Stability of tangential discontinuity for the vortex pancakes

TL;DR

This paper investigates the internal structure of high vorticity regions in 3D Euler flows, revealing a layered vortex structure that stabilizes against Kelvin-Helmholtz instability during turbulence onset.

Contribution

It uncovers the layered vortex structure within pancake-like vorticity regions, explaining their stability and self-similar evolution in turbulence development.

Findings

High vorticity regions have a three-layer vortex structure.

Layered structure prevents Kelvin-Helmholtz instability.

Self-similar evolution follows a power law.

Abstract

Within the incompressible three-dimensional Euler equations, we study the pancake-like high vorticity regions, which arise during the onset of developed hydrodynamic turbulence. We show that these regions have an internal fine structure consisting of three vortex layers. Such a layered structure, together with the power law of self-similar evolution of the pancake, prevents development of the Kelvin-Helmholtz instability.