Numerical Discovery of a New Mode Pitchfork Bifurcation for Natural Convection of Water Enclosed in Two Dimensional Rectangular Cavities

A second order Euler-Taylor-Galerkin finite element method of fractional steps was used in the numerical study of the evolution process of pitchfork bifurcations of water enclosed in rectangular cavities. A new phenomenon of vortex merging was found in layer flow while the length-to-width ratio is higher than some certain value. The vortex merging phenomenon is defined a new mode for pitchfork bifurcation. Such mode of pitchfork bifurcation can be found in both regimes of conductive and transition. Moreover, aided by the variation of flow topologies and velocity profiles of velocity v vs. x at y=0.5 for each cavity, corresponding critical Rayleigh numbers were numerical predicted by using the bisection method.