Physical Review E
Oscillatory doubly diffusive convection in a large aspect ratio Hele-Shaw cell is considered. The partial differential equations are reduced via center-unstable manifold reduction to the normal form equations describing the interaction of even and odd parity standing waves near onset. These equations take the form of the equations for a Hopf bifurcation with approximate D4 symmetry, verifying the conclusions of the preceding paper [A.S. Landsberg and E. Knobloch, Phys. Rev. E53, 3579 (1996)]. In particular, the amplitude equations differ in the limit of large aspect ratios from the usual Ginzburg-Landau description in having additional nonlinear terms with O(1) coefficients. Numerical simulations of the amplitude equations for experimental parameter values are presented and compared with the results of recent experiments by Predtechensky et al. [Phys. Rev. Lett. 72, 218 (1994); Phys. Fluids 6, 3923 (1994)].
A.S. Landsberg and E. Knobloch. (1996). Oscillatory Doubly Diffusive Convection in a Finite Container. Physical Review E 53: 3601.