Two-dimensional nonlinear convection in a vertical rotating cylindrical annulus with flat adiabatic stress-free lids, heated from the inside and with radial gravity, is numerically analyzed for a low value of the Prandtl number, s = 0.025. When the Rayleigh number exceeds a critical value, the conduction state becomes unstable and steady columns parallel
to the axis of rotation, and characterized by a finite integer azimuthal wavenumber, n, are the preferred form of convection at the onset for l...
Two-dimensional nonlinear convection in a vertical rotating cylindrical annulus with flat adiabatic stress-free lids, heated from the inside and with radial gravity, is numerically analyzed for a low value of the Prandtl number, s = 0.025. When the Rayleigh number exceeds a critical value, the conduction state becomes unstable and steady columns parallel
to the axis of rotation, and characterized by a finite integer azimuthal wavenumber, n, are the preferred form of convection at the onset for large rotation rates. Despite the presence of rotation, equations retain the O(2) symmetry for z-independent columnar solutions. Both by using continuation techniques and by a time-integration of the evolution equations, primary nonlinear solutions are obtained for a moderate value of the radius ratio, and are found to give way to periodic solutions in the form of direction reversing traveling waves. The new solution keeps the same wavenumber and breaks the reflection symmetry of the columns.
As a consequence, an oscillatory mean flux appears that decreases the efficiency of the heat transport in the radial direction. By further increasing the Rayleigh number, a transition from the oscillatory to a chaotic flow takes place. This chaotic state is reached via a pitchfork
bifurcation that breaks the rotation symmetry R2p/3 of the orbit, followed by a subcritical Neimark-Sacker bifurcation that gives rise to a quasi-periodic solution. Finally, the invariant torus breaks up and a chaotic regime appears.