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; due to pertubations caused 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.

The surface wave formed in a Rayleigh-Taylor instability is caused mainly by surface tension. Like i mentioned before, a liquid tends to minimize its surface area and $n$ droplets of volume $V/n$ have more surface area than a liquid column of volume $V$. Initially, the film is uniform and surface tension will minimize the area by starting to form waves. The surface tension is related to the capillary pressure.

Old (slightly irrelevant) answer: When i wrote this answer i was considering a different type of pertubation than the ones you meant

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; due to pertubations caused 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. Rectification: Even in a perfectly symmetric system the pertubation will occur because of surface tensile forces albeit much more slowly than in the case the system is perturbed by some external factor.

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.

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; due to pertubations caused 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.