### 4.1 Model ingredients

All kinematic solar dynamo models have some basic “ingredients” in common, most importantly (i) a
solar structural model, (ii) a differential rotation profile, and (iii) a magnetic diffusivity profile (possibly
depth-dependent).
Helioseismology has pinned down with great accuracy the internal solar structure, including the internal
differential rotation, and the exact location of the core-envelope interface. Unless noted otherwise, all
illustrative models discussed in this section were computed using the following analytic formulae for the
angular velocity and magnetic diffusivity :

with
and
With appropriately chosen parameter values, Equation (15) describes a solar-like differential rotation
profile, namely a purely latitudinal differential rotation in the convective envelope, with equatorial
acceleration and smoothly matching a core rotating rigidly at the angular speed of the surface
mid-latitudes.
This rotational transition takes place across a spherical shear layer of half-thickness coinciding with the
core-envelope interface at (see Figure 5, with parameter values listed in caption). As per
Equation (17), a similar transition takes place with the net diffusivity, falling from some large, “turbulent”
value in the envelope to a much smaller diffusivity in the convection-free radiative core, the
diffusivity contrast being given by . Given helioseismic constraints, these represent minimal
yet reasonably realistic choices.
It should be noted already that such a solar-like differential rotation profile is quite complex from the
point of view of dynamo modelling, in that it is characterized by three partially overlapping shear regions: a
strong positive radial shear in the equatorial regions of the tachocline, an even stronger negative radial
shear in its the polar regions, and a significant latitudinal shear throughout the convective envelope and
extending partway into the tachocline. As shown in panel B of Figure 5, for a tachocline of half-thickness
, the mid-latitude latitudinal shear at is comparable in magnitude to the
equatorial radial shear; its potential contribution to dynamo action should not be casually
dismissed.