Locality of vortex stretching for the 3D Euler equations
Analysis of PDEs
2023-02-01 v1 Differential Geometry
Fluid Dynamics
Abstract
We consider the 3D incompressible Euler equations under the following situation: small-scale vortex blob being stretched by a prescribed large-scale stationary flow. More precisely, we clarify what kind of large-scale stationary flows really stretch small-scale vortex blobs in alignment with the straining direction. The key idea is constructing a Lagrangian coordinate so that the Lie bracket is identically zero (c.f. the Frobenius theorem), and investigate the locality of the pressure term by using it.
Cite
@article{arxiv.2204.01909,
title = {Locality of vortex stretching for the 3D Euler equations},
author = {Yuuki Shimizu and Tsuyoshi Yoneda},
journal= {arXiv preprint arXiv:2204.01909},
year = {2023}
}