2.3 Kinematic models

A first drastic simplification of the MHD system of equations consists in dropping Equation (2View Equation) altogether by specifying a priori the form of the flow field u. This kinematic regime remained until relatively recently the workhorse of solar dynamo modelling. Note that with u given, the MHD induction equation becomes truly linear in B. Moreover, helioseismology (Christensen-Dalsgaard, 2002) has now pinned down with good accuracy two important solar large-scale flow components, namely differential rotation throughout the interior, and meridional circulation in the outer half of the solar convection zone (for reviews, see Gizon, 2004Jump To The Next Citation Point; Howe, 2009Jump To The Next Citation Point). Given the low amplitude of observed torsional oscillations in the solar convective envelope, and the lack of significant cycle-related changes in the internal solar differential rotation inferred by helioseismology to this date, the kinematic approximation is perhaps not as bad a working assumption as one may have thought, at least for the differential rotation part of the mean flow u.
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