O. Batiste and E. Knobloch
Oscillatory binary fluid convection in finite containers
In: Perspectives and Problems in Nonlinear Science.
(E. Kaplan, J. Marsden and K. Sreenivasan, eds.)
Springer-Verlag, Berlin., 2003, 91-144.
Linear and weakly nonlinear theory of overstable convection in large
but bounded containers is reviewed and the results compared with detailed
numerical simulations of binary fluid convection in a two-dimensional
domain with realistic boundary conditions. For sufficiently negative
separation ratios convection sets in as growing oscillations; the
corresponding eigenfunctions take the form of `chevrons' of either odd or
even parity. These may bifurcate sub- or supercritically. Simulations of
^3He^4He and water-ethanol mixtures show that the oscillations may equilibrate in finite amplitude chevron states, or that these states are unstable to
blinking or repeated transient states. The results compare favorably with