Geometry of turbulent dissipation and the Navier–Stokes regularity problem

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 est...

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Autores principales:	Janet Rafner, Zoran Grujić, Christian Bach, Jakob Andreas Bærentzen, Bo Gervang, Ruo Jia, Scott Leinweber, Marek Misztal, Jacob Sherson
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/0ba91c502e23493995c73a0c85e2448f
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spelling	oai:doaj.org-article:0ba91c502e23493995c73a0c85e2448f2021-12-02T18:27:50ZGeometry of turbulent dissipation and the Navier–Stokes regularity problem10.1038/s41598-021-87774-y2045-2322https://doaj.org/article/0ba91c502e23493995c73a0c85e2448f2021-04-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-87774-yhttps://doaj.org/toc/2045-2322Abstract 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.Janet RafnerZoran GrujićChristian BachJakob Andreas BærentzenBo GervangRuo JiaScott LeinweberMarek MisztalJacob ShersonNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-9 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Janet Rafner Zoran Grujić Christian Bach Jakob Andreas Bærentzen Bo Gervang Ruo Jia Scott Leinweber Marek Misztal Jacob Sherson Geometry of turbulent dissipation and the Navier–Stokes regularity problem
description	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.
format	article
author	Janet Rafner Zoran Grujić Christian Bach Jakob Andreas Bærentzen Bo Gervang Ruo Jia Scott Leinweber Marek Misztal Jacob Sherson
author_facet	Janet Rafner Zoran Grujić Christian Bach Jakob Andreas Bærentzen Bo Gervang Ruo Jia Scott Leinweber Marek Misztal Jacob Sherson
author_sort	Janet Rafner
title	Geometry of turbulent dissipation and the Navier–Stokes regularity problem
title_short	Geometry of turbulent dissipation and the Navier–Stokes regularity problem
title_full	Geometry of turbulent dissipation and the Navier–Stokes regularity problem
title_fullStr	Geometry of turbulent dissipation and the Navier–Stokes regularity problem
title_full_unstemmed	Geometry of turbulent dissipation and the Navier–Stokes regularity problem
title_sort	geometry of turbulent dissipation and the navier–stokes regularity problem
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/0ba91c502e23493995c73a0c85e2448f
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Geometry of turbulent dissipation and the Navier–Stokes regularity problem

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