Rafner Janet, Grujić Zoran, Bach Christian, Bærentzen Jakob Andreas, Gervang Bo, Jia Ruo, Leinweber Scott, Misztal Marek, Sherson Jacob
ScienceAtHome, Center for Hybrid Intelligence, Department of Physics and Astronomy, Aarhus University, Aarhus, Denmark.
Department of Mathematics, University of Virginia, Charlottesville, VA, USA.
Sci Rep. 2021 Apr 23;11(1):8824. doi: 10.1038/s41598-021-87774-y.
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.
三维不可压缩纳维-斯托克斯（NS）方程所描述的初始规则流中是否会形成奇点的问题，是数学物理中的一个基本问题。NS正则性问题是超临界的，也就是说，在数学分析所能确立的内容与排除奇点所需的条件之间存在一个“尺度间隙”。最近引入的一个基于对强涡度区域适当定义的“稀疏尺度”的数学框架，自20世纪60年代以来首次实现了NS超临界性的尺度缩减。在此，我们使用在涡度大小“爆发”附近进行的空间高分辨率计算模拟，对该框架进行首次数值测试。结果证实，该尺度非常适合检测耗散的开始，并提供了数值证据，表明正在进行的数学研究可能成功弥合尺度间隙。
