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Geometry of turbulent dissipation and the Navier-Stokes regularity problem.
Rafner, Janet; Grujic, Zoran; Bach, Christian; Bærentzen, Jakob Andreas; Gervang, Bo; Jia, Ruo; Leinweber, Scott; Misztal, Marek; Sherson, Jacob.
Afiliação
  • Rafner J; ScienceAtHome, Center for Hybrid Intelligence, Department of Physics and Astronomy, Aarhus University, Aarhus, Denmark.
  • Grujic Z; Department of Mathematics, University of Virginia, Charlottesville, VA, USA.
  • Bach C; ScienceAtHome, Center for Hybrid Intelligence, Department of Physics and Astronomy, Aarhus University, Aarhus, Denmark.
  • Bærentzen JA; Department of Computer Graphics, Technical University of Denmark, Lyngby, Denmark.
  • Gervang B; Department of Engineering, Aarhus University, Aarhus, Denmark.
  • Jia R; Darden School of Business, University of Virginia, Charlottesville, VA, USA.
  • Leinweber S; Apple INC., San Francisco, CA, USA.
  • Misztal M; 3Shape TRIOS A/S, Copenhagen, Denmark.
  • Sherson J; ScienceAtHome, Center for Hybrid Intelligence, Department of Physics and Astronomy, Aarhus University, Aarhus, Denmark. sherson@phys.au.dk.
Sci Rep ; 11(1): 8824, 2021 Apr 23.
Article em En | MEDLINE | ID: mdl-33893342
ABSTRACT
The question of whether a singularity can form in an initially regular flow, described by the 3D incompressible Navier-Stokes (NS) equations, is a fundamental problem in mathematical physics. The NS regularity problem is super-critical, i.e., there is a 'scaling gap' between what can be established by mathematical analysis and what is needed to rule out a singularity. A recently introduced mathematical framework-based on a suitably defined 'scale of sparseness' of the regions of intense vorticity-brought the first scaling reduction of the NS super-criticality since the 1960s. Here, we put this framework to the first numerical test using a spatially highly resolved computational simulation performed near a 'burst' of the vorticity magnitude. The results confirm that the scale is well suited to detect the onset of dissipation and provide numerical evidence that ongoing mathematical efforts may succeed in closing the scaling gap.

Texto completo: 1 Coleções: 01-internacional Base de dados: MEDLINE Idioma: En Ano de publicação: 2021 Tipo de documento: Article

Texto completo: 1 Coleções: 01-internacional Base de dados: MEDLINE Idioma: En Ano de publicação: 2021 Tipo de documento: Article