A new method for fast transforms in parity-mixed PDEs: Part II. Application to confined rotating convection

To demonstrate the utility of the parity filtering methods described by Vasil et al. [G. Vasil, N. Brummell, K. Julien, A new method for fast transforms in parity-mixed PDEs: Part I. Numerical techniques and analysis, J. Comput. Phys. (2008)], we introduce a numerical code designed to solve for Rayleigh–Bénard convection in a confined rotating box using the new methods we have formulated. That is, using a straightforward pseudospectral framework, we incorporate techniques for efficiently computing parity-mixed Coriolis accelerations in a time-dependent numerical solver. The goals of the presented numerical code are to provide a tool to investigate aspects of confined rotating convection experiments with a simple model, and to illustrate the application of parity filtering. In our numerical tests, we find that a correct accounting for parity leads to clear and interesting behavior that has been observed in laboratory experiments but that has not been observed in previous numerical simulations in periodic domains.