Exact energy stability of Bénard-Marangoni convection at infinite Prandtl number
arXiv:1702.02752 · doi:10.1017/jfm.2017.323
Abstract
Using the energy method we investigate the stability of pure conduction in Pearson's model for Bénard-Marangoni convection in a layer of fluid at infinite Prandtl number. Upon extending the space of admissible perturbations to the conductive state, we find an exact solution to the energy stability variational problem for a range of thermal boundary conditions describing perfectly conducting, imperfectly conducting, and insulating boundaries. Our analysis extends and improves previous results, and shows that with the energy method global stability can be proven up to the linear instability threshold only when the top and bottom boundaries of the fluid layer are insulating. Contrary to the well-known Rayleigh-Bénard convection setup, therefore, energy stability theory does not exclude the possibility of subcritical instabilities against finite-amplitude perturbations.
11 pages, 2 figures. Preprint submitted to the Journal of Fluid Mechanics. Version 2: minor text and notational changes, added a new appendix A, added detail to Section 3