Solar activity takes place in narrow bands of latitude that move like solitary waves from mid-latitudes toward the solar equator. This behaviour points to the existence of a thin layer in the Sun that may serve as a waveguide. With its grand minima, the cycle is intermittent in a way that does not occur in the simplest chaos models. To be useful as a primitive model of the cycle, a differential equation should be of high enough order to display such strong intermittency. These and other features of solar fluid dynamics led to the adumbration of an intermediate shear layer between the convection zone and the radiative core. This layer, like the weather layers in planetary atmospheres, produces coherent structures – sunspots and perhaps vortices. Similar layers may play a role in stellar activity in cool stars other than the Sun and perhaps even in hot stars if their atmospheres are turbulent.

The maculate Sun

Rotation and turbulence in stars are significant for an understanding of stellar evolution and for the fluid dynamics of accretion discs. We can watch these processes most closely in our own Solar System. Observations of the Sun, the giant planets and the earth reveal coherent structures whose study has been one of the most exciting adventures in the mathematical science of the twentieth century. (At a meeting in the Newton Institute, we ought to recall this.)