Two-dimensional model for an αΩ-dynamo with meridional circulation and an associated Hamilton–Jacobi equation

A two-dimensional model for an αΩ-dynamo is constructed, taking into account meridional flows. A Hamilton–Jacobi equation for the resulting system of magnetic-field generation equatons is constructed using an asymptotic method analogous to the WKB method. This equation makes it possible to analytically study the influence of meridional flows on the duration of the solar magnetic-activity cycle and the evolution of magnetic waves.