Here is the MIT version:
On the MIT site I learned about siphoning into a cesspool or sewer, yet I still wondered about the vortex. Fortunately, speedball1 at askmehelpdek.com gives an answer: (http://www.askmehelpdesk.com/plumbing/toilet-swirl-but-no-vortex-265131.html). It's all about a small hole at the bottom of the bowl. However, that was not enough.
Here is a patent that gives some more information (I was still wondering about the vortex):