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

Abstract

We consider the three-dimensional 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.