Coherent structures in an energy-enstrophy theory for axisymmetric flows

Physics of Fluids

Volumn 15, Issue 2, 2003, Pages 478-487

  Lim, Chjan C ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

JETS; PERTURBATION TECHNIQUES; REYNOLDS NUMBER; STATISTICAL MECHANICS;

ENERGY-ENSTROPHY THEORY;

FLOW OF FLUIDS;

AXISYMMETRIC FLOW; ENERGY; STATISTICAL ANALYSIS;

EID: 0037291987     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1529660     Document Type: Article

References (29)

1. S. R. Turner, An Introduction to Combustion, Concepts and Applications, 2nd ed. (McGraw-Hill, New York, 1972).
2. C. Ho and P. Huerre, "Perturbed free shear flows," Annu. Rev. Fluid Mech. 16, 365 (1984).
3. S. Crow and F. Champagne, "Orderly structure in jet turbulence," J. Fluid Mech. 48, 547 (1971).
4. M. Gharib, E. Rambod, and K. Shariff, "A universal time scale for vortex ring formation," J. Fluid Mech. 360, 121 (1998).
5. K. Mohseni, H. Ran, and T. Colonius, "Numerical experiments on vortex ring formation," J. Fluid Mech. 430, 267 (2001).
6. K. Mohseni, "Statistical equilibrium theory for axisymmetric flows: Kelvin's variational principle and an explanation of the vortex ring pinch-off process," Phys. Fluids 13, 1924 (2001).
7. S. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, MA, 2000), p. 101.
8. F. M. White, Viscous Flows, 2nd ed. (McGraw-Hill, New York, 1974), pp. 472-474.
9. J. Miller, "Statistical mechanics of Euler equations in two dimensions," Phys. Rev. Lett. 65, 2137 (1990).
10. R. Robert and J. Sommeria, "Statistical equilibrium states for two-dimensional flows," J. Fluid Mech. 229, 291 (1991).
11. D. Montgomery and G. Joyce, "Statistical mechanics of 'negative temperature' states," Phys. Fluids 17, 1139 (1974).
12. T. S. Lundgren and Y. B. Pointin, "Statistical mechanics of two-dimensional vortices," J. Stat. Phys. 17, 323 (1977).
13. A. J. Chorin, Vorticity and Turbulence (Springer-Verlag, New York, 1994).
14. R. H. Kraichnan, "Statistical dynamics of two-dimensional flows," J. Fluid Mech. 67, 155 (1975).
15. C. Leith, "Diffusion approximation for 2D turbulence." Phys. Fluids 11. 671 (1968).
16. G. K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge University Press, Cambridge, 1953).
17. A. Majda and M. Holen, "Dissipation, topography and statistical theories of large scale coherent structure," CPAM 50, 1183 (1997).
18. T. H. Berlin and M. Kac, "The spherical model of a ferromagnet," Phys. Rev. 86, 821 (1952).
19. C. C. Lim, "Properties of energy-enstrophy theories for 2D vortex statistics," in Proceedings of the 4th IUTAM Conference, Shanghai, China, August 2002, edited by W.-Z. Chien (Shanghai University Press, Shanghai, 2002), pp. 814-819.
20. D. Blackmore and O. Knio, "KAM theory analysis of the dynamics of 3 coaxial vortex rings," Physica D 140, 321 (2000).
21. L. J. Campbell and K. O'Neil, "Statistics of 2-D point vortices and high energy vortex states," J. Stat. Phys., 269 (1993).
22. A. Szeri and P. Holmes, "Nonlinear stability of axisymmetric swirling flows," Philos. Trans. R. Soc. London, Ser. A 326, 327 (1988).
23. T. B. Benjamin, "Theory of the vortex breakdown phenomenon," J. Fluid Mech. 14, 593 (1962).
24. J. Nebus, "Monte Carlo simulations of quasi-2D turbulence," Ph.D. thesis, RPI, 2002, http://www.rpi.edu/-limc
25. R. Jordan and B. Turkington, "Ideal magnetofluid turbulence in 2D," J. Stat. Phys. 87, 661 (1997).
26. J. Ginibre, "Statistical ensembles of complex, quartenion, and real matrices," J. Math. Phys. 6, 440 (1964).
27. P. Constantin, C. Foias, I. Kukavica, and A. Majda, "Dirichlet quotients and periodic 2-D Navier-Stokes equations," J. Math. Pures Appl. 76, 125 (1997).
28. P. Constantin, "Geometric and analytical studies in turbulence," in Trends and Perspectives in Applied Mathematics, edited by L. Sirovich (Springer Verlag, New York, 1993).
29. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, New York, 1961).