Abstract
AbstractTurbulent fluid flows are ubiquitous in nature and technology, and are mathematically described by the incompressible Navier-Stokes equations. A hallmark of turbulence is spontaneous generation of intense whirls, resulting from amplification of the fluid rotation-rate (vorticity) by its deformation-rate (strain). This interaction, encoded in the non-linearity of Navier-Stokes equations, is non-local, i.e., depends on the entire state of the flow, constituting a serious hindrance in turbulence theory and even establishing regularity of the equations. Here, we unveil a novel aspect of this interaction, by separating strain into local and non-local contributions utilizing the Biot-Savart integral of vorticity in a sphere of radius R. Analyzing highly-resolved numerical turbulent solutions to Navier-Stokes equations, we find that when vorticity becomes very large, the local strain over small R surprisingly counteracts further amplification. This uncovered self-attenuation mechanism is further shown to be connected to local Beltramization of the flow, and could provide a direction in establishing the regularity of Navier-Stokes equations.
Publisher
Springer Science and Business Media LLC
Subject
General Physics and Astronomy,General Biochemistry, Genetics and Molecular Biology,General Chemistry
Reference44 articles.
1. Tennekes, H. & Lumley, J. L. A First Course in Turbulence (MIT Press, Cambridge, Mass., 1972).
2. Tsinober, A. An informal conceptual introduction to turbulance (Springer, Berlin, 2009).
3. Fefferman, C. Existence and smoothness of the Navier-Stokes equations (Clay Mathematical Institute, Cambridge, MA, 2006).
4. Doering, C. R. The 3D navier-stokes problem. Annu. Rev. Fluid Mech. 41, 109–128 (2009).
5. Beale, J. T., Kato, T. & Majda, A. Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Commun. Math. Phys. 94, 61–66 (1984).
Cited by
41 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献