There are another cases witch can illustrate the hydrodynamical instabilities, but the precedent ones are the most commonely found in physical literature. These cases can be tsudied either under dynamical system stability theory or by direct simulation using some computational code like Fluent, Phoenics,...
A good thing is to compare results comming from different ways of studies. Many mathematical moderne tools are continiousely developped so as to solve the hard problem of determining the exact behaviour of such instabilities. But it's a complicate problem, and only cases with simple geometry and a number of assumptions are completely solved.