Onset of double-diffusive convection in a near-critical fluid*

Near the liquid-vapor critical point, the physical properties of binary fluids exhibit large variations, whose effects on the onset of double-diffusive convection are studied. The physical model is an infinite horizontal layer of near-critical binary fluid bounded by two rigid walls, with Dirichlet boundary conditions for both temperature and concentration. A numerical linear stability analysis is conducted, showing that the vertical symmetry is broken, irregular penetrative instability occurs, and cat’s eye patterns are identified in the fingering and oscillatory regime, respectively. A new parameter Θ is defined which measures how the variations of physical properties influence flow fields. It is seen through numerical simulations that the Boussinesq approximation with constant physical properties has limited applicability, and that the Boussinesq equations with variable properties and density will describe all features seen. This conclusion is based on comparisons with simulations on the fully compressible, variable properties system.