Analysis is used to show that a solution of the Navier–Stokes equations can be
computed in terms of wave-like series, which are referred to as waves below. The
mean flow is a wave of infinitely long wavelength and period; laminar flows contain
only one wave, i.e. the mean flow. With a supercritical instability, there are a mean
flow, a dominant wave and its harmonics. Under this scenario, the amplitude of the
waves is determined by linear and nonlinear terms. The linear case is the target
of flow-instability studies. The nonlinear case involves energy transfer among the
waves satisfying resonance conditions so that the wavenumbers are discrete, form a
denumerable set, and are homeomorphic to Cantor's set of rational numbers. Since
an infinite number of these sets can exist over a finite real interval, nonlinear
Navier–Stokes equations have multiple solutions and the initial conditions determine
which particular set will be excited. Consequently, the influence of initial conditions can
persist forever. This phenomenon has been observed for Couette–Taylor instability,
turbulent mixing layers, wakes, jets, pipe flows, etc. This is a commonly known
property of chaos.