Recent simulations [1,2] of binary fluid convection with a negative separation ratio reveal the presence of multiple numerically stable spatially localized steady states we have called 'convectons'. These states consist of a finite number of convection rolls embedded in a nonconvecting background and are present at supercritical Rayleigh numbers. Below a critical Rayleigh number the convectons are replaced by relaxation oscillations in which the steady state is gradually eroded until no rolls are present (the slow phase), whereupon a new convecton regrows from small amplitude (the fast phase) and the process repeats. Both He3-He4 mixtures [1] and water-ethanol mixtures [2] exhibit this remarkable behavior. Stability requires that the convectons are present in the regime where the conduction state is convectively unstable but absolutely stable. The multiplicity of stable convectons can be attributed to the presence of a 'pinning' region in parameter space, or equivalently to a process called homoclinic snaking [3,4]. In the pinning region the fronts bounding the convecton are pinned to the underlying roll structure; outside it the fronts depin and allow the convecton to grow at the expense of the small amplitude state (large Rayleigh numbers) or shrink back to the small amplitude state (low Rayleigh numbers). The convectons may exist beyond the onset of absolute instability but the background state is then filled with small amplitude traveling waves. A theoretical understanding of these results will be developed. Related behavior is present in natural doubly diffusive convection [5] and in surface tension-driven convection.
[1] O. Batiste and E. Knobloch. Simulations of localized states of stationary convection in He3-He4 mixtures. Phys. Rev. Lett. 95, 244501 (2005). [2] O. Batiste, E. Knobloch, A. Alonso, I. Mercader. Spatially localized binary fluid convection. J. Fluid Mech. 560, 149 (2006). [3] J. Burke and E. Knobloch. Localized states in the generalized Swift-Hohenberg equation. Phys. Rev. E 73, 056211 (2006). [4] J. Burke and E. Knobloch. Homoclinic snaking: structure and stability. Chaos 17, 037102 (2007). [5] A. Bergeon and E. Knobloch. Spatially localized states in natural doubly diffusive convection. Phys. Fluids 20, 034102 (2008).