A remark on the zeroth law and instantaneous vortex stretching on the incompressible 3D Euler equations

2019/02/06 by In‐Jee Jeong, Jeong, In-Jee, Tsuyoshi Yoneda +1 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1902.02032

openalex publication_date 2019/02/06 · openalex created_date 2019/02/21 · openalex updated_date 2026/07/28

Abstract

By DNS of Navier-Stokes turbulence, Goto-Saito-Kawahara (2017) showed that turbulence consists of a self-similar hierarchy of anti-parallel pairs of vortex tubes, in particular, stretching in larger-scale strain fields creates smaller-scale vortices. Inspired by their numerical result, we examine the Goto-Saito-Kawahara type of vortex-tubes behavior using the 3D incompressible Euler equations, and show that such behavior induces energy cascade in the absence of nonlinear scale-interaction. From this energy cascade, we prove a modified version of the zeroth-law. In the Appendix, we derive Kolmogorov's -5/3-law from the GSK point of view.

Citations

• Ill-posedness results in critical spaces for some equations arising in hydrodynamics
• Review of the Onsager "Ideal Turbulence" Theory

Cited by

• On Singular Vortex Patches, I: Well-posedness Issues

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