Generation of Small-Scale Structures in Well-Developed Turbulence

The incompressible Navier-Stokes equations are considered in the limit of infinite Reynolds number. Flow instability is supposed to give rise to steady large-scale structures. The onset and development of small-scale turbulence is analyzed. It is shown that the developing small-scale fluctuations are characterized by intermittency. The highest intensity of vorticity fluctuations is attained in vortex filaments. The solution obtained is used to calculate the velocity pair correlation function in the limit of r → 0. The result agrees with the Kolmogorov law K(r) ∝ r 2/3.