Not every solution of equations of motion can actually occur in Nature, even if it is exact. Those which do actually occur not only must obey the equations of fluid dynamics, but must be also stable (Landau and Lifshitz [LL87, Sec. 26]).

In order that a specific steady state S can be observed in nature, the state must be stable. In other words, when some external perturbation happens to disturb a physical system, its original state must be recovered, i.e. the perturbation superposed on the basic state S must decay with time. In nature there always exists a source of disturbance. One of the basic observations in physics is as follows: if a certain macroscopic physical state repeatedly occurs in nature, then it is highly possible that the state is characterized by a certain type of stability.

If a small perturbation grows with time (exponentially in most cases), then the original state S is said to be unstable. In such a case, the state would have little chance to be observed in nature. If the perturbation neither grows nor decays, but stays at the initial perturbed level, then it is said to be neutrally stable.

When the initial state is unstable and the amplitude of perturbation grows, then a nonlinear mechanism which was ineffective at small amplitudes makes its appearance in due course of time. This nonlinearity often suppresses further exponential growth of perturbation (though not always so) and the amplitude tends to a new finite...