Rayleigh-Benard Eigenvalue Problem

This lecture covers the solution of the Rayleigh-Benard eigenvalue problem, focusing on the finite difference schemes for first and second derivatives, as well as rigid boundary conditions. The lecture also discusses the spatial growth and nonlinear lubrication equations, emphasizing the temporal dispersion relation and the steady flow purely spatial dispersion relation. The presentation concludes with a detailed analysis of typical structures observed in Marangoni convection, including the transition to square patterns. MATLAB scripts and PowerPoint slides are used to illustrate the concepts.