Secondary and oscillatory gravitational instabilities in canonical three-dimensional models of crystal growth from the melt, part1: Rayleigh-Bènard systems

Secondary and oscillatory instabilities in thermal gravitational convection have been the focus of intensive studies over recent years due to their relevance in materials science, and in particular in the field of crystal growth from the melt. The purpose of the present discussion is to provide a comparative and critical review of the subject through examination of existing studies and very recent contributions. It complements earlier reviews (Lappa [1,2]) that were limited to the survey of steady three-dimensional symmetry breaking effects and/or the primary bifurcation of the flow.