Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible euler equations

doi:10.1007/s00332-006-0800-3

	Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible euler equations
	Hou, Thomas Y.; Li, Ruo
刊名	JOURNAL OF NONLINEAR SCIENCE
	2006-12-01
卷号	16 期号:6 页码:639-664
ISSN号	0938-8974
DOI	10.1007/s00332-006-0800-3
英文摘要	We study the interplay between the local geometric properties and the non-blowup of the 3D incompressible Euler equations. We consider the interaction of two perturbed antiparallel vortex tubes using Kerr's initial condition [15] [Phys. Fluids 5 (1993), 1725]. We use a pseudo-spectral method with resolution up to 1536 x 1024 x 3072 to resolve the nearly singular behavior of the Euler equations. Our numerical results demonstrate that the maximum vorticity does not grow faster than doubly exponential in time, up to t = 19, beyond the singularity time t = 18.7 predicted by Kerr's computations [15], [18]. The velocity, the enstrophy, and the enstrophy production rate remain bounded throughout the computations. As the flow evolves, the vortex tubes are flattened severely and turned into thin vortex sheets, which roll up subsequently. The vortex lines near the region of the maximum vorticity are relatively straight. This local geometric regularity of vortex lines seems to be responsible for the dynamic depletion of vortex stretching.
WOS研究方向	Mathematics ; Mechanics ; Physics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000241890200004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/3206]
专题	中国科学院数学与系统科学研究院
通讯作者	Hou, Thomas Y.
作者单位	1.CALTECH, Pasadena, CA 91125 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100080, Peoples R China 3.Peking Univ, LMAM, Beijing 100871, Peoples R China 4.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
推荐引用方式 GB/T 7714	Hou, Thomas Y.,Li, Ruo. Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible euler equations[J]. JOURNAL OF NONLINEAR SCIENCE,2006,16(6):639-664.
APA	Hou, Thomas Y.,&Li, Ruo.(2006).Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible euler equations.JOURNAL OF NONLINEAR SCIENCE,16(6),639-664.
MLA	Hou, Thomas Y.,et al."Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible euler equations".JOURNAL OF NONLINEAR SCIENCE 16.6(2006):639-664.