Study of cellular flow structure and pitchfork bifurcation in a laterally-heated cube

This paper is the continuation of our study of flow development from a motionless conductive state in a thermally driven cavity. A series of complex nonlinear bifurcations was addressed in a three-dimensional partially heated rectangular cavity. Prior to chaos, the dynamic phenomena in the investigated nonlinear system include pitchfork bifurcation, Hopf bifurcation, periodic ultraharmonics, and quasi-periodic bifurcation. In this study the formation of different cellular flow structures and the scenario of pitchfork bifurcation are addressed. The solutions for the incompressible fluid flow investigated at different Rayleigh numbers are computed from the divergence-free compensated solution algorithm and the wavenumber-optimized upwinding scheme for accurately approximating the convection terms. The three-dimensional cellular flow details and the physically meaningful vortical flow insight are extracted to improve our understanding of the change of three-dimensional vortical and cellular flow features with respect to the Rayleigh number in the thermal driven cavity.