Extended series analysis of full octahedral flow: Numerical evidence for hydrodynamic blowup

Fluid Dynamics Research

Volumn 33, Issue 1-2, 2003, Pages 207-221

  Pelz, Richard B ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; HYDRODYNAMICS; VORTEX FLOW;

ENSTROPHY SERIES;

INCOMPRESSIBLE FLOW;

COMPUTATIONAL FLUID DYNAMICS; EULER FLOW; FOURIER TRANSFORM; INCOMPRESSIBLE FLOW; MATHEMATICAL ANALYSIS; VORTICITY;

EID: 0038508841     PISSN: 01695983     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0169-5983(03)00039-X     Document Type: Article

References (25)

1. Baker G.A. Grave-Morris P. Padé Approximants 1996 Cambridge University Press Cambridge
2. Behr E. Necas J. Wu H. On blow-up of solutions for Euler equations Math. Modelling Numer. Anal. 35 2001 229-238
3. Boratav O.N. Pelz R.B. Direct numerical simulation of transition to turbulence from a high-symmetry initial condition Phys. Fluids 6 1994 2757-2784
4. Brachet M.E. Meiron D.I. Orszag S.A. Nickel B.G. Morf R.H. Frisch U. Small-scale structure of the Taylor-Green vortex J. Fluid. Mech. 130 1983 441-452
5. Brachet M.E. Meneguzzi M. Vincent A. Politano H. Sulem P.L. Numerical evidence of smooth self-similar dynamics and possibility of subsequent collapse for three-dimensional ideal flows Phys. Fluids A 4 12 1992 2845-2854
6. Drazin P.G. Tourigny Y. Numerical study of bifurcations by analytic continuation of a function defined by a power series SIAM J. Appl. Math. 56 1996 1-18
7. Drazin P.G. Tourigny Y. Extending the utility of perturbation series in problems of waves and stability Rend. Circ. Mat. Palermo, Seris II 45 Suppl. 1996 209-219
8. Fefferman, C., 2000. Existence - Smoothness of the Navier-Stokes Equations. http://www.claymath.org/prizeproblems/navierstokes.htm
9. Frisch, U., 1983. Fully developed turbulence and singularitie. In: Ioss, G., Helleman, R.H.G., Stora, R. (Eds.), Chaotic Behavior of Deterministic Systems: LesHouches, session XXXVI, North-Holland, Amsterdam, pp. 665-704.
10. Goldstein S. Three-dimensional vortex motion in a viscous fluid Philos. Mag. 30 1940 85-102
11. Granlund, T., 2002. GNU MP 4.1: the GNU multiple precision arithmetic library. http://www.swox.com/gmp/
12. Grauer R. Marliani C. Germaschewski K. Adaptive mesh refinement for singular solutions of the incompressible Euler equations Phys. Rev. Lett. 80 19 1998 4177-4180
13. Kerr R.M. Evidence for a singularity in the three-dimensional, incompressible Euler equations Phys. Fluids A 5 1993 1725-1746
14. Kida S. Three-dimensional periodic flows with high-symmetry J. Phys. Soc. Japan 54 1985 2132-2140
15. Morf R.H. Orszag S.A. Frisch U. Spontaneous singularity in three-dimensional inviscid, incompressible flow Phys. Rev. Letts. 44 9 1980 572-574
16. Pelz R.B. Locally self-similar, finite-time collapse in a high-symmetry vortex filament model Phys. Rev. E 55 1997 1617-1620
17. Pelz, R.B., 2001. Analysis of a candidate flow for hydrodynamic blowup. In: Ricca, R.L. (Ed.), An Introduction to the Geometry and Topology of Fluids Flows, Kluwer, Dordrecht, pp. 329-341.
18. Pelz, R.B., 2002. Discrete groups, symmetric flows and hydrodynamic blowup. In: Bajer, K., Moffat, H.K. (Eds.), Tubes, Sheets and Singularities in Fluid Dynamics, Kluwer, Dordrecht, pp. 269-284.
19. Pelz R.B. Gulak Y. Evidence for a real-time singularity in hydrodynamics from time series analysis Phys. Rev. Lett. 79 25 1997 4998-5001
20. Taylor G.I. Green A.E. Mechanism of the production of small eddies from large ones Proc. Roy. Soc. A 158 1937 499-521
21. Tourigny Y. Drazin P.G. The asymptotic behavior of algebraic approximants Proc. R. Soc. London. A 456 2000 1117-1137
22. Tourigny Y. Drazin P.G. The dynamics of Padé approximation Nonlinearity 15 2002 787-805
23. Van Dyke M. Computer extension of perturbation series in fluid mechanics SIAM J. Appl. Math. 28 1975 720-734
24. Wherrett B.S. Group Theory for Atoms, Molecules and Solids 1986 Prentice-Hall International Englewood Cliffs, NJ
25. Zaturska M.B. Drazin P.G. Banks W.H.H. On the flow of a viscous fluid driven along a channel by suction at porous walls Fluid Dyn. Res. 4 1988 151-178