According to this theory, previous results for the caseB∝rare typical of a certain range of magnetic field profiles, but ifBdecreases withrfaster thanr−½we find instead that (i) the critical Rayleigh number increases sharply as the magnetic field strength increases beyond “magnetostrophic” values and (ii) the recently-discovered magnetic instabilities triggered bybottom-heavydensity gradients do not occur. IfBincreases withrfaster thanr3/2, on the other hand, the major change to theB∝rpicture of events is that the system becomes unstable to comparatively fast magnetic instabilities as soon as the field passes magnetostrophic values.

ISSN:0309-1929    

DOI:10.1080/03091928308210123

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

A cylindrical annulus containing a conducting fluid and rapidly rotating about its axis is a useful model for the Earth's core. With a shear flowU0(s)∮, magnetic fieldB0(s)∮, and temperature distributionTo(s) (where (s, ∮, z) are cylindrical polar coordinates), many important properties of the core can be modelled while a certain degree of mathematical simplicity is maintained. In the limit of rapid rotation and at geophysically interesting field strengths, the effects of viscous diffusion and fluid inertia are neglected. In this paper, the linear stability of the above basic state to instabilities driven by gradients ofB0andU0is investigated. The global numerical results show both instabilities predicted by a local analysis due to Acheson (1972, 1973, 1984) as well as a new resistive magnetic instability. For the non-diffusive field gradient instability we looked at both monotonic fields [for which the local stability parameter Δ, defined in (1.4), is a constant] and non-monotonic fields (for which Δ is a function ofs). For both cases we found excellent qualitative agreement between the numerical and local results but found the local criterion (1.6) for instability to be slightly too stringent. For the non-monotonic fields, instability is confined approximately to the region which is locally unstable. We also investigated the diffusive buoyancy catalysed instability for monotonic fields and found good quantitative agreement between the numerical results and the local condition (1.9). The new resistive instability was found for fields vanishing (or small) at the outer boundary and it is concentrated in the region of that boundary. The resistive boundary layer plays an important part in this instability so it is not of a type which could be predicted using a local stability analysis (which takes no account of the presence of boundaries).

ISSN:0309-1929    

DOI:10.1080/03091928308210124

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor