Effects of boundary conditions on the onset of convection with tilted magnetic field and rotation vectors

The problem of the onset of thermal convection is considered, firstly when a uniform tilted magnetic field is present, and secondly in a frame rotating about an oblique axis. If up–down symmetry is broken we expect to find only bifurcations that lead to travelling waves. Numerical studies show, however, that in a Boussinesq fluid the spectrum of eigenvalues can be symmetrical about the real axis, even when the boundary conditions are asymmetrical. Here we show analytically that this symmetry property indeed holds for a wide range of boundary conditions and hence that both steady solutions and standing waves are allowed.     

Thermal convection in a twisted horizontal magnetic field

The onset of convection in a layer of an electrically conducting fluid heated from below is considered in the case when the layer is permeated by a horizontal magnetic field of strength B ₀ the orientation of which varies sinusoidally with height. The critical value of the Rayleigh number for the onset of convection is derived as a function of the Chandrasekhar number Q. With increasing Q the height of the convection rolls decreases, while their horizontal wavelength slowly increases. Potential applications to the penumbral filaments of sunspots are briefly discussed.     

A laboratory model of thermal convection under a central force field

Abstract

A laboratory model of thermal convection under a central force field has been constructed using a strong, alternating electric field gradient in a dielectric liquid. Both the electric field gradient and a temperature gradient are maintained between concentric vertical cylinders. The onset of thermal convection is detected by heat transfer and temperature measurements. It is governed by an electrical Rayleigh number, in which the electric force replaces gravity. Marginal stability analysis gives a critical electrical Rayleigh number in agreement with the experimentally determined value.     

Finite amplitude convection and magnetic field generation in a rotating spherical shell

Abstract

Finite amplitude solutions for convection in a rotating spherical fluid shell with a radius ratio of η=0.4 are obtained numerically by the Galerkin method. The case of the azimuthal wavenumber m=2 is emphasized, but solutions with m=4 are also considered. The pronounced distinction between different modes at low Prandtl numbers found in a preceding linear analysis (Zhang and Busse, 1987) is also found with respect to nonlinear properties. Only the positive-ω-mode exhibits subcritical finite amplitude convection. The stability of the stationary drifting solutions with respect to hydrodynamic disturbances is analyzed and regions of stability are presented. A major part of the paper is concerned with the growth of magnetic disturbances. The critical magnetic Prandtl number for the onset of dynamo action has been determined as function of the Rayleigh and Taylor numbers for the Prandtl numbers P=0.1 and P=1.0. Stationary and oscillatory dynamos with both, dipolar and quadrupolar, symmetries are close competitors in the parameter space of the problem.     

Nonlinear convection in an imposed horizontal magnetic field

Abstract

Nonlinear two-dimensional magnetoconvection, with a Boussinesq fluid driven across the field-lines, is taken as a model for giant-cell convection in the sun and late-type stars. A series of numerical experiments shows the sensitivity of the horizontal scale of convection to the applied field and to the Rayleigh number R. Overstable oscillations occur in cells as broad as they are deep, but increasing R leads to steady motions of much greater wavelength. Purely geometrical effects can cause oscillation: this work implies that strong horizontal field will in general lead to time-dependent convection.     

Flow past spheres and spheroids in the presence of a toroidal magnetic field

Summary Stewartson [1]²) has considered the inviscid flow past a sphere in the presence of a uniform magnetic field andMurray andLudford [2] have investigated a similar problem in which the magnetic field originates from an axially symmetric dipole field situated at the centre of the sphere. In connection with the study of earth's magnetic field, the toroidal part of this field plays a dominant part. This gives rise to the importance of studying the effect of a toroidal magnetic field on flows past different bodies of revolution; specially past spheres and spheroids. In the present note inviscid flows past a sphere, and a spheroid, are considered, for the case of a toroidal magnetic field originating in the fluid. In the case of the sphere the field inside the sphere consists of an electric dipole directed along the axis of symmetry together with a uniform electric field which produces a uniform current along the axis. In the case of the spheroid, the field inside it is due to an electric dipole and quadrupole directed along the axis of symmetry, together with a uniform electric field which produces a uniform current along this axis.     

