Spatial localization in rotating convection and magnetoconvection
Department of Physics, University of California, Berkeley, CA 94720, USA
a e-mail: firstname.lastname@example.org
Received: 11 September 2013
Revised: 25 November 2013
Published online: 23 January 2014
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.
© EDP Sciences, Springer-Verlag, 2014