The atmospheric Rayleigh-Bénard problem on the f -plane

When applied to a system of sizeable vertical extent that can undergo adiabatic expansion/compression, the Rayleigh-Bénard treatment of convection between two parallel plates, kept at constant temperature, needs to be amended with the consideration of potential temperature as the conserved thermodynamic variable. The fixed-temperature boundary conditions are therefore expressed as a combination of potential temperature and pressure, and this causes the solutions to be a mixture of the odd and even modes of the classical problem. Here, solutions are presented for a rotating system, which supports both stationary and oscillatory modes. While the stationary modes are all stabilized by this mechanism, as was shown previously for a nonrotating system, the oscillatory modes can have a lower critical Rayleigh number than their traditional counterpart, when the Prandtl number is approximately between 0.2 and 1.0.