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3D Euler about a 2D symmetry plane
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Bustamante, Miguel D. and Kerr, Robert M. (Robert McDougall). (2008) 3D Euler about a 2D symmetry plane. Physica D: Nonlinear Phenomena, Vol.237 (No.1417). pp. 19121920. ISSN 01672789
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Official URL: http://dx.doi.org/10.1016/j.physd.2008.02.007
Abstract
Initial results from new calculations of interacting antiparallel Euler vortices are presented with the objective of understanding the origins of singular scaling presented by Kerr [R.M. Kerr, Evidence for a singularity of the threedimensional, incompressible Euler equations, Phys. Fluids 5 (1993) 17251746] and the lack thereof by Hou and Li [TY. Hou, R. Li, Dynamic depletion of vortex stretching and nonblowup of the 3D incompressible Euler equations, J. Nonlinear Sci. 16 (2006) 639664]. Core profiles designed to reproduce the two results are presented, new more robust analysis is proposed, and new criteria for when calculations should be terminated are introduced and compared with classical resolution studies and spectral convergence tests. Most of the analysis is on a 512 x 128 x 2048 mesh, with new analysis on a just completed 1024 x 256 x 2048 used to confirm trends. One might hypothesize that there is a finitetime singularity with enstrophy growth like Omega similar to (Tc  t)(gamma Omega) and vorticity growth like parallel to omega parallel to(infinity) similar to (Tc  t)(gamma). The new analysis would then support gamma Omega approximate to 1/2 and gamma > 1. These represent modifications of the conclusions of Kerr [op. cit.]. Issues that might arise at higher resolution are discussed. (C) 2008 Elsevier B.V. All rights reserved.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics Q Science > QC Physics 

Divisions:  Faculty of Science > Engineering Faculty of Science > Mathematics 

Library of Congress Subject Headings (LCSH):  Lagrange equations, Singularities (Mathematics), Fluid mechanics, Vortexmotion  
Journal or Publication Title:  Physica D: Nonlinear Phenomena  
Publisher:  Elsevier BV  
ISSN:  01672789  
Official Date:  15 August 2008  
Dates: 


Volume:  Vol.237  
Number:  No.1417  
Number of Pages:  9  
Page Range:  pp. 19121920  
Identifier:  10.1016/j.physd.2008.02.007  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Restricted or Subscription Access  
Funder:  Leverhulme Foundation, University of Warwick. Centre for Scientific Computing  
Grant number:  F/00 215/AC (LF)  
References:  [1] L. Euler, Principia motus fluidorum., Novi Commentarii Acad. Sci. 

URI:  http://wrap.warwick.ac.uk/id/eprint/29497 
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