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.