The Kolmogorov turbulence theory in the light of six-dimensional Navier-Stokes' equation

Abstract

The classical turbulence theory by Kolmogorov is reconsidered using Navier-Stokes' equation generalized to 6D physical-plus-eddy space. Strong pseudo-singularity is shown to reveal itself along the boundary `ridge' line separating the dissipation and inertial sub-ranges surrounding the origin of the eddy space. A speculation is made that this singularity is generated by two dipoles of opposite sign aligned on the common axis. It is supported by the observation that the universal power spectrum calculated rediscovers the Kolmogorov's -5/3 power law as independent of the dimensional approach.