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.

  2. Geostrophic flow, tangentially geostrophic at CMB;

    3.

    . flow governed by pressure and Coriolis force;

    . flow along isobar curves;

    . symmetric and zonal scaloidal component zero;

    . flow following cylinders coaxial with rotation axis.

  3. Magnetostrophic flow: geostrophic + Lorentz force;

    4. . same as in point (2) but additionally torsional oscillations, stationary waves linking
    all the cylinders.

  4. Steady flow;

    5. . 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.

  5. 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).