Onset of stationary and oscillatory convection in a tilted porous cavity saturated with a binary fluid: Linear stability analysis

In the present work, we study the onset of double-diffusive convective regi mes in a tilted rectangular cavity, filled with a porous medium, saturated by a binary fluid. Two opposite walls are maintained at different but unifo rm temperatures and concentrations while the two other walls are impermeabl e and adiabatic. When the thermal and solutal buoyancy forces are comparabl e in intensity but have opposite signs, the motionless double-diffusive reg ime with linear temperature and concentration profiles is a solution of the problem. The first parr of the study consists of a linear stability analys is of the motionless regime. We determine the critical thermal Rayleigh num ber for the onset of stationary and oscillatory convection, Indeed, we poin t out that there exist primary Hopf bifurcations for the studied problem in porous medium, while in the same configuration with a fluid medium only pr imary stationary bifurcations exist. When the first primary bifurcation cre ates a steady state branch of solutions, the bifurcation is either transcri tical or pitchfork depending on the aspect ratio, A and the tilt, phi of th e cavity. The onset of oscillatory convection (Hopf bifurcation) depends no t only on A and phi but also on the Lewis number, Le and the normalized por osity, epsilon. Then, we determine the parts of the (Le, epsilon) parameter space for which the first primary bifurcation is stationary or oscillatory . In particular, it is found that in the case Le greater than or equal to 1 and for epsilon Le(2)<1 the first primary bifurcation is always a Hopf bif urcation for any A and phi except for phi = 90 degrees. For epsilon Le(2) > 1 only stationary primary bifurcations exist. In the case Le<1, zones where stationary and oscillatory primary bifurcations exist are separated by a c urve depending on A and phi. The last part of this work consists of a serie s of numerical simulations. The onset of stationary and oscillatory convect ion is obtained numerically at the critical Rayleigh number predicted by li near analysis. We also verified the frequency of oscillations for several s ets of dimensionless parameters. The numerical simulations show multiple su bcritical solutions. (C) 1999 American Institute of Physics. [S170-6631(99) 00306-2].