Steady bimodal convection in a cylinder at large Prandtl numbers Available to Purchase

Steady bimodal convection of an infinite Prandtl‐number Boussinesq fluid in a cylinder is considered. An asymptotic analysis similar to the one used by Buell and Catton [Phys. Fluids 29, 23 (1986)] for axisymmetric convection yields a solvability condition that determines the radial wavenumber. The analysis is valid for convection far away from the origin, the lateral boundary, and any pattern dislocations. The azimuthal wavenumber is treated as a parameter, although in real systems it is dependent on the initial and boundary conditions. Results are presented for Rayleigh numbers between 14 000 and 60 000, and for azimuthal wavenumbers between 5 and 7. It is shown that for increasing Rayleigh numbers, the selected radial wavenumber and the heat transfer tend to become independent of the azimuthal wavenumber. No quantitative experimental data are available, but one qualitative comparison is good.