The Bénard problem: a sixth-order equation

The Bénard problem: a sixth-order equation. Chandrasekhar (1961) has shown that the above (Bénard) problem can be solved in terms of the vorticity, which reduces the problem to a sixth-order eigenvalue problem for the perturbation in temperature. Your task is to work through the algebra and set up this sixth-order problem. Then you can try to extend the code given in the text using the spectral method and finding the critical wavenumber at which the stability sets in. The lowest value of the Rayleigh number was 1707.762, and the corresponding wavenumber was 3.117. Verify these results.