Rayleigh-Benard Convection I found this nice paper about RB convection. However I am confused by what is going on page 6. In particular why we are suddenly using Helmholtz equation to find spatially periodic solutions. Aren't we working with convection, so why are we looking at it from a wave like point of view? Or maybe I'm just missing the point all together. 
Furthermore I would like to run a quick experiment to collect data. I was planning on using a heating place, a small glass tube filled with olive oil and a thermometer. Any tips? Suggestions? 
 A: Hope it's not a little too late for this answer!!!
Why are we looking at this from a "wave-point-of-view"
Rayleigh's experiments were on spermacetti (whale oil) in a cylindrical container with an aspect ratio of depth to radius $h_0/r\lt\lt 1$. This can be treated as a membrane with a certain stiffness. Hence, it is common to find a wave . The instabilities you see in RB/MB convection are called short wavelength instabilities and these wavelengths can be calculated using linear/non-linear stability analysis and can be faithfully captured with well controlled experiments.
Short note on (non)linear stability analysis
In case you aren't aware of what this is. It is simply perturbing a system with a wave with a disturbance of the form $A \sin (k x)$ and with some clever maxima/minima differential calculus and algebra, figuring out the most destructive wavelength that emerges.
($A$ is the amplitude of the wave and is generally $0.01 h_0$, $k$ is the 
wavenumber $k = 2 \pi x/L$ and $L$ is the domain size).
Some useful references/papers
Besides Killercam's reference to Drazin, if you are really interested in RB or MB (Marangoni Benard) convection, I would suggest that you read Rayleigh's 1916 paper and Thomson's 1855 paper in addition to Kundu's textbook , particularly chapter 12.
Running experiments with olive oil
As for running experiments with olive oil in a cylinder: be careful; the dimensions of the cylinder (aspect ratio) can change the structures from the hexagonal RB/MB cells to perhaps a Rayleigh-Taylor type instability.
Extra fun stuff
If you find that your interest is roused by RB/MB convection, eventually you look at long wave instabilities that affect liquid film.
References
Thomson, J. On certain curious motions observable at the surfaces of wine and other alcoholic liquors Phil. Mag. Ser., 1855, 10, 330-333
Rayleigh On convective currents in a horizontal layer of fluid when the higher temperature is on the under side. Philo. Mag. Series, 1916, 32, 529-546
