Turbulence and Singularity of the Velocity Field

Abstract

The small-scale properties of turbulence are related to the singularity of the velocity field in the inviscid limit. The energy spectrum in the inertial range is expressed in terms of the fractal dimension and Holder's exponent of the singularity. It is pointed out that the entrainment process is important in the dynamics of active eddies in the β-model theory of turbulence.