The effect of a meridional flow on Parker's interface dynamo

Parker's interface dynamo is generalized to the case when a homogeneous flow is present in the high-diffusivity (upper) layer in the lateral direction (i.e. perpendicular to the shear flow in the lower layer). This is probably a realistic first representation of the situation near the bottom of the solar convective zone, as the strongly subadiabatic stratification of the tachocline (lower layer in the interface dynamo) imposes a strong upper limit on the speed of any meridional flow there. Analytic solutions to the eigenvalue problem are presented for the cases of vanishing diffusivity contrast and infinite diffusivity contrast. Unlike the trivial case of a homogeneous system, the ability of the meridional flow to reverse the propagation of the dynamo wave is strongly reduced in the interface dynamo. In particular, in the limit of high diffusivity contrast relevant to the solar case it is found that a meridional flow of realistic amplitude cannot reverse the direction of propagation of the dynamo wave. The implications of this result for the solar dynamo problem are discussed.