Abstract
Thermal convection in a two-dimensional rectangular cavity heated from below appears as a result of the pitchfork bifurcation of the motionless state when the cavity is placed horizontally. The structural stability of the pitchfork bifurcation to the tilt of the cavity is investigated by the weakly nonlinear stability theory. The four sides of the cavity are assumed to be rigid and perfectly thermal conducting. It is shown that the pitchfork bifurcation is structurally unstable to the tilt of the cavity if the bifurcated flow is anti-symmetric, and is structurally stable if it is symmetric in the horizontal direction. The results obtained from the weakly nonlinear stability theory are compared with the numerical results calculated directly from the basic equations by the Newton-Raphson method.
