Vortex stretching and anomalous dissipation for the incompressible 3D Navier-Stokes equations

TL;DR

This paper investigates how vortex stretching in a specific 3D incompressible flow configuration leads to anomalous energy dissipation, providing insights into turbulence phenomena.

Contribution

It demonstrates that vortex stretching in a 2.5D setting causes anomalous dissipation, advancing understanding of turbulence mechanisms in Navier-Stokes flows.

Findings

Vortex stretching induces anomalous dissipation.

Small-scale vortex blobs are stretched by large-scale structures.

The results connect vortex dynamics with energy dissipation anomalies.

Abstract

We consider the 3D incompressible Navier-Stokes equations under the following $2+\frac{1}{2}$-dimensional situation: small-scale horizontal vortex blob being stretched by large-scale, anti-parallel pairs of vertical vortex tubes. We prove anomalous dissipation induced by such vortex-stretching.