Symbolic computation and the Rayleigh-Bénard stability problem - Giestas, Margarida Canedo (2012)
This paper analyzes the linear stability of an horizontal layer of fluid consisting of a mixture of water and salt. The layer is hotter at the bottom and cooler at the top thus having a tendency to destabilize. To counteract this a salt concentration gradient (denser at the bottom and lighter at the top) is sometimes present, either naturally as in the ocean or created artificially as in solar ponds. The relevant governing equations are the linearized continuum mechanics balance laws applied to an incompressible, heat-conducting and salt-diffusing fluid, leading to a system of partial differential equations, from which the stability of a given base state has to be assessed with respect to arbitrary initial perturbations. This problem involves intensive symbolic computations that can be much facilitated by the use of a Computer Algebra System (CAS).