Amplitude equations for isothermal double diffusive convection

Amplitude equations are derived for isothermal double diffusive convection near threshold for both the stationary and oscillatory instabilities as well as in the vicinity of the codimension-2 point. The convecting fluid is contained in a thin Hele-Shaw cell that renders the system two dimensional, and convection is sustained by vertical concentration gradients of two species with different diffusion rates. The locations of the tricritical point for the stationary instability and the codimension-2 point are found. It is shown that these points can be made well separated (in the Rayleigh number ${\mathrm{R}}_{\mathrm{s}}$ of the slow diffusing species) as the Lewis number varies. Hence the behavior near these points should be experimentally accessible.