Turbulent solution of the Navier–Stokes equations

Abstract

To study the nonlinear physics of incompressible turbulent flow, the unaveraged Navier–Stokes equations are solved numerically. Initial three-dimensional cosine velocity fluctuations and periodic boundary conditions are used. No mean gradients are present. The three components of the mean-square velocity fluctuations are equal for the initial conditions chosen. The resulting solution shows characteristics of turbulence, such as the nonlinear excitation of small-scale fluctuations. For the higher Reynolds numbers the initially nonrandom flow develops into an apparently random turbulence. Thus, randomness or turbulence can apparently arise as a consequence of the structure of the Navier–Stokes equations.