Computes the linear stability in the Rayleigh-Bénard problem.
The curve of critical Rayleigh number as function of wavenumber is computed and plotted and the minimum value of the Rayleigh number is obtained along with the corresponding value of the wavenumber. The first unstable mode can also be plotted, both as profiles of the z dependence and as temperature-velocity maps.
The present code uses the Chebyshev differentiation matrices. It was developed as part of a project which led to several publications in which the details of the method can be found:
- Labrosse S, Morison A, Deguen R, and Alboussière T. Rayleigh-Bénard convection in a creeping solid with a phase change at either or both horizontal boundaries. J. Fluid Mech., 2018. DOI.
- Morison A, Labrosse S, Deguen R, and Alboussière T. Timescale of overturn in a magma ocean cumulate. Earth Planet. Sci. Lett., 2019. DOI.
- Morison A, Labrosse S, Deguen R, and Alboussière T. Onset of thermal convection in a solid spherical shell with melting at either or both boundaries. Geophys. J. Int., 2024. DOI.