2006/04/01 by Gregory L. Eyink · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #physics.ao-ph #physics.flu-dyn
paper · pdf · doi:10.1016/j.crhy.2006.01.008
10 pages, prepared for the conference "Statistical Mechanics of Non-Extensive Systems", 24 - 25 October 2005, Paris
openalex publication_date 2006/04/01 · arxiv created 2006/05/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
The circulation around any closed loop is a Lagrangian invariant for classical, smooth solutions of the incompressible Euler equations in any number of space dimensions. However, singular solutions relevant to turbulent flows need not preserve the classical integrals of motion. Here we generalize the Kelvin theorem on conservation of circulations to distributional solutions of Euler and give necessary conditions for the anomalous dissipation of circulations. We discuss the important role of Kelvin's theorem in turbulent vortex-stretching dynamics and conjecture a version of the theorem which may apply to suitable singular solutions.