A Shallow-Water Theory for the Sun's Active Longitudes

We show that the global MHD shallow-water instability of differential rotation and toroidal field bands in the solar tachocline provides a possible mechanism for the formation and evolution of active longitudes seen in synoptic maps of photospheric magnetic fields. The mechanism involves the production of upward bulges at selected longitudes in the overshoot tachocline that contain significant toroidal fields.