Large wavenumber convection in the rotating annulus

The annulus model considers convection between concentric cylinders with sl oping endwalls. It is used as a simplified model of convection in a rapidly rotating sphere. Large azimuthal wavenumbers are preferred in this problem , and this has been exploited to develop an asymptotic approach to nonlinea r convection in the annulus. The problem is further reduced because the Tay lor-Proudman constraint simplifies the dependence in the direction of the r otation vector, so that a nonlinear system dependent only on the radial var iable and time results. As Rayleigh number is increased a sequence of bifur cations is found, from steady solutions to periodic solutions and 2-tori, t ypically ending in chaotic behaviour. Both the magnetic (MHD convection) an d non-magnetic problem has been considered, and in the non-magnetic case ou r bifurcation sequence can be compared with those found by previous two-dim ensional numerical simulations.