Core flow modeling

Approximation used at CMB and in the core

  1. Toroidal flow only;
  2. . the magnetic field is transported by the toroidal flow;

    . in agreement with stably stratified layer in the core near the CMB.

  3. Geostrophic flow, tangentially geostrophic at CMB;
  4. . flow governed by pressure and Coriolis force;

    . flow along isobar curves;

    . symmetric and zonal scaloidal component zero;

    . flow following cylinders coaxial with rotation axis.

  5. Magnetostrophic flow: geostrophic + Lorentz force;
  6. . same as in point (2) but additionally torsional oscillations, stationary waves linking
    all the cylinders.

  7. Steady flow;
  8. . no time dependence of the flow;

    . flow fit on secular variation of the magnetic field;

    . but unable to reproduce fine details of the secular variation of the magnetic field.

  9. Steady flow in a drifting frame;

. flow steady in a frame tied to the core;

. flow fit on secular variation of the magnetic field;

. solid rotation of the core with respect to the mantle;

. very stiff torsional oscillation;

. eastward drift provides a better fit than westward;

. consistent with eastward differential rotation of the inner core.



Time evolution of the fluid flow at the top of the core (Le Huy et al., 2000)

1.Outstanding features of the main field and its secular variation
A remarkable standing feature of the field at the CMB consists of two pairs of intense flux patches, one located under Artic Canada and South-East of Tierra del Fuego and the other under Siberia and South-East of Australia. They have remained largely the same for 300 years (Bloxham and Gubbins, 1985).

Another outstanding feature of the secular variation over the last three centuries is the regular westward drift, at a rate of about 0.28 per year of the vertical component of the field centered on the equator since 1700. This does not mean a global westward drift of the secular variation field.

2.Computation of the flow at the CMB
The Bloxham and Jackson model (1992) presents the most homogeneous historical description of the magnetic field. The spatial dependence of the field is represented by a spherical harmonic expansion and the time dependence by a cubic B-spline basis.

The computation of the large-scale flow uses the frozen-flux and tangentially geostrophic hypothesis. The velocity field at the top of the core can be represented as the sum of a poloidal and a toroidal term. These terms themselves can be expanded in surface harmonics.

The general organization of the flow tends to conserve some gross features over the whole considered time-span. The geometry of - the degree 1 component of the poloidal scalar - the degree 2 component of the toroidal scalar has remained remarkably constant over the last 300 years; and the flow has a large ingredient symmetrical with respect to the equator. Nevertheless, the antisymmetric component is not negligible (the energy associated with this component represents about 30gt% of the energy of the total average flow).

3.The geomagnetic jerks and the behaviour of the flow during the last few decades
The geomagnetic jerks are sudden changes in the trend of the secular variation or "secular variation impulses". Former analyses established the global character and the internal origin of the jerks.

The components of the flow and of the acceleration jump for the same degrees have similar morphologies. However, there is a distinct shift in longitude (about 40-50), between the flow and the acceleration jump, for a given degree.

4.Time variable toroidal part of the field
A couple of components of the toroidal part of the magnetic field is sufficent to describe the time variation of the magnetic field (except the drift).