Coherent vortex structures and 3D enstrophy cascade

Details Coherent vortex structures and 3D enstrophy cascade Coherent vortex structures and 3D enstrophy cascade

2011-06-30

arxiv.org/abs/1107.0058v3

Mathematics

Analysis of PDEs

15 pp; added a couple of new paragraphs and in particular, a sample computation illustrating the response of the ensemble aver

Scientific paper

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 - 1/2-H\"older 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.

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