Interhemispheric contrasts in the ionospheric convection response to changes in the interplanetary magnetic field and substorm activity: a case-study

Interhemispheric contrasts in the ionospheric convection response to variations of the interplanetary magnetic field (IMF) and substorm activity are examined, for an interval observed by the Polar Anglo-American Conjugate Experiment (PACE) radar system between 1600 and 2100 MLT on 4 March 1992. Representations of the ionospheric convection pattern associated with different orientations and magnitudes of the IMF and nightside driven enhancements of the auroral electrojet are employed to illustrate a possible explanation for the contrast in convection flow response observed in radar data at nominally conjugate points. Ion drift measurements from the Defence Meteorological Satellite Program (DMSP) confirm these ionospheric convection flows to be representative for the prevailing IMF orientation and magnitude. The location of the fields of view of the PACE radars with respect to these patterns suggest that the radar backscatter observed in each hemisphere is critically influenced by the position of the ionospheric convection reversal boundary (CRB) within the radar field of view and the influence it has on the generation of the irregularities required as scattering targets by high-frequency coherent radar systems. The position of the CRB in each hemisphere is strongly controlled by the relative magnitudes of the IMF B_z and B_y components, and hence so is the interhemispheric contrast in the radar observations.     

SuperDARN studies of the ionospheric convection response to a northward turning of the interplanetary magnetic field

The response of the dayside ionospheric flow to a sharp change in the direction of the interplanetary magnetic field (IMF) measured by the WIND spacecraft from negative B_z and positive B_y, to positive B_z and small B_y, has been studied using SuperDARN radar, DMSP satellite, and ground magnetometer data. In response to the IMF change, the flow underwent a transition from a distorted twin-cell flow involving antisunward flow over the polar cap, to a multi-cell flow involving a region of sunward flow at high latitudes near noon. The radar data have been studied at the highest time resolution available (2 min) to determine how this transition took place. It is found that the dayside flow responded promptly to the change in the IMF, with changes in radar and magnetic data starting within a few minutes of the estimated time at which the effects could first have reached the dayside ionosphere. The data also indicate that sunward flows appeared promptly at the start of the flow change (within 2 min), localised initially in a small region near noon at the equatorward edge of the radar backscatter band. Subsequently the region occupied by these flows expanded rapidly east-west and poleward, over intervals of 7 and 14 min respectively, to cover a region at least 2 h wide in local time and 5° in latitude, before rapid evolution ceased in the noon sector. In the lower latitude dusk sector the evolution extended for a further 6 min before quasi-steady conditions again prevailed within the field-of-view. Overall, these observations are shown to be in close conformity with expectations based on prior theoretical discussion, except for the very prompt appearance of sunward flows after the onset of the flow change.     

Nonlinear free thermal convection in a spherical shell:A variable viscosity model

Introduction The velocity field of surface plate motion can be split into a poloidal and a toroidal parts.At the Earth′s surface,the toroidal component is manifested by the existence of transform faults,and the poloidal component by the presence of convergence and divergence,i.e.spreading and subduc-tion zones.They have coupled each other and completely depicted the characteristics of plate tec-tonic motions.The mechanism of poloidal field has been studied fairly clearly which is related to …     

火星磁场和行星发电机理论

火星磁场是火星主要观测物理场之一,火星磁场研究对火星探索具有重要的科学意义.本文侧重介绍火星磁场探测所取得的主要成果,在介绍火星行星磁场起源的行星发电机理论的基础上,重点讨论了动力学机制、起始时间、停止的原因等关键性问题,并指出了研究中存在的一些问题.     

Free convection along a non-uniformly heated vertical plate with a variable transverse magnetic field

Summary In this article, we have solved the problem of natural convection along a vertical plate with variable temperature and a transverse non-uniform magnetic field. It also represents a unified analysis of the works of other including the present author, on natural convection with or without transverse magnetic field, and with uniform or non-uniform plate temperature.The author is indebted to Prof.K. B. Ranger, Department of Mathematics, for his continuous and active interest in my research work. I am also grateful to him for offering me a fellowship from his N.R.C. (Canada) research fund.     

Patterns of thermal convection in slowly rotating,weakly magnetic fluid shells

The effects of rotation and a toroidal magnetic field on the preferred pattern of small amplitude convection in spherical fluid shells are considered. The convective motions are described in terms of associated Legendre functions P_l^|m| (cos θ). For a given pair of Prandtl number P and magnetic Prandtl number $\text{P}$_m the physically realized solution is represented either by m = 0 or |m| = l depending on the ratio of the rotation rate Λ to the magnetic field amplitude H. The case of m = 0 is preferred if this ratio ranges below a critical value, which is a function of the shell thickness, and |m| = l otherwise.     

