CONVECTONS

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).