On the Structure of Small-Scale Motion in the Core of the Earth

In 1996, St Pierre (1996) reported numerical simulations of a buoyant blob migrating across the earth's outer core and subject to the combined effects of rotation and an azimuthal magnetic field. He noted that the blob rapidly fragments into a series of plate-like structures. Quite independently, Davidson (1995, 1997) discovered a similar behaviour in the context of low- R m turbulence (without a Coriolis force) and showed that this phenomenon has its roots in the destruction of angular momentum by the Lorentz force. The purpose of this paper is to pull together these earlier studies and, in particular, to determine whether or not St. Pierre's platelets are also a consequence of the destruction of angular momentum. We confirm that this is indeed the case.     

Effect of a uniform magnetic field on nonlinear magnetocenvection in a rotating fluid spherical shell

Abstract

Dynamic interaction between magnetic field and fluid motion is studied through a numerical experiment of nonlinear three-dimensional magnetoconvection in a rapidly rotating spherical fluid shell to which a uniform magnetic field parallel to its spin axis is applied. The fluid shell is heated by internal heat sources to maintain thermal convection. The mean value of the magnetic Reynolds number in the fluid shell is 22.4 and 10 pairs of axially aligned vortex rolls are stably developed. We found that confinement of magnetic flux into anti-cyclonic vortex rolls was crucial on an abrupt change of the mode of magnetoconvection which occurred at Δ = 1 ～ 2, where A is the Elsasser number. After the mode change, the fluid shell can store a large amount of magnetic flux in itself by changing its convection style, and the magnetostrophic balance among the Coriolis, Lorentz and pressure forces is established. Furthermore, the toroidal/poloidal ratio of the induced magnetic energy becomes less than unity, and the magnetized anti-cyclones are enlarged due to the effect of the magnetic force. Using these key ideas, we investigated the causes of the mode change of magnetoconvection. Considering relatively large magnetic Reynolds number and a rapid rotation rate of this model, we believe that these basic ideas used to interpret the present numerical experiment can be applied to the dynamics in the Earth's and other planetary cores.     

Large wavenumber convection in the rotating annulus

Abstract

The annulus model considers convection between concentric cylinders with sloping endwalls. It is used as a simplified model of convection in a rapidly rotating sphere. Large azimuthal wavenumbers are preferred in this problem, and this has been exploited to develop an asymptotic approach to nonlinear convection in the annulus. The problem is further reduced because the Taylor-Proudman constraint simplifies the dependence in the direction of the rotation vector, so that a nonlinear system dependent only on the radial variable and time results. As Rayleigh number is increased a sequence of bifurcations is found, from steady solutions to periodic solutions and 2-tori, typically ending in chaotic behaviour. Both the magnetic (MHD convection) and non-magnetic problem has been considered, and in the non-magnetic case our bifurcation sequence can be compared with those found by previous two-dimensional numerical simulations.     

Convection in rotating annular channels heated from below. Part 1. Linear stability and weakly nonlinear mean flows

Convection in a Boussinesq fluid in an annular channel rotating about a vertical axis with lateral rigid sidewalls, stress-free top and bottom, uniformly heated from below is investigated. The sidewalls are assumed to be either perfectly insulating or conducting. Three different types of convection are identified when the channel is rotating sufficiently fast: (i) global oscillatory convection preferred for small Prandtl numbers in channels with intermediate or large aspect ratios (width to height ratio), (ii) wall-localized oscillatory convection representing the most unstable mode for moderate or large Prandtl numbers in channels with intermediate or large aspect ratios and (iii) global stationary convection preferred in channels with sufficiently small aspect ratios regardless of the size of the Prandtl number. The corresponding weakly nonlinear problem describing differential rotation and meridional circulation is also examined, showing that geostrophic, multiple-peaked (two prograde and two retrograde) differential rotation can be maintained by the Reynolds stresses in wall-localized convective eddies in a rapidly rotating channel.     

Nonlinear pulsations of horizontal jets

A shallow-water model with horizontally nonuniform density is used to study the dynamics of jet flows that arise under the influence of buoyancy and the Coriolis force. Within this approach, the jet is described by a self-similar compactly-localized solution and interpreted as a band of shear flow having a temperature contrast with the ambient fluid. In addition to stationary states, the dynamics of such jets admit cyclonic rotation with a constant angular velocity and transverse nonlinear pulsations. The phase portrait corresponding to this model shows that regimes with pulsating jets develop along closed trajectories bounded by the separatrix loop. The theory predicts that the period for warm jet pulsations is longer than the inertial oscillation period caused by the Earth’s rotation, while for cold jet pulsations, it is shorter. Thus, only warm jets can have a noticeable effect on the atmospheric dynamics in the synoptic range. In particular, they may well be responsible for additional spectral peaks that appear in this range of wind speed fluctuations.     

大气中的包络Rossby孤立波——纬度效应的作用

本文进一步对旋转正压大气中的包络Rossby孤立波进行了研究，结果发现当Rossby波的波数m（m为纬向波数）满足1≤m≤2时，旋转正压大气中才存在包络Rossby孤立波，并且只有m＝2的包络Rossby孤立波才具有阻塞高压的结构。我们还对这种m＝２的包络Rossby孤立波随纬度变化的持续性进行了计算，得到了许多结果。     

地转效应实验平台低转速下均匀度相位分布测量

采用微机、光电脉冲技术并通过中断工作方式实现对旋转平台在低转速下转速均匀度相位分布的精密测量．为估计转台对旋转流体实验造成的误差提供数据，实现转台的转速精密测量，转速补偿和转速控制等方面的智能化     

Rotating flow past a short,sliced cylinder at finite Rossby number

Abstract

Flow past a short obstacle in a rotating reference frame generates a wake that is crucial to the overall flow structure if the Rossby number is of the order of the quarter power of the Ekman number. We present here a theory for such flows for the case when the obstacle's top is an oblique, planar surface. The results arise from a combination of asymptotic analysis and numerical computation, and show that even weak asymmetry generates significant global effect on the entire flow-field. Comparisons with the experiments reported by Foster and Davies (1996) are generally good when the high edge is at 90° to the oncoming flow.     

Buoyancy-driven perturbations in a rapidly rotating,electrically conducting fluid: part II – dynamo action

The helicity, electromotive force and α-effect produced in a homogeneous, rapidly rotating, electrically conducting fluid by an isolated source of buoyancy at small Elsasser number are calculated, visualized and analyzed. Due to physical symmetries of the system, the integrals of helicity and electromotive force over all space are zero. However, each has a significant non-zero value when integrated over the cross section of the Taylor column. The local α-effect is found to be significantly anisotropic; it is strongest when the applied magnetic field is toroidal and the resulting EMF is parallel to the applied field.     

Linear theory of rotating fluids using spherical harmonics part I: Steady flows

Abstract

It is shown that a systematic development of physical quantities using spherical harmonics provides analytical solutions to a whole class of linear problems of rotating fluids.

These solutions are regular throughout the whole domain of the fluid and are not much affected by the equatorial singularity of steady boundary layers in spherical geometries.

A comparison between this method and the one based on boundary layer theory is carried out in the case of the steady spin-up of a fluid inside a sphere.