A hierarchy of length scales for weak solutions of the three-dimensional Navier-Stokes equations

2010/12/16 by John Gibbon, J. D. Gibbon, Gibbon, J. D.
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Chaotic Dynamics (nlin.CD) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #math-ph #math.AP #math.MP #nlin.CD

paper · pdf · doi:10.48550/arxiv.1012.3604

Dedicated to David Levermore on the occasion of his 60th birthday. To appear in Comm. Math. Sci. (version 2)

openalex publication_date 2010/12/16 · arxiv created 2011/05/28 · arxiv updated 2011/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Moments of the vorticity are used to define and estimate a hierarchy of time-averaged inverse length scales for weak solutions of the three-dimensional, incompressible Navier-Stokes equations on a periodic box. The estimate for the smallest of these inverse scales coincides with the inverse Kolmogorov length but thereafter the exponents of the Reynolds number rise rapidly for correspondingly higher moments. The implications of these results for the computational resolution of small scale vortical structures are discussed.

Citations

• Fluid dynamic limits of kinetic equations. I. Formal derivations

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