Abstract
Some of the rotating annulus experiments with radial differential heating show stepwise transitions of flow regimes from steady axi-symmetric flow to vacillation via a steady wave regime as the rotation rate increases. The stepwise regime transitions are investigated numerically with a semi-spectral model of a three-dimensional Boussinesq fluid, and the results are interpreted with bifurcation theories. The transition between axi-symmetric flow and a steady wave regime is characterized by hysteresis ; the criterion for the disappearance of an established steady wave differs from the criterion for the onset of the steady wave. The branch of the steady wave solution does not bifurcate from that of the axi-symmetric flow at the point where the axi-symmetric flow becomes unstable. Instead, the steady wave branch has another type of critical point (interpreted as a "limit point" ) at which it disappears. The transition from steady wave to tilted-trough vacillation is interpreted as a Hopf bifurcation ; a periodically fluctuating solution bifurcates from the steady wave branch when the steady wave solution loses its stability.
