Coherent vortex structures and 3D enstrophy cascade

TL;DR

This paper demonstrates that certain geometric and scale conditions can lead to the existence of a 3D enstrophy cascade, extending concepts from 2D turbulence to three-dimensional flows.

Contribution

It introduces a novel set of conditions, including vorticity coherence and a modified Kraichnan scale, that ensure 3D enstrophy cascade in physical scales.

Findings

Establishes a link between vorticity coherence and enstrophy cascade

Shows conditions under which 3D enstrophy cascade exists

Extends 2D turbulence concepts to 3D flows

Abstract

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.