3D Euler about a 2D symmetry plane

Physica D: Nonlinear Phenomena

Volumn 237, Issue 14-17, 2008, Pages 1912-1920

  Bustamante, Miguel D ^a   Kerr, Robert M ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Euler equations; Fluid singularities; Vortex dynamics

Indexed keywords

EULER EQUATIONS; VORTEX FLOW;

CONVERGENCE TEST; DYNAMIC DEPLETION; FINITE TIME SINGULARITY; HIGHER RESOLUTION; INCOMPRESSIBLE EULER EQUATIONS; SYMMETRY PLANES; VORTEX DYNAMICS; VORTEX STRETCHING;

NONLINEAR EQUATIONS;

EID: 47049103057     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2008.02.007     Document Type: Article

References (17)

1. Euler L. Principia motus fluidorum. Novi Commentarii Acad. Sci. Petropolitanae 6 (1761) 271-311
2. Beale J.T., Kato T., and Majda A. Remarks on the breakdown of smooth solutions for the 3 D Euler equations. Commun. Math. Phys. 94 (1984) 61
3. Kerr R.M. Evidence for a singularity of the three-dimensional, incompressible Euler equations. Phys. Fluids 5 (1993) 1725-1746
4. Constantin P., Fefferman C., and Majda A. Geometric constraints on potentially singular solutions for the 3D Euler equations. Comm. Partial Differential Equations 21 (1996) 559-571
5. Kerr R.M. Velocity and scaling of collapsing Euler vortices. Phys. Fluids 17 (2005) 075103
6. Grauer R., Marliani C., and Germaschewski K. Adaptive mesh refinement of singular solutions of the incompressible Euler equations. Phys. Rev. Lett. 80 (1998) 4177-4180
7. Orlandi P., and Carnevale G. Nonlinear amplification of vorticity in inviscid interaction of orthogonal Lamb dipoles. Phys. Fluids 19 (2007) 057106
8. Hou T.Y., and Li R. Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations. J. Nonlinear Sci. 16 (2006) 639-664
9. Kerr R.M., and Hussain F. Simulation of vortex reconnection. Physica D 37 (1989) 474-484
10. Kerr R.M. Evidence for a singularity of the three-dimensional incompressible Euler equations. In: Zaslavsky G.M., Tabor M., and Comte P. (Eds). Topological Aspects of the Dynamics of Fluids and Plasmas, Proceedings of the NATO-ARW Workshop at the Institute for Theoretical Physics, University of California at Santa Barbara (1992), Kluwer Academic Publishers, Dordrecht, Netherlands 309-336
11. Hou T.Y., and Li R. Computing nearly singular solutions using pseudo-spectral methods. J. Comp. Phys. 226 (2007) 379-397
12. Sulem C., Sulem P.-L., and Frisch H. Tracing complex singularities with spectral methods. J. Comp. Phys. 50 (1983) 138-161
13. Cichowlas C., and Brachet M.E. Evolution of complex singularities in Kida-Pelz and Taylor-Green inviscid flows. Fluid Dynamics Res. 36 (2004) 239-248
14. Frisch U., Matsumoto T., and Bec J. Singularities of Euler flow? Not out of the blue!. J. Stat. Phys. 113 (2003) 761-781
15. Deng J., Hou T.Y., and Yu X. Improved geometric condition for non-blowup of the 3D incompressible Euler equation. Commun. Partial Differential Equations 31 (2006) 293-306
16. T. Grafke, H. Homann, J. Dreher, R. Grauer, Numerical simulations of possible finite time singularities in the incompressible Euler equations: Comparison of numerical methods 2007 (these Proceedings)
17. Brachet M.E., Meiron D.I., Orszag S.A., Nickel B.G., Morf R.H., and Frisch U. Small-scale structure of the Taylor-Green vortex. J. Fluid Mech. 130 (1983) 411-452