We present shell dynamo models for the solar convection zone with positive
alpha -effect in the northern hemisphere and a meridional circulation which
is directed equatorward at the bottom and poleward at the top of the conve
ction zone. Two different rotation patterns are used: a simple variation of
the rotation rate with depth and the rotation law as derived by helioseism
ology. Depending on the Reynolds number associated with the meridional ow,
the dynamo shows a whole "zoo" of solutions. For sufficiently small values
of the eddy magnetic diffusivity (10(11) cm(2)/s), field advection by the m
eridional ow becomes dominant and even changes the character of the butterf
ly diagram. Flow amplitudes of a few m/s are then sufficient to turn the or
iginally "wrong" butterfly diagram into a "solar-type" butterfly diagram, i
.e. with activity belts drifting equatorward. This effect can easily be dem
onstrated with a super-rotation law (partial derivative Omega/partial deriv
ativer > 0) with Omega independent of the latitude. The situation is much m
ore complicated for the "real" rotation law with the observed strong negati
ve shear at high latitudes. With zero meridional ow, oscillating solutions
are found without any latitudinal migration of the toroidal field belts, ne
ither poleward nor equatorward. Small but finite ow amplitudes cause the ma
gnetic field belts to drift poleward while in case of fast ow they move equ
atorward.