Multi-mode study of time-dependent thermal convection with hexagonal planforms

Time-dependent nonlinear thermal convection problems in astrophysics are investigated analytically, applying a truncated-modal-expansion technique to obtain numerical solutions for three-dimensional cellular motions and account for density variations, rotation, and magnetic fields. The hexagonal-planform approach of Lopez and Murphy (1983) is extended to the multimodal case, and some numerical results are presented graphically. It is found that a single-mode system is sufficient at high Prandtl numbers, but that the low-Prandtl-number flows typical of stellar regions are characterized by the generation of vertical vorticity and nonlinear interactions between the modes and between the velocity and vorticity.