Pertubations are part of any real system caused by asymmetries in the system, or changes in air pressure, or someone walking by or a train speeding by, etc. etc.
A perfectly undisturbed symmetric system as you describe in your first picture is very difficult to obtain experimentally. Such a system is therefore a purely theoretical situation.
An example of the influence of pertubations is in determining the transition from the laminar to the turbulent regime in a channel flow. Generally, we say this occurs at $\mathrm{Re}\approx2000$ but notice the approximation sign as due to pertubations causes by external factors the transition may occur one day at $\mathrm{Re}\approx1900$ while another day at $\mathrm{Re}\approx2100$ for the same experiment.
Note that in the case of the Rayleigh-Taylor instability there is an assumed pertubation of the form: $$e=e_0+\delta\left(t\right)\cos\left(\kappa x\right)$$ This means that the theoretical treatment assumes the pertubations are already present, i.e. the pertubations do not grow spontaneously from a initially undisturbed uniform film.