Weakened vortex stretching effect in three scale hierarchy for the 3D Euler equations

TL;DR

This paper investigates a three-scale hierarchy in 3D Euler equations, demonstrating that large-scale vortex stretching weakens the stretching effect at smaller scales, affecting the stress tensor and vortex dynamics.

Contribution

It introduces a novel three-scale hierarchical framework and shows how large-scale flows weaken the vortex stretching at smaller scales in the 3D Euler equations.

Findings

Large-scale vortex stretching weakens middle-scale stretching.

The stress tensor associated with vortices is reduced due to large-scale effects.

The vortex dynamics are significantly influenced by multi-scale interactions.

Abstract

We consider the 3D incompressible Euler equations under the following three scale hierarchical situation: large-scale vortex stretching the middle-scale, and at the same time, the middle-scale stretching the small-scale. In this situation, we show that, the stretching effect of this middle-scale flow is weakened by the large-scale. In other words, the vortices being stretched could have the corresponding stress tensor being weakened.