Geometry of turbulent dissipation and the Navier–Stokes regularity problem
| Autor: | Jacob F. Sherson, Marek Krzysztof Misztal, Scott Leinweber, Zoran Grujić, Jakob Andreas Bærentzen, Janet Rafner, Christian Bach, Bo Gervang, Ruo Jia |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
0301 basic medicine
Physics Multidisciplinary Scale (ratio) Science 010102 general mathematics Mathematical analysis Dissipation Applied mathematics 01 natural sciences Article Reduction (complexity) 03 medical and health sciences 030104 developmental biology Singularity Flow (mathematics) Fluid dynamics Compressibility Medicine 0101 mathematics Closing (morphology) Scaling |
| Zdroj: | Rafner, J, Grujić, Z, Bach, C, Bærentzen, J A, Gervang, B, Jia, R, Leinweber, S, Misztal, M & Sherson, J 2021, ' Geometry of turbulent dissipation and the Navier–Stokes regularity problem ', Scientific Reports, vol. 11, 8824 . https://doi.org/10.1038/s41598-021-87774-y Scientific Reports Rafner, J, Grujić, Z, Bach, C, Bærentzen, J A, Gervang, B G, Jia, R, Leinweber, S, Misztal, M K & Sherson, J 2021, ' Geometry of turbulent dissipation and the Navier–Stokes regularity problem ', Scientific Reports, vol. 11, no. 1, 8824 . https://doi.org/10.1038/s41598-021-87774-y Scientific Reports, Vol 11, Iss 1, Pp 1-9 (2021) |
| DOI: | 10.1038/s41598-021-87774-y |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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