### 4.1 Model ingredients

All 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). Meridional circulation in the convective envelope, long considered unimportant from the
dynamo point of view, has gained popularity in recent years, initially in the Babcock-Leighton context but
now also in other classes of models.
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 (17) 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 (19), 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
minimalistic 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 on 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.
Ultimately, the magnetic diffusivities and differential rotation in the convective envelope owe their
existence to the turbulence therein, more specifically to the associated Reynolds stresses. While it has been
customary in solar dynamo modelling to simply assume plausible functional forms for these quantities (such
as Equations (17, 18, 19) above), one recent trend has been to calculate these quantities in an internally
consistent manner using an actual model for the turbulence itself (see, e.g., Kitchatinov and
Rüdiger, 1993). While this approach introduces additional - and often important - uncertainties at the
level of the turbulence model, it represents in principle a tractable avenue out of the kinematic
regime.