Self-organization in Navier-Stokes turbulence

Fluid turbulence is undoubtedly a complex phenomenon, but the relation between the fundamental laws and the emergence of large-scale coherent eddies from differential interactions in a random background has remained elusive. Such a connection is attempted in this paper. The key analytical step is to express the Navier-Stokes equations in the Hermitian wavelet representation, which adds one independent spectral variable to the spatial description at any instant. In this expanded representation, the equations reduce naturally to a form consistent with pairwise nonlinear interactions governed by known kernels. The emergence of strong eddies from a random background, and their eventual breakdown, are illustrated by a 2-dimensional simulation.