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
available experiments.