Spatial localization in rotating convection and magnetoconvection

Stationary spatially localized states are present in both rotating convection and magnetoconvection. In two-dimensional convection with stress-free boundary conditions, the formation of such states is due to the interaction between convection and a large scale mode: zonal velocity in rotating convection and magnetic potential in magnetoconvection. We develop a higher order theory, a nonlocal fifth order Ginzburg-Landau equation, to describe the effects of spatial modulation near a codimension-two point. Two different bifurcation scenarios are identified. Our results shed light on numerical studies of two-dimensional convective systems with stress-free boundary conditions. This paper is dedicated to Professor Helmut Brand on the occasion of his 60th birthday.