Euler-alpha and vortex blob regularization of vortex filament and vortex sheet motion

Journal of Fluid Mechanics

Volumn 555, Issue , 2006, Pages 149-176

  Holm, D D ^a,b   Nitsche, M ^c   Putkaradze, V ^d  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

^c UNIVERSITY OF NEW MEXICO   (United States)

^d Department of Environmental and Radiological Health Sciences   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

INCOMPRESSIBLE FLOW; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; TURBULENCE;

EULER-ALPHA MODEL; FLUID VELOCITY; UNREGULARIZED FLOW; VORTEX BLOB MODEL; VORTEX FILAMENT MOTION; VORTEX SHEET MOTION;

VORTEX FLOW;

INCOMPRESSIBLE FLOW; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; TURBULENCE; VORTEX FLOW;

INCOMPRESSIBLE FLOW; LAGRANGIAN ANALYSIS; NAVIER-STOKES EQUATIONS; VORTEX FLOW;

EID: 33749452018     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112006008846     Document Type: Article

References (37)

1. Anderson, C. 1985 A vortex method for flows with slight density variations. J. Comput. Phys. 61, 417-444.
2. Baker, G. R. & Pham, L. D. 2005 A comparison of blob methods for vortex sheet roll-up. J. Fluid Mech. 547, 297-316.
3. Baker, G. R. & Shelley, M. J. 1990 On the connection between thin vortex layers and vortex sheets. J. Fluid Mech. 215, 161-194.
4. Beale, J. T. & Majda, A. 1985 High order accurate vortex methods with explicit velocity kernels. J. Comput. Phys. 58, 188-223.
5. Bulirsch, R. 1965 Numerical calculation of elliptic integrals and elliptic functions. Numer. Maths 7, 78-90.
6. Caflisch, R. E., Ercolani, N., Hou, T. & Y. Landis, Y. 1993 Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems. Commun. Pure Appl. Maths 46, 453-499.
7. Caflisch, R. E., Hou, T. Y. & Lowengrub, J. 1999 Almost optimal convergence of the point vortex method for vortex sheets using numerical filtering. Math. Comput. 68, 1465-1496.
8. Camassa, R. & Holm, D. D. 1993 An integrable shallow-water equation with peaked solitons. Phys. Rev. Lett. 71, 1661-1664.
9. Chen, S., Foias, C., Holm, D. D., Olson, E., Titi, E. S. & Wynne, S. 1999 The Camassa-Holm equations as a closure model for turbulent channel and pipe flow. Phys. Rev. Lett. 81, 5338-5341.
10. Chorin, A. J. & Bernard, P. S. 1973 Discretization of a vortex sheet, with an example of roll-up. J. Comput. Phys. 13, 423-429.
11. Cottet, G.-H. & Koumoutsakos, P. D. 2000 Vortex Methods: Theory and Practice. Cambridge University Press.
12. Cowley, S. J., Baker, G. & Tanveer, S. 1999 On the formation of Moore curvature singularities in vortex sheets. J. Fluid Mech. 378, 233-267.
13. Foias, C., Holm, D. D. & Titi, E. S. 2001 The Navier-Stokes-alpha model of fluid turbulence. Physica D 152-153, 505-519.
14. Holm, D. D. 2003 Rasetti-Regge Dirac bracket formulation of Lagrangian dynamics of vortex filaments. Maths Comput. Simulation 62, 53-63.
15. Holm, D. D., Marsden, J. E. & Ratiu, T. S. 1998a Euler-Poincaré models of ideal fluids with nonlinear dispersion. Phys. Rev. Lett. 80, 4173-4176.
16. Holm, D. D., Marsden, J. E. & Ratiu, T. S. 1998b The Euler-Poincaré equations and semidirect products with applications to continuum theories. Adv. Maths 137, 1-81.
17. Hou, T., Lowengrub, J. & Shelley, M. 1997 The long time motion of vortex sheets with surface tension. Phys. Fluids 9, 1933-1954.
18. Krasny, R. 1986a A study of singularity formation in a vortex sheet by the point-vortex approximation. J. Fluid Mech. 167, 65-93.
19. Krasny, R. 1986b Desingularization of periodic vortex sheet roll-up. J. Comput. Phys. 65, 292-313.
20. Krasny, R. 1987 Computation of vortex sheet roll-up in the Trefftz plane. J. Fluid Mech. 184, 123-155.
21. Krasny, R. & Nitsche, M. 2002 The onset of chaos in vortex sheet flow. J. Fluid Mech. 454, 47-69.
22. Kuznetsov, E. Z. & Mikhailov, A. V. 1990 On the topological meaning of canonical Clebsch variables. Phys. Lett. A 77, 37-38.
23. Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
24. Leonard, A. 1985 Computing three-dimensional incompressible flows with vortex elements. Annu. Rev. Fluid Mech. 17, 523-559.
25. Majda, A. J. & Bertozzi, A. L. 2002 Vorticity and Incompressible Flow. Cambridge University Press.
26. Marsden, J. E. & Weinstein, A. 1983 Coadjoint orbits, vortices and Clebsch variables for incompressible fluids. Physica D 7, 305-323.
27. Meiburg, E. 1995 Three-dimensional vortex dynamics simulations. In Fluid Vortices (ed. S. I. Green), pp. 651-685. Kluwer.
28. Meiron, D. I., Baker, G. R. & Orszag, S. A. 1982 Analytical structure of vortex sheet dynamics. Part 1. Kelvin-Helmholtz instability. J. Fluid Mech. 114, 283-298.
29. Moore, D. W. 1979 The spontaneous appearance of a singularity in the shape of an evolving vortex sheet. Proc. R. Soc. Lond. A 365, 105-119.
30. Nitsche, M. & Krasny, R. 1994 A numerical study of vortex ring formation at the edge of a circular tube. J. Fluid Mech. 276, 139-161.
31. Puckett, E. G. 1993 Vortex methods: An introduction and survey of selected research topics. In Incompressible Fluid Dynamics - Trends and Advances (ed. R. A. Nicolaides & M. D. Gunzburger), pp. 335-407. Cambridge University Press.
32. Rosenhead, L. 1930 The spread of vorticity in the wake behind a cylinder. Proc. R. Soc. Lond. A 127, 590-612.
33. Oliver, M. & Shkoller, S. 2001 The vortex blob method as a second-grade non-Newtonian fluid. Commun. Partial Diffl Equat. 26, 295-314.
34. Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.
35. Shelley, M. 1992 A study of singularity formation in vortex sheet motion by a spectrally accurate vortex method. J. Fluid Mech. 244, 493-526.
36. Shkoller, S. 2000 Analysis on groups of diffeomorphisms of manifolds with boundary and the averaged motion of a fluid. J. Diffl Geom. 55, 145-191.
37. Tryggvason, G., Dahm, W. J. A. & Sbeih, K. 1991 Fine structure of vortex sheet roll-up by viscous and inviscid simulation. Trans. ASME I: J. Fluids Engng 113, 31-36.