An asymptotic solution of a kinematic -dynamo with meridional circulation

Abstract Asymptotic methods are used to study a one-dimensional kinematic -Parker dynamo wave model in the limit when the strength of the -sources, as measured by the dynamo number , is large. The model includes the influence of meridional circulation with a characteristic poleward velocity (strictly a magnetic Reynolds number) , and builds on the earlier work of Popova and Sokoloff (Meridional circulation and dynamo waves. Astron. Nachr. 2008, 329, 766–768). On increasing , the equatorward phase velocity of the Parker dynamo wave is decreased and, when a particular value of (say ) is reached, non-oscillatory solutions ensue. Though a complete analytic solution is not possible for , the nature of the transition from travelling waves to non-oscillatory solution, as the value of varies across , is readily understood within the asymptotic framework. It is remarkable that such a simple one-dimensional model can illustrate the possibility of either travelling waves or non-oscillatory solutions dependent on the...