Coherent Vortex Structures and 3D Enstrophy Cascade

Existence of 2D enstrophy cascade in a suitable mathematical setting, and under suitable conditions compatible with 2D turbulence phenomenology, is known both in the Fourier and in the physical scales. The goal of this paper is to show that the same geometric condition preventing the formation of singularities – ${frac{1}{2}}$ -Hölder coherence of the vorticity direction – coupled with a suitable condition on a modified Kraichnan scale, and under a certain modulation assumption on evolution of the vorticity, leads to existence of 3D enstrophy cascade in physical scales of the flow.