Group foliations of the <i>β</i>-plane barotropic vorticity equation

Despite the large number of publications on symmetry analysis of the barotropic vorticity equation on the β-plane, its group foliations have not been considered previously. The present publication aims to address this shortcoming. Group foliations are constructed for the equation, and based on them, invariant solutions are derived, some of which generalize previously known exact analytical solutions. There is also a discussion of the pros and cons of the group foliation approach including consideration of some numerical issues.