This is quite silly, but the relationship between the discrete Fourier transform (DFT) and the Fourier series (FS) is clouded by annoying factors. I will try to connect both in this article. The motivation is to employ DFT techniques in a computer simulation. In the latter, one usually has a finite simulation box, which makes Fourier series the most interesting (a connection to the Fourier transform may also be made, see below).
For the time being, this is just a stub to upload stuff for a discussion in CFD-online!
The Rayleigh-Taylor instability is a well-known benchmarck for CFD codes. The idea is to start with two phases, on on top of the other, the lighter one being underneath. The interface is slightly perturbed, and this plume appears. I describe a quick and dirty way of getting this instability.
Do you hate capital letters? I do, since FORTRAN. Fortunately, people are learning they should not be used. Specially editors. Nevertheless, here comes office 2013 with brand new capitalized ribbons. Straight capital letters, I mean, not small caps.
Anyway, I found somewhere a trick to make sure menus stay in lower case: append a space before, or after, the ribbon name (right-click on any ribbon to change their names). This name, by the way, is correctly typed (!).