Turbulent magnetic fields in the Sun

Nigel Weiss recounts his Presidential Address 2001, given to the RAS A&G Ordinary Meeting on 9 February 2001.
Recent high-resolution observations, from the ground and from space, have revealed the fine structure of magnetic features at the surface of the Sun. At the same time, advances in computing power have at last made it possible to develop models of turbulent magnetoconvection that can be related to these observations. The key features of flux emergence and annihilation, as observed by the MDI experiment on SOHO, are reproduced in kinematic calculations, while three-dimensional numerical experiments reveal the dynamical processes that are involved. The pattern of convection depends on the strength of the magnetic field: as the mean field decreases, slender rising plumes give way to a regime where magnetic flux is separated from the motion and then to one where locally intense magnetic fields nestle between broad and vigorously convecting plumes. Moreover, turbulent convection is itself able to act as a small-scale dynamo, generating disordered fields near the solar surface.     

Small-scale magnetic buoyancy and magnetic pumping effects in a turbulent convection

We determine the nonlinear drift velocities of the mean magnetic field and nonlinear turbulent magnetic diffusion in a turbulent convection. We show that the nonlinear drift velocities are caused by three kinds of the inhomogeneities; i.e., inhomogeneous turbulence, the nonuniform fluid density and the nonuniform turbulent heat flux. The inhomogeneous turbulence results in the well-known turbulent diamagnetic and paramagnetic velocities. The nonlinear drift velocities of the mean magnetic field cause the small-scale magnetic buoyancy and magnetic pumping effects in the turbulent convection. These phenomena are different from the large-scale magnetic buoyancy and magnetic pumping effects which are due to the effect of the mean magnetic field on the large-scale density stratified fluid flow. The small-scale magnetic buoyancy and magnetic pumping can be stronger than these large-scale effects when the mean magnetic field is smaller than the equipartition field. We discuss the small-scale magnetic buoyancy and magnetic pumping effects in the context of the solar and stellar turbulent convection. We demonstrate also that the nonlinear turbulent magnetic diffusion in the turbulent convection is anisotropic even for a weak mean magnetic field. In particular, it is enhanced in the radial direction. The magnetic fluctuations due to the small-scale dynamo increase the turbulent magnetic diffusion of the toroidal component of the mean magnetic field, while they do not affect the turbulent magnetic diffusion of the poloidal field.     

Thermal convection and the dynamo during rapid rotation

A dynamo model for an incompressible liquid in a rectangular rapidly rotating box is considered. The model is based on a pseudospectral method adapted for multiprocessor technology. The effect of rotation in Boussinesq models on some of the basic characteristics of flows is studied: the spatial form of fields, helicity generation, and spectra of fields. A mechanism stabilizing the magnetic field rise associated with the transition of the system to a nonlinear regime is analyzed separately. The results obtained in the paper provide deeper insights into the processes of magnetoconvection in the cores of planets.     

Longitudinal vibration of a slender bar with nonuniform characteristics in presence of a magnetic field

Summary In the present article the magnetic influence on the free vibrations of a slender bar with characteristics slightly different from those of a uniform one has been discussed. It presents a simple approximate solution to this problem. Moreover the frequency equation has been derived.     

Slow motion of a viscous conducting fluid past ellipsoids in the presence of a toroidal magnetic field

Summary An attempt has been made here, to obtain solutions for the velocity and magnetic field, for a flow past an ellipsoid, in the presence of a toroidal magnetic field, when magnetic Reynold number and Hartman number are small.     

Turbulent transport of angular momentum and differential rotation

Abstract

With the help of simplifying approximations, we have derived expressions for the non-diffusive fluxes of the angular momentum which are brought about by the action of Coriolis forces on the convective motion. The original turbulence, which is not perturbed by the Coriolis forces, is considered given and weakly anisotropic, the anisotropy having a preferred radial direction. The eddy viscosities are evaluated. Hence, a closed equation for the angular velocity is derived, and then solved for the case of slow rotation. It is shown that the differential rotation is generated most effectively in the case of moderate rotation when the Rossby number is of order unity. At small Rossby numbers, the rotation differentiality is inhibited. A negative eddy viscosity is suggested for the case of rapid rotation. Some implications for the Sun and other astrophysical objects are discussed.