A model to determine open or closed cellular convection

The horizontal asymmetry of cellular convection is demonstrated to be detectable by consideration of the vertical asymmetry of the driving force. A two-dimensional numerical model for convection in an internally heated and cooled fluid is presented, based on equations for the conservation of temperature and vorticity. Attention is focused on the steady-state finite-amplitude solutions for fixed Rayleigh number, Prandtl number, and aspect ratio. Temperature in the model corresponds to potential temperature under dry conditions and the equivalent potential temperature under saturated conditions. Slowly varying convection driven by asymmetric boundary fluxes is expressed in terms of steady-state convection driven by an asymmetric internal heat source. It is shown that heating near the ground produces open convection patterns where most of the fluid is descending, while cooling near the top of the flow leads to closed cellular patterns with a preponderance of ascending fluid. Extension of the model to three dimensions is indicated.