Detour induced by the piston effect in the oscillatory double-diffusive convection of a near-critical fluid

Abstract

The nonlinear oscillatory double-diffusive convection in a thermodynamically near-critical binary fluid layer is investigated to explore the interactions between the piston effect and natural convection in the presence of subcritical bifurcation. The bifurcation diagram of the system is studied. Two subcritical bifurcation branches are depicted, which, together with the trivial branch of pure diffusion, are connected by two hysteresis loops. To understand the role of the piston effect, the Boussinesq counterpart of the near-critical system is considered and compared. Results show that the onset of convection is significantly altered by the piston effect. For the Boussinesq system, the lower boundary layer becomes unstable, brings on finite-amplitude perturbations, and leads to a statistically steady state. However, the near-critical system features a two-stage evolution. In the first stage, the lower boundary layer becomes unstable and then returns to stability. As soon as the temperature field relaxes into the second stage, a change of criterion occurs, and the fluid becomes unstable again. The residual convection motions amplify and finally result in finite-amplitude convection. By this means, the near-critical system becomes insensitive to the existence of the higher equilibrium state in hysteresis loops, and detours relative to the Boussinesq system are observed. This paper gives new insights into the piston effect and its interactions with natural convection from a dynamic system point of view. The conclusions can be extended to other situations where subcritical bifurcations exist.