Dynamical patterns in Bénard-Marangoni convection in a square container

Both stationary and oscillatory patterns are noted to emerge, through a sequence of bifurcations in the observed control parameters, during Benard-Marangoni convection in a square, small aspect ratio vessel. The stationary patterns break the symmetry, and the oscillatory ones are classifiable as three different types. These phenomena can be characterized within a framework that approximates the Takens-Bogdanov bifurcation. (AIAA)